The aperiodic nature of geomagnetic field variations, both in intensity and direction, can aid in dating archaeological artefacts, volcanic rocks, and sediment records that carry a palaeomagnetic signal. The success of palaeomagnetic dating relies upon our knowledge of past field variations at specific locations. Regional archaeo- and palaeomagnetic reference curves and predictions from global geomagnetic field models provide our best description of field variations through the Holocene. State-of-the-art palaeomagnetic laboratory practices and accurate independent age controls are prerequisites for deriving reliable reference curves and models from archaeological, volcanic, and sedimentary palaeomagnetic data. In this review paper we give an overview of these prerequisites and the available reference curves and models, discuss techniques for palaeomagnetic dating, and outline its limitations. In particular, palaeomagnetic dating on its own cannot give unique results, but rather serves to refine or confirm ages obtained by other methods. Owing to the non-uniform character of magnetic field variations in different regions, care is required when choosing a palaeomagnetic dating curve, so that the distance between the dating curve and the record to be dated is not too large. Accurate reporting and incorporation of new, independently dated archaeo- and palaeomagnetic results into databases will help to improve reference curves and global models for all regions on Earth.

}, keywords = {4, archaeomagnetic data, Archaeomagnetic dating, centuries, dipole-moment, earths magnetic-field, geochronology, geology, geomagnetic secular variation, historic lavas, lake-sediments, Palaeomagnetic dating, palaeosecular variation, paleosecular variation, Physical Geography, relative paleointensity, resolution, sediment cores}, isbn = {1871-1014}, doi = {10.1016/j.quageo.2018.11.004}, url = {The geomagnetic field displays complicated variations over a broad range of frequencies. These variations can be decomposed by frequency and linked to physical processes using frequency domain spectral methods. These spectral methods are well developed but have not previously been applied to study the energy balance of geodynamo simulations. We illustrate their potential by analyzing output from numerical dynamo simulations that have previously been studied for their apparently Earth-like properties. We show that high coherence between variations in axial dipole energy at the outer boundary of the simulation and total magnetic energy within the fluid shell occur at frequencies below similar to 0.1 kyr(-1). This suggests that paleomagnetically-observable signals with periods exceeding 10 kyrs contain information about magnetic energy changes in the bulk core. We then use spectral analysis to investigate differences in the rate of growth and decay of the axial dipole field. This behaviour, characterised by rapid growth and slow decay, is observed when signals with frequencies higher than 0.03 kyr(-1) have been filtered out. The origin of this asymmetric growth and decay is assessed using coherence spectra between rates of change in kinetic and magnetic energy, ohmic and viscous dissipation, and work done by the buoyancy and Lorentz forces. We show that asymmetry is associated with an imbalance between ohmic dissipation and work done by the Lorentz force; when changes in magnetic energy are more coherent with ohmic dissipation the field grows rapidly and decay slowly. Variations in Ohmic dissipation reflect changes in field strength in our models, while changes in viscous dissipation are associated with amplitude fluctuations of the large-scale flow that exists on millennial timescales. Our work shows that spectral analysis coupling observable and global products of the dynamo process can elucidate the physical origin of periodic processes occurring on timescales exceeding 10 kyrs.

}, keywords = {asymmetry, balance, decay, Geochemistry \& Geophysics, Geomagnetic dipole variations, geomagnetic-field, growth, Numerical geodynamo simulations energy, secular variation, spectral analysis}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2018.10.002}, url = {Study of the late Quaternary geomagnetic field contributes significantly to understanding the origin of millennial-scale paleomagnetic secular variations, the structure of geomagnetic excursions, and the long-term shielding by the geomagnetic field. A compilation of paleomagnetic sediment records and archeomagnetic and lava flow data covering the past 100ka enables reconstruction of the global geomagnetic field on such long-term scales. We use regularized inversion to build the first global, time-dependent, geomagnetic field model spanning the past 100ka, named GGF100k (Global Geomagnetic Field over the past 100 ka). Spatial parametrization of the model is in spherical harmonics and time variations with cubic splines. The model is heavily constrained by more than 100 continuous sediment records covering extended periods of time, which strongly prevail over the limited number of discrete snapshots provided by archeomagnetic and volcanic data. Following an assessment of temporal resolution in each sediment{\textquoteright}s magnetic record, we have introduced smoothing kernels into the forward modeling when assessing data misfit. This accommodates the smoothing inherent in the remanence acquisition in individual sediment paleomagnetic records, facilitating a closer fit to both high- and low-resolution records in regions where some sediments have variable temporal resolutions. The model has similar spatial resolution but less temporal complexity than current Holocene geomagnetic field models. Using the new reconstruction, we discuss dipole moment variations, the time-averaged field, and paleomagnetic secular variation activity. The new GGF100k model fills the gap in the geomagnetic power spectrum in the frequency range 100-1,000Ma(-1).

}, keywords = {antarctic south atlantic, core, dipole moment, excursion, Geochemistry \& Geophysics, geomagnetic excursion, geomagnetic field, GGF100k, high-resolution record, ice, magnetic record, moment variation, north-atlantic, paleointensity, paleomagnetic secular variation, paleosecular variation activity, paleosecular variations, relative, relative paleointensity}, isbn = {1525-2027}, doi = {10.1029/2018gc007966}, url = {We use numerical dynamo simulations to investigate rapid changes in geomagnetic field intensity. The work is motivated by paleomagnetic observations of {\textquoteright}geomagnetic spikes{\textquoteright}, events where the field intensity rose and then fell by a factor of 2-3 over decadal timescales and a confined spatial region. No comparable events have been found in the historical record and so geomagnetic spikes may contain new and important information regarding the operation of the geodynamo. However, they are also controversial because uncertainties and resolution limitations in the available data hinder efforts to define their spatiotemporal characteristics. This has led to debate over whether such extreme events can originate in Earth{\textquoteright}s liquid core. Geodynamo simulations produce high spatio-temporal resolution intensity information, but must be interpreted with care since they cannot yet run at the conditions of Earth{\textquoteright}s liquid core. We employ reversing and non-reversing geodynamo simulations run at different physical conditions and consider various methods of scaling the results to allow comparison with Earth. In each simulation we search for {\textquoteright}extremal events{\textquoteright}, defined as the maximum intensity difference between consecutive time points, at each location on a 2 degrees latitude-longitude grid at Earth{\textquoteright}s surface, thereby making no assumptions regarding the spatio-temporal character of the event. Extremal events display spike-shaped time-series in some simulations, though they can often be asymmetric about the peak intensity. Maximum rates of change reach 0.75 mu Tyr(-1) in several simulations, the lower end of estimates for spikes, suggesting that such events can originate from the core. The fastest changes generally occur at latitudes \> 50 degrees, which could be used to guide future data acquisitions. Extremal events in the simulations arise from rapid intensification of flux patches as they migrate across the core surface, rather than emergence of flux from within the core. The prospect of observing more spikes in the paleomagnetic record appears contingent on finding samples at the right location and time to sample this particular phase of flux patch evolution. (C) 2018 Published by Elsevier B.V.

}, keywords = {boundary, constraints, core, Earth{\textquoteright}s, earths core, field intensity, flow, Geochemistry \& Geophysics, geodynamo models, geodynamo simulations, geomagnetic spikes, magnetic-field, mantle, scaling laws, secular variation}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2018.09.037}, url = {We address the problem of unpolarized light spectroscopy of geological materials. Using infrared radiation, the aim of this technique is to learn about the absorbing species, such as hydroxyl. The use of unoriented samples leads to the need to perform a rigorous statistical analysis, so that the three principal absorbances of the crystal can be retrieved. We present here such an analysis based on a derivation of the probability density function for a single random measurement. Previous methods for retrieval of the absorbances are shown to be suboptimal, producing biased results that are sometimes even unphysical (e.g., negative estimates for an inherently positive quantity). The mathematical structure of the problem is developed to use the maximum likelihood estimation method, and we show how to optimize for the three absorbance parameters. This leads to good parameter retrieval on both synthetic and real data sets.

}, keywords = {crystals, Geochemistry \& Geophysics, Hydrous and Anhydrous Minerals, hydroxyl, infrared, light, mineralogy, quantitative absorbency spectroscopy, spectroscopy, unpolarized, Water in Nominally}, isbn = {0003-004X}, doi = {10.2138/am-2018-6152}, url = {We present a global compilation of paleomagnetic data spanning the past 100 ka. Sediment data comprise 61,687 declinations, 70,936 inclinations, and 69,596 relative paleointensities. Many sites are located in the northern Atlantic and western Pacific, with approximately twice as many data from the Northern Hemisphere as from the Southern Hemisphere. The 14,954 volcanic and archeomagnetic data are sparse, especially in the Southern Hemisphere. Directional and intensity information are aggregated under the paleosecular variation (PSV) index to assess occurrence of excursions over the past 100 ka. The Laschamp excursion (approximate to 41 ka) is clearly defined across globally distributed sediment records with an average duration of 1,300 years. Regional stacks obtained using bootstrap resampling show a more pronounced Laschamp excursion in the Northern Hemisphere than in the Southern, and in the Atlantic Hemisphere compared with the Pacific. No anomalous indices occurred around the Mono Lake excursion or other periods in the bootstrap curves. This may result from low sedimentation rates, discrepancies in age scales, large age errors, and/or the lack of global character of any transitional events. These data and associated new uncertainty estimates for the sediment records provide a good foundation for global, time-dependent, spherical harmonic field modeling for the past 100 ka.

}, keywords = {antarctic south atlantic, archeomagnetic data, correlation, excursion, Geochemistry \& Geophysics, geomagnetic excursion, geomagnetic secular variation, high-resolution record, inter-hemispheric, Laschamp, late, late quaternary sediments, magnetization lock-in, mono lake excursion, Ocean Drilling Program, pacific, paleomagnetic secular variation, paleomagnetic sediment data, Quaternary, relative paleointensity data, western equatorial}, isbn = {1525-2027}, doi = {10.1029/2017gc007271}, url = {Globally distributed paleomagnetic data from discrete volcanic sites have previously been used for statistical studies of paleosecular variation and the structure of the time-averaged field. We present a new data compilation, PSV10, selected from high-quality paleodirections recorded over the past 10 Ma and comprising 2,401 sites from 81 studies. We require the use of modern laboratory and processing methods, a minimum of four samples per site, and within-site Fisher precision parameter, k(w), 50. Studies that identify significant tectonic effects or explicitly target transitional field states are excluded, thereby reducing oversampling of transitional time intervals. Additionally, we apply two approaches using geological evidence to minimize effects of short-term serial correlation. PSV10 is suitable for use in new global geomagnetic and paleomagnetic studies as it has greatly improved spatial coverage of sites, especially at equatorial and high latitudes. VGP dispersion is latitudinally dependent, with substantially higher values in the Southern Hemisphere than at corresponding northern latitudes when no VGP cutoff is imposed. Average inclination anomalies for 10 degrees latitude bins range from about +32 degrees to -7.52 degrees for the entire data set, with the largest negative values occurring at equatorial and mid-northern latitudes. New 0-5 Ma TAF models (LN3 and LN3-SC) based on selections of normal polarity data from PSV10 indicate a Non-zonal variations in field structure are observed near the magnetic equator and in regions of increased radial flux at high latitudes over the Americas, the Indian Ocean, and Asia.

}, keywords = {brunhes-chron, correlation, earths, Geochemistry \& Geophysics, geomagnetic-field, geomagnetism, indian-ocean, lava flows, magnetic-field, mexican volcanic belt, nonzonal, palaeosecular variation, paleomagnetic secular variation, paleosecular variation, past 5, PSV10, Serial, time-averaged field, western mexico}, isbn = {1525-2027}, doi = {10.1002/2017gc007318}, url = {Variations of the geomagnetic field prior to direct observations are inferred from archeo- and paleomagnetic experiments. Seemingly unusual variations not seen in the present-day and historical field are of particular interest to constrain the full range of core dynamics. Recently, archeomagnetic intensity spikes, characterized by very high field values that appear to be associated with rapid secular variation rates, have been reported from several parts of the world. They were first noted in data from the Levant at around 900 BCE. A recent re-assessment of previous and new Levantine data, involving a rigorous quality assessment, interprets the observations as an extreme local geomagnetic high with at least two intensity spikes between the 11th and 8th centuries BCE. Subsequent reports of similar features from Asia, the Canary Islands and Texas raise the question of whether such features might be common occurrences, or whether they might even be part of a global magnetic field feature. Here we use spherical harmonic modeling to test two hypotheses: firstly, whether the Levantine and other potential spikes might be associated with higher dipole field intensity than shown by existing global field models around 1,000 BCE, and secondly, whether the observations from different parts of the world are compatible with a westward drifting intense flux patch. Our results suggest that the spikes originate from intense flux patches growing and decaying mostly in situ, combined with stronger and more variable dipole moment than shown by previous global field models. Axial dipole variations no more than 60\% higher than observed in the present field, probably within the range of normal geodynamo behavior, seem sufficient to explain the observations.

}, keywords = {archeomagnetism, argentina, birkat-ram, earths magnetic-field, eastern china, el-trebol patagonia, geology, global magnetic field models, golan heights, holocene-pleistocene sediments, intensity spike, Israel, palaeosecular variation, paleomagnetism, relative paleointensity, secular variation}, isbn = {2296-6463}, doi = {10.3389/feart.2018.00017}, url = {Geomagnetic intensity fluctuations provide important constraints on time-scales associated with dynamical processes in the outer core. PADM2M is a reconstructed time series of the 0-2 Ma axial dipole moment (ADM). After smoothing to reject high frequency variations PADM2M{\textquoteright}s average growth rate is larger than its decay rate. The observed asymmetry in rates of change is compatible with longer term diffusive decay of the ADM balanced by advective growth on shorter time scales, and provides a potentially useful diagnostic for evaluating numerical geodynamo simulations. We re-analyze the PADM2M record using improved low-pass filtering to identify asymmetry and quantify its uncertainty via bootstrap methods before applying the new methodology to other kinds of records. Asymmetry in distribution of axial dipole moment derivatives is quantified using the geomagnetic skewness coefficient, sg. A positive value indicates the distribution has a longer positive tail and the average growth rate is greater than the average decay rate. The original asymmetry noted by Ziegler and Constable (2011) is significant and does not depend on the specifics of the analysis. A long-term record of geomagnetic intensity should also be preserved in the thermoremanent magnetization of oceanic crust recovered by inversion of stacked profiles of marine magnetic anomalies. These provide an independent means of verifying the asymmetry seen in PADM2M. We examine three near bottom surveys: a 0 to 780 ka record from the East Pacific Rise at 19 degrees S, a 0 to 5.2 Ma record from the Pacific Antarctic Ridge at 51 degrees S, and a chron C4Ar-C5r (9.3-11.2 Ma) record from the NE Pacific. All three records show an asymmetry similar in sense to PADM2M with geomagnetic skewness coefficients, s(g) \> 0. Results from PADM2M and C4Ar-C5r are most robust, reflecting the higher quality of these geomagnetic records. Our results confirm that marine magnetic anomalies can carry a record of the asymmetric geomagnetic field behavior first found for 0-2 Ma in PADM2M, and show that it was also present during the earlier time interval from 9.3-11.2 Ma. (C) 2017 The Authors. Published by Elsevier B.V.

}, keywords = {anomalies, cumulative viscous remanence, dipole moment variations, intensity, layer, ma, marine magnetic anomalies, near-bottom, paleointensity, paleomagnetic field, paleomagnetic field strength, records, saw-toothed pattern, scale, tiny wiggles}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2017.03.020}, url = {Extreme variations of Earth{\textquoteright}s magnetic field occurred in the Levant region around 1000 BC, when the field intensity rapidly rose and fell by a factor of 2. No coherent link currently exists between this intensity spike and the global field produced by the core geodynamo. Here we show that the Levantine spike must span \>60 degrees longitude at Earth{\textquoteright}s surface if it originates from the core-mantle boundary (CMB). Several low intensity data are incompatible with this geometric bound, though age uncertainties suggest these data could have sampled the field before the spike emerged. Models that best satisfy energetic and geometric constraints produce CMB spikes 8-22 degrees wide, peaking at O(100) mT. We suggest that the Levantine spike reflects an intense CMB flux patch that grew in place before migrating northwest, contributing to growth of the dipole field. Estimates of Ohmic heating suggest that diffusive processes likely govern the ultimate decay of geomagnetic spikes.

}, keywords = {constraints, convection, earths core, intensity, magnetic-field, nutation, outer-core, secular variation, spherical-shell, torsional waves}, isbn = {2041-1723}, doi = {10.1038/ncomms15593}, url = {Magnetic indices provide quantitative measures of space weather phenomena that are widely used by researchers in geomagnetism. We introduce an index focused on the internally generated field that can be used to evaluate long term variations or climatology of modern and paleomagnetic secular variation, including geomagnetic excursions, polarity reversals, and changes in reversal rate. The paleosecular variation index, P-i, represents instantaneous or average deviation from a geocentric axial dipole field using normalized ratios of virtual geomagnetic pole colatitude and virtual dipole moment. The activity level of the index, sigma P-i, provides a measure of field stability through the temporal standard deviation of P-i. P-i can be calculated on a global grid from geomagnetic field models to reveal large scale geographic variations in field structure. It can be determined for individual time series, or averaged at local, regional, and global scales to detect long term changes in geomagnetic activity, identify excursions, and transitional field behavior. For recent field models, P-i ranges from less than 0.05 to 0.30. Conventional definitions for geomagnetic excursions are characterized by P-i exceeding 0.5. Strong field intensities are associated with low P-i unless they are accompanied by large deviations from axial dipole field directions. sigma P-i provides a measure of geomagnetic stability that is modulated by the level of PSV or frequency of excursional activity and reversal rate. We demonstrate uses of P-i for paleomagnetic observations and field models and show how it could be used to assess whether numerical simulations of the geodynamo exhibit Earth-like properties.

}, keywords = {data, dipole-moment, earths magnetic-field, ka, north-atlantic, paleointensity, records, satellite, scale, secular variation, transition}, isbn = {1525-2027}, doi = {10.1002/2016gc006668}, url = {Direct observations of the geomagnetic field show that secular variation is strong in the Atlantic hemisphere, and comparatively reduced in the Pacific region. The dipole has been decaying since at least 1840 AD, driven by growth and migration of reverse flux patches in the southern hemisphere. We investigate whether anything like this modern pattern of geomagnetic secular variation persists and can be detected in global paleomagnetic field models. Synthesis of results from two new time-varying spherical harmonic models shows that geographically distinct geomagnetic secular variation extends to at least 10000 BP. The models use the same database but differ in methodology, leading to some regional differences in results. Consistent large-scale surface features include strong average fields in the northern hemisphere and weaker fields with greater overall variability in the south. Longitudinal structure is present, with weaker average fields in the western Pacific than in the east, and prominent negative inclination anomalies extending beneath Indonesia, across Africa and to Brazil, but weaker anomalies in the central Pacific. Marginally positive inclination anomalies occur west of the Americas. Paleosecular variation activity peaks at high southern latitudes, and there is a pattern of reduced activity at equatorial and mid-latitudes beneath the Pacific. Although the dipole has exhibited both growth and decay over the interval 0-10 000 BP, our results show that geomagnetic paleosecular variation is preferentially focused in similar geographic regions to secular variation seen in the modern field. (C) 2016 The Authors. Published by Elsevier B.V.

}, keywords = {averaged, boundary, core-mantle, dipole, earths magnetic-field, geomagnetic secular variation, geomagnetism, inner-core, magnetic anomaly, models, numerical dynamos, paleomagnetic field, paleomagnetic field models, paleomagnetism, South Atlantic, tomography}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2016.08.015}, url = {The Magnetics Information Consortium (MagIC) database provides an archive with a flexible data model for paleomagnetic and rock magnetic data. The PmagPy software package is a cross-platform and open-source set of tools written in Python for the analysis of paleomagnetic data that serves as one interface to MagIC, accommodating various levels of user expertise. PmagPy facilitates thorough documentation of sampling, measurements, data sets, visualization, and interpretation of paleomagnetic and rock magnetic experimental data. Although not the only route into the MagIC database, PmagPy makes preparation of newly published data sets for contribution to MagIC as a byproduct of normal data analysis and allows manipulation as well as reanalysis of data sets downloaded from MagIC with a single software package. The graphical user interface (GUI), Pmag GUI enables use of much of PmagPy{\textquoteright}s functionality, but the full capabilities of PmagPy extend well beyond that. Over 400 programs and functions can be called from the command line interface mode, or from within the interactive Jupyter notebooks. Use of PmagPy within a notebook allows for documentation of the workflow from the laboratory to the production of each published figure or data table, making research results fully reproducible. The PmagPy design and its development using GitHub accommodates extensions to its capabilities through development of new tools by the user community. Here we describe the PmagPy software package and illustrate the power of data discovery and reuse through a reanalysis of published paleointensity data which illustrates how the effectiveness of selection criteria can be tested.

}, keywords = {0520 Data analysis: algorithms and implementation, 0525 Data management, 0530 Data presentation and visualization, 1594 Instruments and techniques, 1599 General or miscellaneous, MagIC database, Magnetics Information Consortium, paleomagnetic and rock magnetic database, PmagPy software package}, isbn = {1525-2027}, doi = {10.1002/2016GC006307}, author = {Tauxe, L. and Shaar, R. and Jonestrask, L. and Swanson-Hysell, N. L. and Minnett, R. and Koppers, A. A. P. and Constable, C. G. and Jarboe, N. and Gaastra, K. and Fairchild, L.} } @article {39234, title = {Earth{\textquoteright}s electromagnetic environment}, journal = {Surveys in Geophysics}, volume = {37}, number = {1}, year = {2016}, note = {n/a}, month = {2016/01}, pages = {27-45}, type = {Review}, abstract = {The natural spectrum of electromagnetic variations surrounding Earth extends across an enormous frequency range and is controlled by diverse physical processes. Electromagnetic (EM) induction studies make use of external field variations with frequencies ranging from the solar cycle which has been used for geomagnetic depth sounding through the 10-10 Hz frequency band widely used for magnetotelluric and audio-magnetotelluric studies. Above 10 Hz, the EM spectrum is dominated by man-made signals. This review emphasizes electromagnetic sources at 1 Hz and higher, describing major differences in physical origin and structure of short- and long-period signals. The essential role of Earth{\textquoteright}s internal magnetic field in defining the magnetosphere through its interactions with the solar wind and interplanetary magnetic field is briefly outlined. At its lower boundary, the magnetosphere is engaged in two-way interactions with the underlying ionosphere and neutral atmosphere. Extremely low-frequency (3 Hz-3 kHz) electromagnetic signals are generated in the form of sferics, lightning, and whistlers which can extend to frequencies as high as the VLF range (3-30 kHz).The roughly spherical dielectric cavity bounded by the ground and the ionosphere produces the Schumann resonance at around 8 Hz and its harmonics. A transverse resonance also occurs at 1.7-2.0 kHz arising from reflection off the variable height lower boundary of the ionosphere and exhibiting line splitting due to three-dimensional structure. Ground and satellite observations are discussed in the light of their contributions to understanding the global electric circuit and for EM induction studies.

}, keywords = {algorithm, amt dead band, atmospheric electricity, Audio-magnetotellurics, circuit, Electromagnetism, Geomagnetic spectrum, inversion, ionosphere, lightning, magnetotellurics, radio transmitters, Schumann resonance, Sferics, sprites, storms}, isbn = {0169-3298}, doi = {10.1007/s10712-015-9351-1}, url = {Absolute and relative geomagnetic paleointensity records reveal variations in geomagnetic dipole strength, either via averaging time series of virtual axial dipole moments, or through formal inversion strategies like the penalized maximum likelihood (PML) method used for the PADM2M (Paleomagnetic Axial Dipole Moment for 0-2 Ma) model. However, departures from the most basic geocentric axial dipole (GAD) structure are obvious on centennial to millennial time scales, and paleomagnetic records from igneous rocks suggest small deviations persist on million year time scales. Spatial variations in heat flow at the core-mantle boundary (inferred from large low shear velocity provinces, LLSVPs) are widely suspected to influence both the average geomagnetic field and its regional secular variation. Long term departures from a GAD configuration should be visible from regional differences in paleointensity reconstructions. We use a PML method to construct time-varying models of regional axial dipole moment (RADMs) from a combined set of absolute and relative palebintensity data, and compare results from the last 300 kyr. RADMs are created from sediment records selected from specific latitude and longitude bands. We also test whether grouping records lying above each of the 2 major LLSVPs (centered on Africa and the Pacific) produce RADMs that are distinct from those above regions lacking anomalous seismic structure. Systematic differences appear in the various regional results. In the most recent part of the record regional differences are broadly similar to the Holocene, CALS10k.1b, time-varying geomagnetic field model spanning 0-10 ka. However, lack of Southern hemisphere records prevents direct confirmation of the hemispheric asymmetry present in CALS10k.1b in both average virtual axial dipole moment and its variability. As expected, the 300 kyr RADMs exhibit greater overall temporal field variability than is seen over 0-10 ka. Average RADM is higher in the Pacific and in Equatorial regions than in the Atlantic and in mid-high latitude northern hemisphere regions. Higher average RADMs are associated with lower overall field variability and less pronounced excursional signatures. Notably, the lower variability in the Pacific sector seen here (defined by either longitude band or LLSVP location) suggests that the modern low paleosecular variation there extends over at least the past few hundred thousand years. RADMs identified with LLSVPs show systematic deviations from the non-LLSVP group of records, with distinct characteristics for the African and Pacific provinces. The African LLSVP generates more pronounced RADM minima associated with geomagnetic excursions, and in general paleointensity decreases associated with excursions occur first in the Atlantic longitude sector and over the African LLSVP. (C) 2015 Elsevier B.V. All rights reserved.

}, keywords = {atlantic, constraints, core, dipole, earths magnetic-field, excursions, geocentric axial, geodynamo, geomagnetic secular variation, geomagnetism, ma, model, paleomagnetism, relative paleointensity, reversals, simulations}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2015.04.022}, url = {Characterization of geomagnetic field behaviour on timescales of centuries to millennia is necessary to understand the mechanisms that sustain the geodynamo and drive its evolution. As Holocene paleomagnetic and archeomagnetic data have become more abundant, strategies for regularized inversion of modern field data have been adapted to produce numerous time-varying global field models. We evaluate the effectiveness of several approaches to inversion and data handling, by assessing both global and regional properties of the resulting models. Global Holocene field models cannot resolve Southern hemisphere regional field variations without the use of sediments. A standard data set is used to construct multiple models using two different strategies for relative paleointensity calibration and declination orientation and a selection of starting models in the inversion procedure. When data uncertainties are considered, the results are similar overall regardless of whether we use iterative calibration and reorientation, or co-estimation of the calibration and orientation parameters as part of the inversion procedure. In each case the quality of the starting model used for initial relative paleointensity calibration and declination orientation is crucial and must be based on the best absolute information available. Without adequate initial calibration the morphology of dipole moment variations can be recovered but its absolute value will be correlated with the initial intensity calibrations, an effect that might be mitigated by ensuring an appropriate fit to enough high quality absolute intensity data with low uncertainties. The declination reorientation mainly impacts regional field structure and in the presence of non-zonal fields will result in a non-zero local average. The importance of declination orientation is highlighted by inconsistencies in the West Pacific and Australian sediment records in CALS10k.1b model. Great care must also be taken to assess uncertainties associated with both paleomagnetic and age data and to evaluate the effects of poor data distribution. New consistently allocated uncertainty estimates for sediment paleomagnetic records highlight the importance of adequate uncertainties in the inversion process, as they determine the relative weighting among the data and overall normalized misfit levels which in turn influence the complexity of the inferred field models. Residual distributions suggest that the most appropriate misfit measure is the L-1 norm (minimum absolute deviation) rather than L-2 (least squares), but this seems to have relatively minor impact on the overall results. For future Holocene field modelling we see a need for comprehensive methods to assess uncertainty in individual archeomagnetic data so that these data or models derived from them can be used for reliable initial relative paleointensity calibration and declination orientation in sediments. More work will be needed to assess whether co-estimation or an iterative approach to inversion is more efficient overall. This would be facilitated by realistic and globally consistent data and age uncertainties from the paleomagnetic community.

}, keywords = {archaeomagnetism, central, earths magnetic-field, el-trebol patagonia, flux lobes, japan, magnetic field, maximum-entropy, palaeointensity, Palaeomagnetic, palaeosecular variation, paleointensity, past 7 millennia, pleistocene sediments, regularization, relative, secular variation, secular variation record}, isbn = {0956-540X}, doi = {10.1093/gji/ggv137}, url = {Background: GEOMAGIA50.v3 is a comprehensive online database providing access to published paleomagnetic, rock magnetic, and chronological data from a variety of materials that record Earth{\textquoteright}s magnetic field over the past 50 ka. Findings: Since its original release in 2006, the structure and function of the database have been updated and a significant number of data have been added. Notable modifications are the following: (1) the inclusion of additional intensity, directional and metadata from archeological and volcanic materials and an improved documentation of radiocarbon dates; (2) a new data model to accommodate paleomagnetic, rock magnetic, and chronological data from lake and marine sediments; (3) a refinement of the geographic constraints in the archeomagnetic/volcanic query allowing selection of particular locations; (4) more flexible methodological and statistical constraints in the archeomagnetic/volcanic query; (5) the calculation of predictions of the Holocene geomagnetic field from a series of time varying global field models; (6) searchable reference lists; and (7) an updated web interface. This paper describes general modifications to the database and specific aspects of the archeomagnetic and volcanic database. The reader is referred to a companion publication for a description of the sediment database. Conclusions: The archeomagnetic and volcanic part of GEOMAGIA50.v3 currently contains 14,645 data (declination, inclination, and paleointensity) from 461 studies published between 1959 and 2014. We review the paleomagnetic methods used to obtain these data and discuss applications of the data within the database. The database continues to expand as legacy data are added and new studies published. The web-based interface can be found at http://geomagia.gfz-potsdam.de

}, keywords = {2 thousand years, age calibration curves, archeomagnetism, database, earths magnetic-field, fired-clay ceramics, GEOMAGIA50, geomagnetism, holocene geomagnetic-field, last 8 millennia, magnetization, non-dipole field, paleomagnetism, secular, thellier paleointensity experiments, thermochemical remanent, variation curve}, isbn = {1880-5981}, doi = {10.1186/s40623-015-0232-0}, url = {Background: GEOMAGIA50.v3 for sediments is a comprehensive online database providing access to published paleomagnetic, rock magnetic, and chronological data obtained from lake and marine sediments deposited over the past 50 ka. Its objective is to catalogue data that will improve our understanding of changes in the geomagnetic field, physical environments, and climate. Findings: GEOMAGIA50.v3 for sediments builds upon the structure of the pre-existing GEOMAGIA50 database for magnetic data from archeological and volcanic materials. A strong emphasis has been placed on the storage of geochronological data, and it is the first magnetic archive that includes comprehensive radiocarbon age data from sediments. The database will be updated as new sediment data become available. Conclusions: The web-based interface for the sediment database is located at http://geomagia.gfz-potsdam.de/geomagiav3/SDquery.php. This paper is a companion to Brown et al. (Earth Planets Space doi:10.1186/s40623-015-0232-0,2015) and describes the data types, structure, and functionality of the sediment database.

}, keywords = {database, deep-sea, depositional remanent magnetization, environmental magnetism, GEOMAGIA50, geomagnetic secular variation, geomagnetism, iaga paleointensity database, inter-hemispheric correlation, north-atlantic, paleomagnetism, radiocarbon measurements, redeposition experiments, relative paleointensity, rock magnetism, Sediment magnetism, sediments}, doi = {10.1186/s40623-015-0233-z}, url = {Detailed knowledge of the long-term spatial configuration and temporal variability of the geomagnetic field is lacking because of insufficient data for times prior to 10 ka. We use realisations from suitable numerical simulations to investigate three important questions about stability of the geodynamo process: is the present field representative of the past field; does a time-averaged field actually exist; and, supposing it exists, how long is needed to define such a field. Numerical geodynamo simulations are initially selected to meet existing criteria for morphological similarity to the observed magnetic field. A further criterion is introduced to evaluate similarity of long-term temporal variations. Allowing for reasonable uncertainties in the observations, observed and synthetic axial dipole moment frequency spectra for time series of order a million years in length should be fit by the same power law model. This leads us to identify diffusion time as the appropriate time scaling for such comparisons. In almost all simulations, intervals considered to have good morphological agreement between synthetic and observed field are shorter than those of poor agreement. The time needed to obtain a converged estimate of the time-averaged field was found to be comparable to the length of the simulation, even in non-reversing models, suggesting that periods of stable polarity spanning many magnetic diffusion times are needed to obtain robust estimates of the mean dipole field. Long term field variations are almost entirely attributable to the axial dipole; nonzonal components converge to long-term average values on relatively short timescales (15-20 kyr). In all simulations, the time-averaged spatial power spectrum is characterised by a zigzag pattern as a function of spherical harmonic degree, with relatively higher power in odd degrees than in even degrees. We suggest that long-term spatial characteristics of the observed field may emerge on averaging times that are within reach for the next generation of global time-varying paleomagnetic field models. (C) 2014 Elsevier B.V. All rights reserved.

}, keywords = {boundary heat-flow, convection, core evolution, dipole-moment, dynamos, Earth{\textquoteright}s core, earths magnetic-field, geodynamo models, geomagnetic frequency spectrum, mantle, models, numerical, reversals, secular variation}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2014.07.042}, url = {Paleomagnetic results from globally distributed lava flows have been collected and analyzed under the time-averaged field initiative (TAFI), a multi-institutional collaboration started in 1996 and designed to improve the geographic and temporal coverage of the 0-5 Ma paleomagnetic database for studying both the time-averaged field and its very long-term secular variations. Paleomagnetic samples were collected from 35 volcanic units, either lava flows or ignimbrites, in Costa Rica in December 1998 and February 2000 from the Cordilleras Central and Guanacaste, the underlying Canas, Liberia and Bagaces formations and from Volcano Arenal. Age estimates range from approximately 40 ka to slightly over 6 Ma. Although initial results from these sites were used in a global synthesis of TAFI data by Johnson et al. (2008), a full description of methodology was not presented. This paper documents the definitive collection of results comprising 28 paleomagnetic directions (24 normal, 4 reversed), with enhanced precision and new geological interpretations, adding two paleointensity estimates and 19 correlated Ar-40/Ar-39 radiometric ages. The average field direction is consistent with that of a geocentric axial dipole and dispersion of virtual geomagnetic poles (17.34.6 degrees) is in general agreement with predictions from several statistical paleosecular variation models. Paleointensity estimates from two sites give an average field strength of 26.3 T and a virtual axial dipole moment of 65 ZAm(2). The definitive results provide a useful augmentation of the global database for the longer term goal of developing new statistical descriptions of paleomagnetic field behavior.

}, keywords = {arc, Costa Rica, geomagnetic secular variation, history, ma, magnetic-field, model, paleointensity, paleosecular variation, past 5, rocks, TAFI}, isbn = {1525-2027}, doi = {10.1002/ggge.20199}, url = {Investigations of the behavior of the geomagnetic field on geological timescales rely on globally distributed data sets from dated lava flows. We present the first suitable data from the Arctic region, comprising 37 paleomagnetic directions from Jan Mayen (71 degrees N, 0.2-461 ka) and Spitsbergen (79 degrees N, 1-9.2 Ma) and five paleointensity results. Dispersion of the Arctic virtual geomagnetic poles over the last 2 Ma (27.34.0 degrees) is significantly lower than that from published Antarctic data sets (32.15.0 degrees). Arctic average virtual axial dipole moment (76.824.3 ZAm(2)) is high in comparison to Antarctica over the same time interval (34.88.2 ZAm(2)), although the data are still too sparse in the Arctic to be definitive. These data support a long-lived hemispheric asymmetry of the magnetic field, contrasting higher, more stable fields in the north with lower average strength and more variable field directions in the south. Such features require significant non-axial-dipole contributions over 10(5)-10(6) years.

}, keywords = {age, dipole-moment, geomagnetic field, intensity, Jan Mayen, lavas, model, paleointensity, paleosecular variation, secular variation, spitsbergen, time}, isbn = {1525-2027}, doi = {10.1002/ggge.20174}, url = {Regeneration of the Earth{\textquoteright}s magnetic field by convection in the liquid core produces a broad spectrum of time variation. Relative palaeointensity measurements in marine sediments provide a detailed record over the past 2 Myr, but an explicit reconstruction of the underlying dynamics is not feasible. A more practical alternative is to construct a stochastic model from estimates of the virtual axial dipole moment. The deterministic part of the model (drift term) describes time-averaged behaviour, whereas the random part (diffusion term) characterizes complex interactions over convective timescales. We recover estimates of the drift and diffusion terms from the SINT2000 model of Valet et al. and the PADM2M model of Ziegler et al. The results are used in numerical solutions of the Fokker-Planck equation to predict statistical properties of the palaeomagnetic field, including the average rates of magnetic reversals and excursions. A physical interpretation of the stochastic model suggests that the timescale for adjustments in the axial dipole moment is set by the dipole decay time tau(d). We obtain tau(d) = 29 kyr from the stochastic models, which falls within the expected range for the Earth{\textquoteright}s core. We also predict the amplitude of convective fluctuations in the core, and establish a physical connection to the rates of magnetic reversals and excursions. Chrons lasting longer than 10 Myr are unlikely under present-day conditions. However, long chrons become more likely if the diffusion term is reduced by a factor of 2. Such a change is accomplished by reducing the velocity fluctuations in the core by a factor of root 2, which could be attributed to a shift in the spatial pattern of heat flux from the core or a reduction in the total core heat flow.

}, keywords = {earths core, excursions, frequency, geodynamo, geomagnetic dipole, Geomagnetic excursions, magnetostratigraphy, mantle, palaeointensity, paleosecular, past 7 millennia, Probability distributions, reversal rate, Reversals: process, secular variation, timescale, variation}, isbn = {0956-540X}, doi = {10.1093/gji/ggt218}, url = {The power of spectral estimation as a tool for studying geophysical processes is often limited by short records or breaks in available time-series. Direct spectral estimation using multitaper techniques designed to reduce variance and minimize leakage can help alleviate the first problem. For records with gaps, systematic interpolation or averaging of multitaper spectra derived from record fragments may prove adequate in some cases, but can be cumbersome to implement. Alternatively, multitapers can be modified for use in direct spectral estimation with intermittently sampled data. However, their performance has not been adequately studied. We investigate reliability and resolution of techniques that adapt prolate and minimum bias (MB) multitapers to accommodate the longest breaks in sampling, comparing the tapering functions (referred to as PRG or MBG tapers) with the standard prolate and MB tapers used for complete data series, and with the section-averaging approach. Using a synthetic data set, we test both jackknife and bootstrap methods to calculate confidence intervals for PRG and MBG multitaper spectral estimates and find the jackknife is both more accurate and faster to compute. To implement these techniques for a variety of data sets, we provide an algorithm that allows the user to balance judicious interpolation against the use of suitably adapted tapers, providing empirical measures of both bias and frequency resolution for candidate sets of tapers. These techniques are tested on diverse geophysical data sets: a record of change in the length of day, a model of the external dipole part of the geomagnetic field produced by the magnetospheric ring current, and a 12 Myr long irregularly sampled relative geomagnetic palaeointensity record with pernicious gaps. We conclude that both PRG and MBG tapers generally perform as well as, or better than, an optimized form of the commonly used section averaging approach. The greatest improvements seem to occur when the gap structure creates data segments of very unequal lengths. Ease of computation and more robust behaviour can make MBG tapers a better choice than PRG except when very fine-scale frequency resolution is required. These techniques could readily be applied for cross-spectral and transfer function estimation and are a useful addition to the geophysical toolbox.

}, keywords = {Earth rotation variations, field, Fourier analysis, intensity, magnetic field, Oligocene, palaeointensity, robust estimation, Time-series analysis}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.2012.05594.x}, url = {Numerical solution of global geomagnetic induction problems in two and three spatial dimensions can be conducted with commercially available, general-purpose, scripted, finite-element software. We show that FlexPDE is capable of solving a variety of global geomagnetic induction problems. The models treated can include arbitrary electrical conductivity of the core and mantle, arbitrary spatial structure and time behaviour of the primary magnetic field. A thin surface layer of laterally heterogeneous conductivity, representing the oceans and crust, may be represented by a boundary condition at the Earthspace interface. We describe a numerical test, or validation, of the program by comparing its output to analytic and semi-analytic solutions for several electromagnetic induction problems: (1) concentric spherical shells representing a layered Earth in a time-varying, uniform, external magnetic field, (2) eccentrically nested conductive spheres in the same field and (3) homogeneous spheres or cylinders, initially at rest, then rotating at a steady rate in a constant, uniform, external field. Calculations are performed in both the time and frequency domains, and in both 2-D and 3-D computational meshes, with adaptive mesh refinement. Root-mean-square accuracies of better than 1 per cent are achieved in all cases. A unique advantage of our technique is the ability to model Earth rotation in both the time and the frequency domain, which is especially useful for simulating satellite data.

}, keywords = {constraints, Earth, eccentrically nested spheres, Electrical properties, geomagnetic induction, heterogeneity, magnetic field, mantle electrical-conductivity, mid-mantle, Numerical solutions, oceans, responses, satellite induction, Satellite magnetics}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.2011.05255.x}, url = {Time series of relative geomagnetic paleointensity variations derived from marine sediments can be calibrated using absolute data derived from igneous materials. The resulting records may be suitable for spectral analysis of geomagnetic dipole variations. This work re-evaluates the 12 My (22.74-34.77 Ma) sediment record from Deep Sea Drilling Project Leg 73, Site 522, that is a key data set for determining the paleomagnetic power spectrum in the frequency range 1-100 My(-1). The 12 My record is marred by uneven sampling, with the interval between samples ranging from 1 to 640 ky, and contains several gaps that are considered too long to interpolate. The relative intensity data are calibrated using 129 globally distributed absolute paleointensity data from the same time interval. The power spectrum of the resulting time series is estimated using direct multi-taper spectral estimation with prolate data tapers adapted to deal with missing sections in the time series. The longest record available for analysis is thereby extended from 5.3 to 12 My. The new paleomagnetic power spectrum confirms the presence of a broad spectral peak at around 8 My(-1) for the early Oligocene and uncovers a peak around 2.5 My(-1) in the late Oligocene. Both peaks may be linked to tiny wiggles in marine magnetic anomalies. The new analysis unambiguously verifies that there is lower overall power in the younger part of the record, where the reversal process appears to dominate the power spectrum of the paleosecular variation. A comparison of the late Oligocene spectrum with that of PADM2M, a model of paleomagnetic axial dipole variations for 0-2 Ma, reveals some broad similarities; both time periods have similar power levels and a reversal rate of 4 My(-1). During the early Oligocene the reversal rate is about a factor of two lower, the field strength is higher, and the secular variation is stronger, suggesting that a strong magnetic field inhibits reversals but produces more variability in field strength. (C) 2011 Elsevier B.V. All rights reserved.

}, keywords = {axial dipole, behavior, drilling-project site-522, geomagnetic power spectrum, geomagnetism, intervals, leg-73, marine magnetic-anomalies, paleointensity, Paleomagnetic dipole moment, paleomagnetic field, paleosecular variation, polarity, reversal frequency, sediments, tiny wiggles, Virtual axial dipole moment}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2011.07.011}, url = {Global geomagnetic field reconstructions on millennial time scales can be based on comprehensive paleomagnetic data compilations but, especially for older data, these still suffer from limitations in data quality and age controls as well as poor temporal and spatial coverage. Here we present updated global models for the time interval 0-3 ka where additions to the data basis mainly impact the South-East Asian, Alaskan, and Siberian regions. We summarize recent progress in millennial scale modelling, documenting the cumulative results from incremental modifications to the standard algorithms used to produce regularized time-varying spherical harmonic models spanning 1000 BC to 1990 AD: from 1590 to 1990 AD gauss coefficients from the historical gufm1 model supplement the paleomagnetic information; in addition to absolute paleointensities, calibrated relative paleointensity data from sediments are now routinely included; iterative data rejection and recalibration of relative intensity records from sediments ensure stable results; bootstrap experiments to generate uncertainty estimates for the model take account of uncertainties in both age and magnetic elements and additionally assess the impact of sampling in both time and space. Based on averaged results from bootstrap experiments, taking account of data and age uncertainties, we distinguish more conservative model estimates CALS3k.nb representing robust field structure at the core-mantle boundary from relatively high resolution models CALS3k.n for model versions n = 3 and 4. We assess the impact of newly available data and modifications to the modelling method by comparing the previous CALS3k.3, the new CALS3k.4, and the conservative new model, CALS3k.4b. We conclude that with presently available data it is not feasible to produce a model that is equally suitable for relatively high-resolution field predictions at Earth{\textquoteright}s surface and robust reconstruction of field evolution, avoiding spurious structure, at the core-mantle boundary (CMB). We presently consider CALS3k.4 the best high resolution model and recommend the more conservative lower resolution version for studies of field evolution at the CMB. (C) 2011 Elsevier B.V. All rights reserved.

}, keywords = {Archaeomagnetic field, central japan, earths, field model, geomagnetism, Holocene, lake-sediments, magnetic-field, Millennial secular, models, nuclide production-rates, paleomagnetic secular variation, past 7 millennia, record, relative paleointensity, stratigraphy, variation}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2011.06.017}, url = {P\>We present a new time-varying model for palaeomagnetic axial dipole moment (PADM) for the past 2 Myr and compare it with earlier virtual axial dipole moment (VADM) reconstructions which have been based on stacking and averaging scaled relative palaeointensity records. The PADM is derived from both absolute and relative palaeointensity data and constructed using a new penalized maximum likelihood (PML) approach to recover a cubic B-spline representation of axial-dipole field variations on million year timescales. The PML method is explicitly intended to reduce bias in estimating the true axial dipole moment that arises in average VADM reconstructions. We apply the PML method to a set of 96 032 published data (1800 palaeointensities from igneous rocks, 3300 archaeointensities and 86 relative palaeointensity time-series of variable lengths and resolutions). Two models are discussed: PADM2Mp is a trial model based on a subset of the nine longest available sedimentary records; PADM2M uses a comprehensive data set (76 records, 81 446 data; 10 records were eliminated) and is our preferred model. PADM2M has a lower mean than existing VADM reconstructions but shows similarities in long-period variability. Some differences in timing, amplitude and resolution of certain features can be attributed to variations in age assignments. Others result from our more comprehensive data set and a reduction in bias attributable to PML modelling. PADM2M has an average axial dipole moment over 0-2 Ma of 5.3 x 1022 Am2 with a standard deviation of 1.5 x 1022 Am2. The Brunhes chron average (6.2 x 1022 Am2) is higher than for earlier epochs of Matuyama (4.8 x 1022 Am2), as seen in some previous studies. The power spectrum for our model agrees with previous estimates of the global palaeomagnetic power spectrum for frequencies up to about 102 Myr-1. We see no distinctive evidence in the power spectrum for orbital forcing of geodynamo behaviour.

}, keywords = {antarctic south atlantic, archaeomagnetism, earths magnetic-field, equatorial pacific, geomagnetic-field intensity, inter-hemispheric correlation, magnetic field, matuyama-brunhes boundary, odp site 983, ontong-java plateau, palaeointensity, Palaeomagnetic, relative paleointensity records, sea sediment cores, secular variation, western}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.2010.04905.x}, url = {The geodynamo in Earth{\textquoteright}s core is responsible for magnetic field changes on diverse timescales, including numerous enigmatic reversals of the dipole field polarity. Understanding the physical processes driving them is an active area of investigation via both paleomagnetic work and numerical simulations of the geodynamo. Some previous studies on geomagnetic field intensity detected a sawtooth pattern of intensity around reversals: a gradual decay in field strength preceding a reversal followed by rapid growth afterwards. Here we characterize distinct statistical properties for increasing and decreasing dipole strength over the past two million years. Examining the geomagnetic field and its time derivative on a range of time scales reveals that for periods longer than about 25 ky there is a clear asymmetry in the statistical distributions for growth versus decay rates of the dipole strength. At 36 ky period, average growth rate is about 20\% larger than the decay rate, and the field spends 54\% of its time decaying, but only 46\% growing. These differences are not limited to times when the field is reversing, suggesting that the asymmetry is controlled by fundamental physical processes underlying all paleosecular variation. The longer decay cycle might suggest the possibility of episodic periods of subcritical dynamo activity where the field is dominated by diffusive processes, followed by transient episodes of strong growth of the axial dipole. However, our work finds no clear separation of timescales for the influence of diffusive and convective processes on dipole moment: both seem to play an important but asymmetric role on the 25-150 ky timescale. (C) 2011 Elsevier B.V. All rights reserved.

}, keywords = {field, geodynamo models, geomagnetism, intensity, paleomagnetism, paleosecular variation, records, reversals, spectrum}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2011.10.019}, url = {Knowledge of the Holocene evolution of Earth{\textquoteright}s magnetic field is important for understanding geodynamo processes in the core, is necessary for studying long-term solar-terrestrial relationships, and can provide useful age constraints for archeologicaland stratigraphic applications. Continuous time-varying global field models based on archeo- and paleomagnetic data are useful tools in this regard. We use a comprehensive data compilation and recently refined modelling strategies to produce CALS10k.1b, the first time-varying spherical harmonic geomagnetic field model spanning 10 ky. The model is an average obtained from bootstrap sampling to take account of uncertainties in magnetic components and ages in the data (and hence has version number 1b instead of 1). This model shows less spatial and temporal resolution than earlier versions for 0-3 ka, and particularly aims to provide a robust representation of the large-scale field at the core-mantle boundary (CMB). We discuss the geomagnetic dipole evolution and changes in Holocene magnetic field morphology at the CMB as shown by the new reconstruction. The results are compatible with earlier models (CALS3k.3 and CALS3k.4) for 0-3 ka, but reveal some clear deficiencies in the 0-7 ka CALS7K.2 model prior to 3 ka. CALS10k.1b is able to resolve mobile and structurally-evolving high latitude radial field flux lobes at the CMB in both hemispheres, as well as persistent non-zonal structure, in the 10 ky average. Contributions to the average field from time-varying structures in the equatorial Indonesian-Australian region are particularly striking. (C) 2011 Elsevier B.V. All rights reserved.

}, keywords = {earths magnetic-field, el-trebol, geomagnetism, golan heights israel, lake sediment cores, magnetic field models, nuclide, palaeosecular variation, paleomagnetic secular variation, paleomagnetism, past 3000 years, patagonia, production-rates, relative paleointensity, secular variation, variation record}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2011.10.031}, url = {The long-term temporal behavior of intense geomagnetic flux patches at the core-mantle boundary and the relation with lower mantle lateral heterogeneity are under debate. We apply an algorithm to detect centers of intense flux patches and track their time-evolution in a recent archeomagnetic field model in order to study the kinematics of such intense magnetic flux patches on millennial timescale. We find that most intense flux patches appear near the edge of the tangent cylinder. Quasi-stationary periods with small oscillations of patches occur more than drifts. Detailed comparison of the archeomagnetic patches{\textquoteright} behavior with that seen in numerical dynamos with tomographic heat flux boundary conditions suggests that core-mantle thermal coupling could be the cause of a statistical preference for some longitudes on the long term, which does not exclude significant time spent away from the preferred longitudes. This could explain the roughly coincident locations of high-latitude patches in the historical geomagnetic field with that of the time-average paleomagnetic field together with the much weaker patches intensity in the latter. Alternating eastward and westward drifts are also observed. The drifts are more westward than eastward, especially in the southern hemisphere, indicating that the time-average zonal core flow may also be driven by core-mantle thermal coupling. An average patch lifetime of similar to 300 years is found, which we hypothesize may indicate the vortex lifetime in the outer core.

}, keywords = {boundary, core flow, earths magnetic-field, geodynamo, geomagnetic-field models, length, millennia, past 3000 years, secular variation, surface}, isbn = {0148-0227}, doi = {10.1029/2011jb008538}, url = {This review examines results from time-varying geomagnetic field models that span several thousand years, and from variations in dipole moment strength up to million year time scales. For the past 400 years, twin magnetic flux lobes bordering the inner core tangent cylinder in both northern and southern hemispheres dominate the geomagnetic field and appear more or less fixed in location. In contrast, the millennial scale view shows that such features are quite mobile and subject to morphological changes on time scales of a few centuries to a thousand years, possibly reflecting large scale reorganization of core flow. The lobes rarely venture into the Pacific hemisphere, and average fields over various time scales generally reveal two or three sets of lobes, of diminished amplitude. Thus millennial scale models are suggestive of thermal core-mantle coupling generating a weak bias in the average field rather than a strong inhibition of large scale field changes. The recovery of variations in dipole moment on million year time scales allows frequency domain analyses to search for characteristic time scales for core dynamics that might be associated with excursion and reversal rate, time taken for reversals, or any signs of control by Earth{\textquoteright}s orbital parameters. The spectrum is characteristically red for the time interval 0-160 Ma, suggesting non-stationarity associated with average reversal rate changes, probably reflecting the impact of superchrons and a continually evolving core. Distinct regimes of power law decay with frequency may reflect different physical processes contributing to the secular variation. Evidence for non-stationarity at shorter time-scales is also present in dipole moment variations over 0-2 Ma with average growth rate faster than the decay process. Rates of change of dipole moment and rapid local field variations found in the paleomagnetic record are evaluated in the context of the 400 year historical record and the spectrum of geomagnetic variations for 0-160 Ma. (C) 2011 Elsevier B.V. All rights reserved.

}, keywords = {4 centuries, axial dipole, axial dipole moment, copper slag, geodynamo, geomagnetic, geomagnetic field, geomagnetism, historical records, intensity, ma, magnetic-field, paleointensity, Paleomagnetic dipole moment, paleosecular variation, past 7 millennia, power spectrum, secular variation, Virtual}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2011.05.004}, url = {The magnetic field of the Earth is by far the best documented magnetic field of all known planets. Considerable progress has been made in our understanding of its characteristics and properties, thanks to the convergence of many different approaches and to the remarkable fact that surface rocks have quietly recorded much of its history. The usefulness of magnetic field charts for navigation and the dedication of a few individuals have also led to the patient construction of some of the longest series of quantitative observations in the history of science. More recently even more systematic observations have been made possible from space, leading to the possibility of observing the Earth{\textquoteright}s magnetic field in much more details than was previously possible. The progressive increase in computer power was also crucial, leading to advanced ways of handling and analyzing this considerable corpus of data. This possibility, together with the recent development of numerical simulations, has led to the development of a very active field in Earth science. In this paper, we make an attempt to provide an overview of where the scientific community currently stands in terms of observing, interpreting and understanding the past and present behavior of the so-called main magnetic field produced within the Earth{\textquoteright}s core. The various types of data are introduced and their specific properties explained. The way those data can be used to derive the time evolution of the core field, when this is possible, or statistical information, when no other option is available, is next described. Special care is taken to explain how information derived from each type of data can be patched together into a consistent description of how the core field has been behaving in the past. Interpretations of this behavior, from the shortest (1 yr) to the longest (virtually the age of the Earth) time scales are finally reviewed, underlining the respective roles of the magnetohydodynamics at work in the core, and of the slow dynamic evolution of the planet as a whole.

}, keywords = {Archeomagnetic records, archeomagnetism, averaged, core, core-mantle boundary, Cretaceous, Earth, Earth{\textquoteright}s, geodynamo, geomagnetic reversals, geomagnetic secular variation, geomagnetism, harmonic magnetic field models, iaga paleointensity database, magnetic, magnetohydrodynamics, maximum-entropy regularization, non-dipole field, normal superchron, Numerical dynamo simulation, observations, paleomagnetic field, paleomagnetic records, paleomagnetism, planetary evolution, simultaneous stochastic inversion, single silicate crystals, Spherical, Statistical magnetic field models, tangentially geostrophic flow}, isbn = {0038-6308}, doi = {10.1007/s11214-010-9644-0}, url = {Variations of the geomagnetic field over past millennia can be determined from archeomagnetic data and paleomagnetic sediment records. The resolution and validity of any field reconstruction depends on the reliability of such indirect measurements of past field values. Considerable effort is invested to ensure that the magnetic minerals carrying the ancient magnetization are good, if not ideal, recorders of the magnetic field. This is achieved by performing a wide array of rock magnetic and microscopy investigations, many of which are outlined here. In addition to data quality, the spatial and temporal distributions of archeomagnetic and sediment records play a significant role in the accuracy of past field reconstruction. Global field reconstructions enable studies of dynamic processes in Earth{\textquoteright}s core. They rely on data compilations which ideally include information about the quality of a measurement and provide a useful archive for selecting data with the best characteristics. There is, however, a trade off between the total number of reliable data and the geographic or temporal coverage. In this review we describe the various types of paleomagnetic recorders, and the kind of measurements that are performed to gather reliable geomagnetic field information. We show which modeling strategies are most suitable, and the main features of the field that can be derived from the resulting models. Finally, we discuss prospects for progress in this kind of research.

}, keywords = {archeomagnetism, boundary, core-mantle, dipole-moment, Earth: magnetic field evolution, earths magnetic-field, Holocene, lake-sediments, microwave, paleo-intensities, relative paleointensity, remanent magnetization, secular variation, thellier paleointensity experiments}, isbn = {0038-6308}, doi = {10.1007/s11214-010-9662-y}, url = {Paleomagnetic and archeomagnetic records are used in both regional and global studies of Earth{\textquoteright}s magnetic field. We present a description and assessment of five newly compiled data sets, also used in the companion paper by Korte et al. (2009) to produce a series of time-varying spherical harmonic models of the geomagnetic field for the last 3000 years. Data are drawn from our compilation of lake sediment records and from the online database, GEOMAGIA50v2. The five selections are available from the EarthRef Digital Archive at http://earthref.org/cgi-bin/erda.cgi?n=944. Data are grouped according to the source of material, and we conducted separate assessments of reliability for archeomagnetic artifacts and lava flows (the ARCH3k_dat data set) and for sediments (SED3k_dat). The overall number of data is 55\% greater than in previous compilations. Constrained data sets were selected using different criteria for each group. Winnowing of archeological data was based on uncertainties supplied by the original data providers. The lake sediment data assessment relied on preassigned age uncertainties and one or more of the following: comparisons with archeomagnetic data from the same region, regional consistency among several lakes, and consistency with global archeomagnetic models. We discuss relative merits of a larger unconstrained data set or a smaller (possibly) more reliable one. The constrained data sets eliminate a priori up to 35\% of the available data in each case and rely on potentially subjective assessments of data quality. Given the limited data available our analyses indicate that iterative rejection of a small number (1-1.5\%) of outlying data during global field modeling is a preferable approach. Specific regional comparisons among the models and data support the conclusion that Korte et al.{\textquoteright}s outlier-free CALS3k.3 model based on all available measurements from sediments and archeological artifacts currently provides the best global representation of the 0-3 ka field; the ARCH3k.1 model provides a better fit to the denser European archeomagnetic data and may be better in that region.

}, keywords = {archeomagnetism, database, earths magnetic-field, el-trebol patagonia, geomagnetic model, golan heights israel, holocene-pleistocene, lake-sediments, palaeosecular variation, paleomagnetic record, paleosecular variation record, relative paleointensity, secular variation record, sediments}, isbn = {1525-2027}, doi = {10.1029/2008gc002295}, url = {Steadily increasing numbers of archeomagnetic and paleomagnetic data for the Holocene have allowed development of temporally continuous global spherical harmonic models of the geomagnetic field extending present and historical global descriptions of magnetic field evolution. The current work uses various subsets of improved data compilations, details of which are given in a companion paper by Donadini et al. (2009), and minor modifications of standard modeling strategies (using temporally and spatially regularized inversion of the data and cubic spline parameterizations for temporal variations) to produce five models with enhanced spatial and temporal resolution for 0-3 ka. Spurious end effects present in earlier models are eliminated by enforcing large-scale agreement with the gufm1 historical model for 1650-1990 A.D. and by extending the model range to accommodate data older than 3 ka. Age errors are not considered as a contribution to data uncertainties but are included along with data uncertainties in an investigation of statistical uncertainty estimates for the models using parametric bootstrap resampling techniques. We find common features but also significant differences among the various models, indicating intrinsic uncertainties in global models based on the currently available Holocene data. Model CALS3k.3 based on all available archeomagnetic and sediment data, without a priori quality selection, currently constitutes the best global representation of the past field. The new models have slightly higher dipole moments than our previous models. Virtual axial dipole moments (VADMs) calculated directly from the data are in good agreement with all corresponding model predictions of VADMs. These are always higher than the spherical harmonic dipole moment, indicating the limitations of using VADMs as a measure of geomagnetic dipole moments.

}, keywords = {archeomagnetism, core, dipole-moment, earths magnetic-field, geomagnetic field models, Holocene, lake sediments, paleointensity, past 3000 years, secular, variation}, isbn = {1525-2027}, doi = {10.1029/2008gc002297}, url = {Statistical analyses of paleomagnetic data from lava flows are used to study geomagnetic field behavior on million year timescales. Previous paleomagnetic studies have lacked high-latitude measurements necessary to investigate the persistence of geomagnetic anomalies observed in the recent and historical field and replicated in some numerical geodynamo simulations. These simulations suggest that reduced convective flow inside the tangent cylinder may affect the magnetic field at high latitude, whereas lower-latitude observations are expressions of columnar/helical flow outside the tangent cylinder. This paper presents new paleointensity and paleodirectional data from 100 volcanic sites in the Erebus Volcanic Province (EVP), Antarctica, and 21 new age determinations by the (40)Ar/(39)Ar incremental heating method. The new EVP data are combined with previously published paleomagnetic and geochronological results, providing 133 sites, 91 having radioisotopic dates. Modified Thellier-Thellier paleointensity estimates are reported for 47 sites (37 have dates). Ages for the combined data set span 0.03 to 13.42 Ma. The 125 high-quality EVP directional data selected from the merged data set have a non-Fisherian distribution and a mean direction with an inclination anomaly of similar to 3 degrees, but 95\% confidence limits include the prediction from a geocentric axial dipole. Virtual geomagnetic pole (VGP) dispersions for Brunhes, Matuyama, and the combined 0-5 Ma data set are consistently high compared with values from middle-to low-latitude regions regardless of the criterion used to determine transitional fields. With VGP latitude cut off at 45 degrees, the dispersion (23.9 +/-2.1 degrees) for the combined 0-5 Ma EVP data set is consistent with earlier high-latitude data and paleosecular variation (PSV) in Model G but not with some more recent statistical PSV models. Mean EVP paleointensity of 31.5 +/-2.4 mu T, derived from 41 high-quality sites, is about half the current value at McMurdo (similar to 63 mu T). The result is essentially independent of data selection criteria. High VGP dispersion and low-intensity values support the global observation of anticorrelation between directional variability and field strength. Simulations of time-varying dipole strength show that uneven temporal sampling may bias the mean EVP intensity estimate, but the possibility of persistently anomalous field behavior at high latitude cannot be excluded.

}, keywords = {(40)Ar/(39)Ar, 0-5 ma, absolute paleointensity, Antarctica, core, earths, lava flows, magnetic-field, paleointensity, paleomagnetism, paleosecular, relative geomagnetic paleointensity, ross sea, secular variation, tangent cylinder, variation}, isbn = {1525-2027}, doi = {10.1029/2008gc002072}, url = {Absolute paleomagnetic field intensity data derived from thermally magnetized lavas and archeological objects provide information about past geomagnetic field behavior, but the average field strength, its variability, and the expected statistical distribution of these observations remain uncertain despite growing data sets. We investigate these issues for the 0-1 Ma field using data compiled in Perrin and Schnepp [Perrin, M., Schnepp, E., 2004. IAGA paleointensity database: distribution and quality of the data set. Phys. Earth Planet. Int. 147, 255-267], 1124 samples of heterogeneous quality and with restricted temporal and spatial coverage. We accommodate variable spatial sampling by using virtual axial dipole moments (VADM) in our analyses. Uneven temporal sampling results in biased estimates for the mean field and its statistical distribution. We correct for these effects using a bootstrap technique, and find an average VADM of 7.26 +/- 0.14 x 10(22) A m(2). The associated statistical distribution appears bimodal with a subsidiary peak at approximately 5 x 10(22) A m(2). We evaluate a range of potential sources for this behavior. We find no visible evidence for contamination by poor quality data when considering author-supplied uncertainties in the 0-1 Ma data set. The influence of material type is assessed using independent data compilations to compare Holocene data from lava flows, submarine basaltic glass (SBG), and archeological objects. The comparison to SBG is inconclusive because of dating issues, but paleointensity estimates from lavas are on average about 10\% higher than for archeological materials and show greater dispersion. Only limited tests of geographic sampling bias are possible. We compare the large number of 0-0.55 Ma Hawaiian data to the global data set with no definitive results. The possibility of over-representation of typically low intensity excursional data is discounted because exclusion of transitional data still leaves a bimodal distribution. No direct test has allowed us to rule out the idea that the observed pdf results from a mixture of two distinct distributions corresponding to two identifiable intensity states for the magnetic field. We investigate an alternative possibility that we were simply unable to recover a hypothetically smoother underlying distribution with a time span of only 1 Myr and the resolution of the current data set. Simulations from a stochastic model based on the geomagnetic field spectrum demonstrate that long period intensity variations can have a strong impact on the observed distributions and could plausibly explain the apparent bimodality. Our 0-1 Ma distribution of VADMs is consistent with that obtained for average relative paleointensity records derived from sediments. (C) 2008 Elsevier B.V. All rights reserved.

}, keywords = {cooling-rate, earths, East Pacific Rise, geomagnetic secular variation, geomagnetism, intensity, kyr, magnetic-field, model, paleointensity, Paleomagnetic secular, paleomagnetism, records, submarine basaltic glass, time, variation}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2008.07.027}, url = {Anisotropy of magnetic susceptibility (AMS) data are widely used as a petrofabric tool because the technique is rapid and nondestructive and because static measurement systems are capable of determining small degrees of anisotropy. The Kappabridge KLY-4S provides high resolution as a result of the large number of measurements acquired while rotating the sample about three orthogonal axes. Here we describe a graphical-based program called AMSSpin for acquiring AMS data with this instrument as well as a modified specimen holder that should further enhance the utility of this instrument. We also outline a method for analysis of the data (that differs in several ways from that of the software supplied with the instrument) and demonstrate that the measurement errors are suitable for using linear perturbation analysis to statistically characterize the results. Differences in the susceptibility tensors determined by our new program and the SUFAR program supplied with the instrument are small, typically less than or comparable to deviations between multiple measurements of the same specimen.

}, keywords = {AMS, Kappabridge, magnetic fabric, susceptibility tensor, tensors}, isbn = {1525-2027}, doi = {10.1029/2008gc001976}, url = {This paper presents a compilation of intensity data covering the past 10 millennia (ArcheoInt). This compilation, which upgrades the one of Korte et al. (2005), contains 3648 data and incorporates additional intensity and directional data sets. A large majority of these data (similar to 87\%) were acquired on archeological artifacts, and the remaining similar to 13\% correspond to data obtained from volcanic products. The present compilation also includes important metadata for evaluating the intensity data quality and providing a foundation to guide improved selection criteria. We show that similar to 50\% of the data set fulfill reasonable reliability standards which take into account the anisotropic nature of most studied objects (potsherds), the stability of the magnetization, and the data dispersion. The temporal and geographical distributions of this sub-data set are similar to those of the main data set, with similar to 72\% of the data dated from the past three millennia and similar to 76\% obtained from western Eurasia. Approximately half of the selected intensity data are associated with at least an inclination value. To constrain the axial and full dipole evolution over the past three millennia requires that we avoid any overrepresentation of the western Eurasian data. We introduce a first-order regional weighting scheme based on the definition of eight widely distributed regions of 30 degrees width within which the selected data are numerous enough. The regional curves of virtual axial dipole moments (VADM) and of mixed VADM-virtual dipole moments (VDM) averaged over sliding windows of 200 years and 500 years testify for strong contributions from either equatorial dipole or nondipole components. The computation of global VADM and mixed VADM/VDM variation curves, assuming an equal weight for each region, yields a dipole evolution marked by a distinct minimum around 0 B.C./A.D. followed by a maximum around the third-fourth century A. D. A second minimum is present around the eighth century A. D. This variation pattern is compatible with the one deduced from earlier, more sophisticated analysis based on the inversion of both intensity and directional data. In particular, there is a good agreement among all VADMs and dipole moment estimates over the historical period, which further strengthens the validity of our weighting scheme.

}, keywords = {absolute, archeointensity, cooling-rate, data compilation, dipole evolution, earths magnetic-field, greek archaeomagnitudes, Holocene, lavas, magnitude, paleointensity, paleomagnetic field, regional, secular variation, thellier paleointensity experiments, thermoremanent magnetization, variations}, isbn = {1525-2027}, doi = {10.1029/2007gc001881}, url = {We present a synthesis of 0 - 5 Ma paleomagnetic directional data collected from 17 different locations under the collaborative Time Averaged geomagnetic Field Initiative ( TAFI). When combined with regional compilations from the northwest United States, the southwest United States, Japan, New Zealand, Hawaii, Mexico, South Pacific, and the Indian Ocean, a data set of over 2000 sites with high quality, stable polarity, and declination and inclination measurements is obtained. This is a more than sevenfold increase over similar quality data in the existing Paleosecular Variation of Recent Lavas (PSVRL) data set, and has greatly improved spatial sampling. The new data set spans 78 degrees S to 53 degrees N, and has sufficient temporal and spatial sampling to allow characterization of latitudinal variations in the time-averaged field (TAF) and paleosecular variation (PSV) for the Brunhes and Matuyama chrons, and for the 0 - 5 Ma interval combined. The Brunhes and Matuyama chrons exhibit different TAF geometries, notably smaller departures from a geocentric axial dipole field during the Brunhes, consistent with higher dipole strength observed from paleointensity data. Geographical variations in PSV are also different for the Brunhes and Matuyama. Given the high quality of our data set, polarity asymmetries in PSV and the TAF cannot be attributed to viscous overprints, but suggest different underlying field behavior, perhaps related to the influence of long-lived core-mantle boundary conditions on core flow. PSV, as measured by dispersion of virtual geomagnetic poles, shows less latitudinal variation than predicted by current statistical PSV models, or by previous data sets. In particular, the Brunhes data reported here are compatible with a wide range of models, from those that predict constant dispersion as a function of latitude to those that predict an increase in dispersion with latitude. Discriminating among such models could be helped by increased numbers of low-latitude data and new high northern latitude sites. Tests with other data sets, and with simulations, indicate that some of the latitudinal signature previously observed in VGP dispersion can be attributed to the inclusion of low-quality, insufficiently cleaned data with too few samples per site. Our Matuyama data show a stronger dependence of dispersion on latitude than the Brunhes data. The TAF is examined using the variation of inclination anomaly with latitude. Best fit two- parameter models have axial quadrupole contributions of 2 - 4\% of the axial dipole term, and axial octupole contributions of 1 - 5\%. Approximately 2\% of the octupole signature is likely the result of bias incurred by averaging unit vectors.

}, keywords = {averaged paleomagnetic field, axial dipole assumption, earths magnetic, field, geological time, k-ar ages, lavas, new-zealand basalts, paleomagnetic, paleosecular, paleosecular variation, past 5 myr, secular variation, time-averaged field, variation, volcanic-rocks}, isbn = {1525-2027}, doi = {10.1029/2007gc001696}, url = {We assess the resolution and reliability of CALS7xK, a recently developed family of global geomagnetic field models. CALS7xK are derived from archaeo- and palaeomagnetic data and provide a convenient temporally varying spherical harmonic description of field behaviour back to 5000 BC. They can be used for a wide range of studies from gaining a better understanding of the geodynamo in the Earth{\textquoteright}s core to enabling the efficient determination of the influence of the geomagnetic field on cosmogenic nuclide productions rates. The models are similar in form to those derived from modern satellite observations, observatory and historical data, and used for the International Geomagnetic Reference Field, but their spatial and temporal resolution are limited by data quality and distribution. We find that spatial power is fully resolved only up to spherical harmonic degree 4 and temporal resolution is of the order of 100 years. Significant end effects associated with the temporal development in natural B-splines affect some features of the models in both the earliest and most recent century. Uncertainties in model predictions of declination, inclination and field intensity in general are smaller than 2 degrees and 1.5 mu T respectively, but can be as large as 8 degrees and 5 mu T for certain regions and times. The resolution studies are complemented by a detailed presentation of dipole moment and dipole tilt as predicted by the model CALS7K.2. These largest scale features are resolved more reliably than complex details of the field structure and are useful, for example, in studies of geomagnetic cutoff rigidities of cosmogenic isotopes. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

}, keywords = {archaeomagnetism, core, dipole moment, dipole-moment, geomagnetic field model, intensity, magnetic-field, past 3000 years, secular variation}, isbn = {0273-1177}, doi = {10.1016/j.asr.2007.03.094}, url = {We describe a new technique for implementing the constraints on magnetic fields arising from two hypotheses about the fluid core of the Earth, namely the frozen-flux hypothesis and the hypothesis that the core is in magnetostrophic force balance with negligible leakage of current into the mantle. These hypotheses lead to time-independence of the integrated flux through certain {\textquoteright}null-flux patches{\textquoteright} on the core surface, and to time-independence of their radial vorticity. Although the frozen-flux hypothesis has received attention before, constraining the radial vorticity has not previously been attempted. We describe a parametrization and an algorithm for preserving topology of radial magnetic fields at the core surface while allowing morphological changes. The parametrization is a spherical triangle tesselation of the core surface. Topology with respect to a reference model (based on data from the Oersted satellite) is preserved as models at different epochs are perturbed to optimize the fit to the data; the topology preservation is achieved by the imposition of inequality constraints on the model, and the optimization at each iteration is cast as a bounded value least-squares problem. For epochs 2000, 1980, 1945, 1915 and 1882 we are able to produce models of the core field which are consistent with flux and radial vorticity conservation, thus providing no observational evidence for the failure of the underlying assumptions. These models are a step towards the production of models which are optimal for the retrieval of frozen-flux velocity fields at the core surface.

}, keywords = {boundary, flow, frozen flux, geomagnetic secular variation, geomagnetism, mantle, perfectly conducting core, secular variation, surface}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.2007.03526.x}, url = {The maximum entropy technique is an accepted method of image reconstruction when the image is made up of pixels of unknown positive intensity (e.g. a grey-scale image). The problem of reconstructing the magnetic field at the core-mantle boundary from surface data is a problem where the target image, the value of the radial field B-r, can be of either sign. We adopt a known extension of the usual maximum entropy method that can be applied to images consisting of pixels of unconstrained sign. We find that we are able to construct images which have high dynamic ranges, but which still have very simple structure. In the spherical harmonic domain they have smoothly decreasing power spectra. It is also noteworthy that these models have far less complex null flux curve topology (lines on which the radial field vanishes) than do models which are quadratically regularized. Problems such as the one addressed are ubiquitous in geophysics, and it is suggested that the applications of the method could be much more widespread than is currently the case.

}, keywords = {algorithm, core magnetic field, flux, geomagnetic inverse problem, geomagnetic modelling, least-squares, maximum entropy, model, surface}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.2007.03530.x}, url = {Time domain correlations of common features among relative paleointensity records from sedimentary cores are invaluable to paleomagnetism and paleoclimatology. Sediments with high accumulation rates might now provide millennial scale correlations of temporal variations in the geomagnetic dipole moment. Errors in the ages of paleomagnetic data samples, however, can make such correlations difficult and unreliable. We use spectral methods to assess the level of coherence expected among individual and stacked high- resolution simulated paleointensity records for the time interval 0 - 75 ka. Correlations between individual paleointensity records are systematically degraded with decreased sedimentation rate and increased magnitude of age errors. We find that with optimistic age errors and interpolation of depth sampled data to evenly spaced time series, only short period signal in high- resolution relative paleointensity is corrupted. For currently available methods of establishing chronologies, we estimate the minimum characteristic timescale of correlative features between pairs of regional stacked records at about 4.5 kyr. From an analysis of NAPIS- 75 and SAPIS data, it appears that the limit is inherent to the regional stacks and not a consequence of comparison of distant, independent data sets. A detailed comparison of the NAPIS- 75 and SAPIS stacks shows that this limit is likely larger, perhaps 6 kyr. At long periods the two regional stacks are more poorly correlated than those from our simulations, suggesting somewhat larger age errors in the individual paleointensity records.

}, keywords = {age errors, deconvolution, field, geomagnetism and paleomagnetism : rapid, geomagnetism and paleomagnetism : time, high-resolution, intensity, interhemispheric correlation, ka, kyr, magnetostratigraphy, mathematical geophysics : time series analysis, north-atlantic, regional stacking, relative geomagnetic paleointensity, resolution, reversals, sedimentary records, spectral analysis, strength, time variations, variations : secular and longer}, isbn = {1525-2027}, doi = {10.1029/2006gc001350}, url = {[ 1] Current millennial-scale time-varying global geomagnetic field models suffer from a lack of intensity data compared to directional data, because only thermoremanently magnetized material can provide absolute information about the past field strength. The number of archeomagnetic artifacts that can provide such data diminishes rapidly prior to 3000 B. C. Sediment cores provide time series of declination and inclination and of variations of magnetization: the latter can reflect relative geomagnetic field variations if suitably normalized. We propose a calibration technique based on predictions from global models and use the CALS7K. 2 model to calibrate relative paleointensity records from 22 globally distributed locations and assess whether they reflect actual field variations. All except a few contain useful information for 0 to 7 ka and could be used to improve the existing models. Using synthetic data from a numerical dynamo simulation, we show that with the existing directional data the distribution of intensity data has an important influence on model quality. Intensity data from a broad range of latitudes seem particularly important. This study opens the possibility of extending global time-varying geomagnetic field models further back in time than the current 7 kyr interval.

}, keywords = {983 gardar drift, age calibration, birkat-ram, cal bp, geomagnetic field model, geomagnetism and, geomagnetism and paleomagnetism : paleointensity, lacustrine sediments, lake sediments, lake-sediments, magnetic-field, palaeosecular variation, paleomagnetic records, paleomagnetism : paleomagnetic secular variation, paleomagnetism : reference fields : regional, global, past 3000 years, relative paleointensity}, isbn = {1525-2027}, doi = {10.1029/2006gc001368}, url = {A time-varying spherical harmonic model of the palaeomagnetic field for 0-7 ka is used to investigate large-scale global geomagnetic secular variation on centennial to millennial scales. We study dipole moment evolution over the past 7 kyr, and estimate its rate of change using the Gauss coefficients of degree 1 (dipole coefficients) from the CALS7K.2 field model and by two alternative methods that confirm the robustness of the predicted variations. All methods show substantial dipole moment variation on timescales ranging from centennial to millennial. The dipole moment from CALS7K.2 has the best resolution and is able to resolve the general decrease in dipole moment seen in historical observations since about 1830. The currently observed rate of dipole decay is underestimated by CALS7K.2, but is still not extraordinarily strong in comparison to the rates of change shown by the model over the whole 7 kyr interval. Truly continuous phases of dipole decrease or increase are decadal to centennial in length rather than longer-term features. The general large-scale secular variation shows substantial changes in power in higher spherical harmonic degrees on similar timescales to the dipole. Comparisons are made between statistical variations calculated directly from CALS7K.2 and longer-term palaeosecular variation models: CALS7K.2 has lower overall variance in the dipole and quadrupole terms, but exhibits an imbalance between dispersion in g(2)(1) and h(2)(1), suggestive of long-term non-zonal structure in the secular variations.

}, keywords = {archaeomagnetism, bias, core, dipole-moment, geomagnetic dipole moment, geomagnetic field models, intensity, magnetic-field, mantle, models, palaeointensity, palaeosecular variation, paleosecular variation, pole, power spectrum}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.2006.03088.x}, url = {Earth{\textquoteright}s dipole field has been diminishing in strength since the first systematic observations of field intensity were made in the mid nineteenth century. This has led to speculation that the geomagnetic field might now be in the early stages of a reversal. In the longer term context of paleomagnetic observations it is found that for the current reversal rate and expected statistical variability in polarity interval length an interval as long as the ongoing 0.78 Myr Brunhes polarity interval is to be expected with a probability of less than 0.15, and the preferred probability estimates range from 0.06 to 0.08. These rather low odds might be used to infer that the next reversal is overdue, but the assessment is limited by the statistical treatment of reversals as point processes. Recent paleofield observations combined with insights derived from field modeling and numerical geodynamo simulations suggest that a reversal is not imminent. The current value of the dipole moment remains high compared with the average throughout the ongoing 0.78 Myr Brunhes polarity interval; the present rate of change in Earth{\textquoteright}s dipole strength is not anomalous compared with rates of change for the past 7 kyr; furthermore there is evidence that the field has been stronger on average during the Brunhes than for the past 160 Ma, and that high average field values are associated with longer polarity chrons. There is no evidence from recent millennial scale time-varying paleofield models to indicate that the field is entering a polarity transition. Nevertheless, it remains a reasonable supposition that the magnetic field will eventually reverse even though the time scale is unpredictable. A more immediate concern is that ongoing secular variation in the magnetic field may be expected to moderate the current high dipole strength on centennial to millennial time scales: it would not be surprising if it dropped substantially, returning closer to the average without necessarily reversing. This could have important consequences for space weather, and also highlights the need for improved understanding of the impact of geomagnetic field strength on the production rates of cosmogenic isotopes that are used to estimate past solar variability. (c) 2006 Elsevier B.V. All rights reserved.

}, keywords = {brunhes, dipole moment, geodynamo, geomagnetic field, intensity, model, paleointensity, paleointensity records, paleomagnetosphere, paths, polarity reversals, reversals, secular variation, simulated geomagnetic reversals, tiny wiggles}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2006.03.038}, url = {[1] We assembled a new paleomagnetic directional data set from lava flows and thin dikes for four regions centered on +/-20 degrees latitude: Hawaii, Mexico, the South Pacific, and Reunion. We investigate geomagnetic field behavior over the past 5 Myr and address whether geographical differences are recorded by our data set. We include inclination data from other globally distributed sites with the +/-20 degrees data to determine the best fitting time-averaged field (TAF) for a two-parameter longitudinally symmetric (zonal) model. Values for our model parameters, the axial quadrupole and octupole terms, are 4\% and 6\% of the axial dipole, respectively. Our estimate of the quadrupole term is compatible with most previous studies of deviations from a geocentric axial dipole (GAD) field. Our estimated octupole term is larger than that from normal polarity continental and igneous rocks, and oceanic sediments, but consistent with that from reversed polarity continental and igneous rocks. The variance reduction compared with a GAD field is similar to 12\%, and the remaining signal is attributed to paleosecular variation (PSV). We examine PSV at +/-20 degrees using virtual geomagnetic pole (VGP) dispersion and comparisons of directional distributions with simulations from two statistical models. Regionally, the Hawaii and Reunion data sets lack transitional magnetic directions and have similar inclination anomalies and VGP dispersion. In the Pacific hemisphere, Hawaii has a large inclination anomaly, and the South Pacific exhibits high PSV. The deviation of the TAF from a GAD contradicts earlier ideas of a "Pacific dipole window,{\textquoteright}{\textquoteright} and the strong regional PSV in the South Pacific contrasts with the generally low secular variation found on short timescales. The TAF and PSV at Hawaii and Reunion are distinct from values for the South Pacific and Mexico, demonstrating the need for time-averaged and paleosecular variation models that can describe nonzonal field structures. Investigations of zonal statistical PSV models reveal that recent models are incompatible with the empirical +/-20 degrees directional distributions and cannot fit the data by simply adjusting relative variance contributions to the PSV. The +/-20 degrees latitude data set also suggests less PSV and smaller persistent deviations from a geocentric axial dipole field during the Brunhes.

}, keywords = {absolute paleointensity, and paleomagnetism : paleomagnetic secular variation, flows, french-polynesia, geomagnetism, hawaiian lava, indian-ocean, mexican volcanic belt, oahu-hawaii, palaeosecular variation, paleomagnetic, paleomagnetic secular variation, paleosecular variation, past 5 myr, time-averaged field, viti-levu}, isbn = {1525-2027}, doi = {10.1029/2005gc001181}, url = {We construct a power spectrum of geomagnetic dipole moment variations or their proxies that spans the period range from some tens of million down to about 100 years. Empirical estimates of the spectrum are derived from the magnetostratigraphic time scale, from marine sediment relative paleointensity records, and from a time varying paleomagnetic field model for the past 7 kyr. The spectrum has the most power at long periods, reflecting the influence of geomagnetic reversals and in general decreases with increasing frequency (decreasing period). The empirical spectrum is compared with predictions from simple models. Discrepancies between the observed and predicted spectra are discussed in the context of: (i) changes in reversal rate, (ii) overall average reversal rate, (iii) cryptochrons, (iv) the time taken for a reversal to occur, and (v) long term paleosecular variations and average estimates of the field strength and variance from other sources. (c) 2005 Elsevier B.V. All rights reserved.

}, keywords = {earths magnetic-field, eccentricity, geodynamo simulations, geomagnetic-field, geomagnetism, intensity, paleointensity, paleomagnetic power spectrum, paleomagnetism, paleosecular, profiles, records, reversals, secular variation, time-series, variations}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2005.03.015}, url = {Evolution of the geomagnetic field{\textquoteright}s dipole strength is studied by geomagnetists from global spherical harmonic models and by paleomagnetists using virtual (axial) dipole moments (VDM, VADM). Based on a recently published global model of the past 7000 yr we study whether these three dipole moment descriptions can be considered equivalent, and compare the results to previous global VADM studies and recent global model dipole moments. We conclude that VADM and VDM results averaged over centennial and millennial time scales are systematically higher than the true dipole moment by about 19\%. The current dipole decrease is part of a process that has been going on for about 1700 yr. The average rate of decrease is lower than the current one, but has varied significantly so that the current rate cannot be regarded as exceptional. (c) 2005 Elsevier B.V. All rights reserved.

}, keywords = {archeomagnetism, field, geomagnetic dipole moment, intensity, paleointensity}, isbn = {0012-821X}, doi = {10.1016/j.epsl.2004.12.031}, url = {A global data set of archeomagnetic and paleomagnetic data covering the past 7000 years has been compiled. It consists of 16,085 results of inclination, 13,080 of declination, and 3188 of intensity for the time span 5000 BC to 1950 AD. Declination and inclination data come partly from existing databases and partly from original literature. A new global compilation of intensity data for the millennial scale is included. Data and dating uncertainties are discussed as we attempted to obtain an internally coherent data set. The global distribution of the data is very inhomogeneous in both time and space. All the data are compared to predictions from the previous 3000 year global model, CALS3K.1. This collection of data will be useful for global secular variation studies and geomagnetic field modeling, although southern hemisphere data are still underrepresented. In particular, we will use it in a further study to update and extend the existing global model, CALS3K.1. The huge increase in data compared to the previous compilation will result in significant changes from current models. As we might have missed some suitable data, we encourage the reader to notify us about any data that have not been included yet and might fit in, as improving our global millennial scale models remains our aim for the future.

}, keywords = {archaeomagnetic measurements, archeomagnetic data, calibration, earths magnetic-field, geomagnetic secular variation, lake, last 2000 years, north-america, pacific nondipole low, paleointensity, paleomagnetic, paleosecular variation record, radiocarbon age, record, roman pottery kiln, secular variation record, sediments, western}, isbn = {1525-2027}, doi = {10.1029/2004gc000800}, url = {We present two continuous global geomagnetic field models for recent millennia: CALS3K.2, covering the past 3000 years, and CALS7K.2, covering 7000 years from 5000 BC to 1950 AD. The models were determined by regularized least squares inversion of archeomagnetic and paleomagnetic data using spherical harmonics in space and cubic B splines in time. They are derived from a greatly increased number of paleomagnetic directional data, compared to previous efforts, and for the first time a significant amount of archeointensity data is used in this kind of global model, allowing the determination of evolution of geomagnetic dipole strength. While data accuracy and dating uncertainties remain a limitation, reliable low-resolution global models can be obtained. The results agree well with previous results from virtual axial dipole moment (VADM) studies from archeomagnetic intensity data apart from a systematic offset in strength. A comparison of model predictions with the previous 3000 year model, CALS3K.1, gives general agreement but also some significant differences particularly for the early epochs. The new models suggest that the prominent two northern hemisphere flux lobes are more stationary than CALS3K.1 implied, extending considerably the time span of stationary flux lobes observed in historical models. Between 5000 BC and 2000 BC there are time intervals of weak dipole moment where dipole power is exceeded by low-degree nondipole power at the core-mantle boundary.

}, keywords = {archeomagnetism, geomagnetic dipole moment, geomagnetic field models, lake sediments, paleointensity, records}, isbn = {1525-2027}, doi = {10.1029/2004gc000801}, url = {Stacks of globally distributed relative paleointensity records from sediment cores are used to study temporal variations in the strength of the geomagnetic dipole. We assess the intrinsic accuracy and resolution of such stacks, which may be limited by errors in paleointensity, non-dipole field contributions, and the age scales assigned to each sediment core. Our approach employs two types of simulations. Numerical geodynamo models generate accurate predictions of time series of magnetic variations anywhere in the world. The predicted variations are then degraded using an appropriate statistical model to simulate expected age and paleointensity errors. A series of experiments identify the major contributors to error and loss of resolution in the resulting stacks. The statistical model simulates rock magnetic and measurement errors in paleointensity, and age errors due to finite sampling and approximations inherent in interpolation, incomplete or inaccurate tie point information, and sedimentation rate variations. Data sampling and interpolation to a designated age scale cause substantial decorrelation, and control the maximum level of agreement attainable between completely accurate records. The particular method of interpolation appears to have little effect on the coherence between accurate records, but denser tie point data improve the agreement. Age errors decorrelate geomagnetic signals, usually at shorter periods, although they can destroy coherence over a broad range of periods. The poor correlation between neighboring paleomagnetic records often observed in real data can be accounted for by age errors of moderate magnitude. In a global dataset of 20 records, modeled after the SINT800 compilation and spanning 300 kyr, our results show that dipole variations with periods longer than about 20 kyr can be recovered by the stacking process. Reasonable contributions to error in the paleointensity itself have a modest influence on the result, as do non-dipole field contributions whose effect is minor at periods longer than 10 kyr. Modest errors in the ages of tie points probably account for most of the degradation in geomagnetic signal. Stacked sedimentary paleomagnetic records can be improved by denser temporal sampling and careful selection of independent high-quality tie points. (C) 2004 Elsevier B.V. All rights reserved.

}, keywords = {accumulation rates, age errors, atlantic, chronostratigraphy, field, geomagnetic dipole moment, geomagnetic paleointensity, intensity, ka, paleomagnetism, sedimentary records, spectral analysis, stacking}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2004.02.011}, url = {Currents induced in Earth by temporal variations in the external magnetic field have long been used to probe mantle electrical conductivity, but almost exclusively from sparsely distributed land observatories. Satellite-borne magnetometers, such as flown on Magsat, Orsted, and Champ, offer the prospect of improved spatial coverage. The approach we have taken is to isolate induction by harmonic Dst ("disturbance storm time{\textquoteright}{\textquoteright}) excitation of the magnetospheric ring current in satellite magnetic measurements: this is done by removing the magnetic contributions of the main (core) magnetic field, the crustal magnetic field, and ionospheric fields (cause of the daily variation) using Sabaka et al.{\textquoteright} s [2000, 2002] CMP3 comprehensive model. The Dst signal is then clearly evident in the midlatitude satellite passes lower than 50 degrees geomagnetic latitude. At higher latitudes, auroral and field aligned currents contaminate the data. We fit the internal and external components of the Dst signal for each equatorial pass, exploiting the fact that the geometry for the internal and external components is different for the azimuthal and radial vector components. The resulting timeseries of internal and external field variations shows that the Dst signals for the dawn passes are half those of the dusk passes. The sum of equatorial external and internal components of the field averaged over dawn and dusk passes provides an excellent estimate for the Dst index, and may in fact be superior when used as a proxy for the purposes of removing induced and magnetospheric fields from satellite magnetic data. We call this estimate satellite Dst. Cross spectral analysis of the internal and external timeseries shows both greater power and higher coherence in the dusk data. We processed the transfer function between internal and external dusk timeseries to provide globally-averaged, frequency dependent impedances that agree well with independently derived estimates. We estimate Earth{\textquoteright}s radial electrical conductivity structure from these impedances using standard regularized inversion techniques. A near-surface conductor is required, of thickness less than 10 km with a conductivity-thickness product almost exactly that of an average Earth ocean. Inversions suggest that an increase in conductivity at 440 km depth, predicted by recent laboratory measurements on high pressure phases of olivine, is not favored by the data, although, as in previous studies, the 670 km discontinuity between the upper and lower mantle is associated with a two orders of magnitude jump in conductivity. A new feature in our inversions is a further increase in lower mantle conductivity at a depth of 1300 km. A global map of the internal (induced) component of the magnetic field provides a qualitative estimate of three-dimensional (3-D) variations in Earth electrical conductivity, demonstrating graphically that the satellite data are responsive to lateral variations in electrical conductivity caused by the continents and oceans.

}, keywords = {electrical-conductivity, electromagnetic induction, field model, geomagnetism and, geomagnetism and palomagnetism : geomatic, induction, mid-mantle, mineral physics : electrical properties, olivine, palomagnetism : time variations-diurnal to secular, satellite induction}, isbn = {1525-2027}, doi = {10.1029/2003gc000634}, url = {[1] The summit crater of Vailulu{\textquoteright}u Seamount, the youngest volcano in the Samoan chain, hosts an active hydrothermal system with profound impact on the ocean water column inside and around its crater ( 2 km wide and 407 m deep at a 593 m summit depth). The turbidity of the ocean water reaches 1.4 NTU, values that are higher than in any other submarine hydrothermal system. The water is enriched in hydrothermal Mn (3.8 ppb) and He-3 (1 x 10(-11) cc/g) and we measured water temperature anomalies near the crater floor up to 0.2degreesC. The hydrothermal system shows complex interactions with the ocean currents around Vailulu{\textquoteright}u that include tidally-modulated vertical motions of about 40 - 50 m, and replenishment of waters into the crater through breaches in the upper half of the crater wall. Inside and outside potential density gradients suggest that hydrothermal venting exports substantial amounts of water from the crater (1.3 +/- 0.2 x 10(8) m(3)/day), which is in good agreement with fluxes obtained from a tracer release experiment inside the crater of Vailulu{\textquoteright}u (0.8 x 10(8) m(3)/day [ Hart et al., 2003]). This mass flux, in combination with the differences in the inside and outside crater temperature, yields a power output of around 760 megawatts, the equivalent of 20 - 100 MOR black smokers. The Mn output of 300 kg/day is approximately ten times the output of a single black smoker.

}, keywords = {(benthic) and hydrothermal processes, axial volcano, chemical : hydrothermal systems, circulation, de-fuca ridge, East Pacific Rise, fluids, heat-flux, hot spots, hydrothermal, information related to geographic, loihi seamount, manganese, marine geology and geophysics : heat flow, mid-atlantic ridge, oceanography : biological and, plumes, region : Pacific Ocean, seamount}, isbn = {1525-2027}, doi = {10.1029/2003gc000626}, url = {Several global geomagnetic field models exist for recent decades, but due to limited data availability models for several centuries to millennia are rare. We present a continuous spherical harmonic model for almost 3 millennia from 1000 B.C. to 1800 A.D., based on a dataset of directional archaeo- and paleomagnetic data and axial dipole constraints. The model, named Continuous Archaeomagnetic and Lake Sediment Geomagnetic Model for the last 3k years (CALS3K.1), can be used to predict both the field and secular variation. Comparisons and tests with synthetic data lead to the conclusion that CALS3K.1 gives a good general, large-scale representation of the geomagnetic field, but lacks small-scale structure due to the limited resolution of the sparse dataset. In future applications the model can be used for comparisons with additional, new data for that time span. For better resolved regions, the agreement of data with CALS3K.1 will provide an idea about the general compatibility of the data with the field and secular variation in that region of the world. For poorly covered regions and time intervals we hope to iteratively improve the model by comparisons with and inclusion of new data. Animations and additional snapshot plots of model predictions as well as the model coefficients and a FORTRAN code to evaluate them for any time can be accessed under http://www.mahi.ucsd.edu/cathy/Holocene/holocene.html. The whole package is also stored in the Earthref digital archive at http://www.earthref.org/... (C) 2003 Elsevier B.V. All rights reserved.

}, keywords = {0-5 ma, age calibration, archaeomagnetism, averaged paleomagnetic field, core-mantle boundary, data-base, geodynamo, geomagnetic field modelling, inversion, magnetic-field, paleomagnetism, secular variation, time}, isbn = {0031-9201}, doi = {10.1016/j.pepi.2003.07.013}, url = {With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Reunion, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

}, keywords = {absolute paleointensity, core-mantle boundary, determinations, Earth{\textquoteright}s magnetic field, earths magnetic-field, geomagnetic, geomagnetic variation, geomagnetism, lava flows, palaeointensity, palaeomagnetism, paleointensity, paleomagnetic inclination data, paleosecular variation, past 5 myr, scientific drilling project, secular variation, statistical methods}, isbn = {0956-540X}, doi = {10.1046/j.1365-246X.2003.01858.x}, url = {A 3-D finite-element simulation of global electromagnetic induction is used to evaluate satellite responses in geomagnetic dipole coordinates for harmonic ring-current excitation of a three-layer mantle overlain by a realistic near-surface conductance distribution. Induced currents are modelled for lithospheric and asthenospheric upper-mantle conductivities in the range sigma= 10(-4) -0.1 S m(-1) . The magnetic scalar intensity B is calculated at a typical satellite altitude of 300 km. At short periods, T = 2 and 12 h, the induction signal owing to the near-surface conductance is large when a resistive upper mantle is present, but drops off with increasing mantle conductivity. At longer periods, T = 2 d, the near-surface induction signal is generally much smaller and nearly independent of upper-mantle conductivity. The near-surface induction signal is very sensitive to the electrical conductivity of the lithospheric mantle, but only moderately sensitive to that of the asthenospheric mantle. Induced currents are confined to the heterogeneous surface shell at periods of less than 2 h, and flow predominantly in the mantle at periods of longer than 2 d. In the intervening period range, induced currents are partitioned between the near-surface and the upper mantle. These results indicate the importance of carrying out a full 3-D analysis in the interpretation of satellite induction observations in the period range from hours to days.

}, keywords = {currents, electrical conductivity, electrical-conductivity, electromagnetic induction, geomagnetic, geomagnetic induction, heterogeneous sphere, magnetic-field, mantle conductivity, model, oceans, sedimentary basins, sq, test computations, upper mantle, variations}, isbn = {0956-540X}, doi = {10.1046/j.1365-246X.2003.01906.x}, url = {The issue of permanent nondipole contributions to the time-averaged field lies at the very heart of paleomagnetism and the study of the ancient geomagnetic field. In this paper we focus on paleomagnetic directional results from igneous rocks of the southwestern U. S. A. in the age range 0-5 Ma and investigate both the time-averaged field and its variability about the mean value. Several decades of work in the southwestern United States have resulted in the publication of paleomagnetic data from over 800 individual paleomagnetic sites. As part of a new investigation of the San Francisco Volcanics, we collected paleomagnetic samples from 47 lava flows, many of which have been previously dated. The new data combined with published data are highly scattered. Contributions to the scatter were considered, and we find that removal of data sets from tectonically active areas and judicious selection according to Fisher{\textquoteright}s [1953] precision parameter results in an axially symmetric data distribution with normal and reverse modes that are indistinguishable from antipodal. Monte Carlo simulations suggest that a minimum of 5 samples per site are needed to estimate the precision parameter sufficiently accurately to allow its use as a determinant of data quality. Numerical simulations from statistical paleosecular variation models indicate the need for several hundred paleomagnetic sites to get an accurate determination of the average field direction and are also used to investigate the directional bias that results from averaging unit vectors rather than using the full field vector. Average directions for the southwestern U. S. A. show small deviations from a geocentric axial dipole field, but these cannot be considered statistically significant. Virtual geomagnetic pole (VGP) dispersions are consistent with those from globally distributed observations analyzed by McElhinny and McFadden [1997]. However, a systematic investigation of the effect of imposing a cutoff on VGPs with large deviations from the geographic axis indicates that while it may reduce bias in calculating the average direction, such a procedure can result in severe underestimates of the variance in the geomagnetic field. A more satisfactory solution would be to use an unbiased technique for joint estimation of the mean direction and variance of the field distribution.

}, keywords = {albuquerque volcanos, averaged geomagnetic-field, data, geomagnetic field, last 5, lava flows, lightning, new-mexico, palaeosecular variation, paleosecular variation, past 5 myr, remagnetization circles, secular, selection, statistics, variation}, isbn = {1525-2027}, doi = {10.1029/2002gc000343}, url = {[1] The magnetic field originating within the Earth can be divided into core and crustal components, which can be characterized by the geomagnetic power spectrum. While the core spectrum is determined quite well by satellite studies, models of the shorter wavelength crustal spectrum disagree considerably. We reexamine aeromagnetic data used by O{\textquoteright}Brien et al. [1999] to obtain a new, improved estimate of the crustal geomagnetic power spectrum. O{\textquoteright}Brien et al. {\textquoteright}s model somewhat failed to give a satisfactory connection between the longer-wavelength satellite studies and a reliable crustal model. We show that this was caused by an inadequate processing step that aimed to remove external variations from the data. We moreover attempt to bound the long-wavelength part of the spectrum using constraints of monotonicity in the correlation of the magnetization. However, this proves to be a weak constraint. Reversing the process, though, we are able to evaluate the correlation function using the reliable part of our geomagnetic spectrum. Thus we can obtain a sensible estimate for the long-wavelength part of the spectrum that is not well constrained by the data. Our new model shows better agreement with earlier satellite studies and can be considered reliable in the spherical harmonic degree range l = 30 to 1200.

}, keywords = {aeromagnetic data, crustal magnetization, geomagnetic power spectrum, geomagnetic stochastic process, geomagnetic-field, models, vector}, isbn = {0148-0227}, doi = {10.1029/2001jb001389}, url = {A major limitation in the analysis of physical quantities measured from a stratigraphic core is incomplete knowledge of the depth to age relationship for the core. Records derived from diverse locations are often compared or combined to construct records that represent a global signal. Time series analysis of individual or combined records is commonly employed to seek quasi-periodic components or characterize the timescales of relevant physical processes. Assumptions that are frequently made in the approximation of depth to age relationships can have a dramatic and harmful effect on the spectral content of records from stratigraphic cores. A common procedure for estimating ages in a set of samples from a stratigraphic core is to assign, based on complementary data, the ages at a number of depths (tie points) and then assume a uniform accumulation rate between the tie points. Imprecisely dated or misidentified tie points and naturally varying accumulation rates give rise to discrepancies between the inferred and the actual ages of a sample. We develop a statistical model for age uncertainties in stratigraphic cores that treats the true, but in practice unknown, ages of core samples as random variables. For inaccuracies in the ages of tie points, we draw the error from a zero-mean normal distribution. For a variable accumulation rate, we require the actual ages of a sequence of samples to be monotonically increasing and the age errors to have the form of a Brownian bridge. That is, the errors are zero at the tie points. The actual ages are modeled by integrating a piecewise constant, randomly varying accumulation rate. In each case, our analysis yields closed form expressions for the expected value and variance of resulting errors in age at any depth in the core. By Monte Carlo simulation with plausible parameters, we find that age errors across a paleomagnetic record due to misdated tie points are likely of the same order as the tie point discrepancies. Those due to accumulation rate variations can be as large as 30 kyr, but are probably less than 10 kyr. We provide a method by which error estimates like these can be made for similar stratigraphic dating problems and apply our statistical model to an idealized marine sedimentary paleomagnetic record. Both types of errors severely degrade the spectral content of the inferred record. We quantify these effects using realistic tie point ages, their uncertainties and depositional parameters. (C) 2002 Elsevier Science B.V. All rights reserved.

}, keywords = {age, calibration, chronostratigraphy, climate-change, electrical-conductivity, errors, geomagnetic-field intensity, greenland, grip ice core, paleomagnetism, records, relative paleointensity, secular variation, spectral analysis, western equatorial pacific}, isbn = {0012-821X}, doi = {10.1016/s0012-821x(02)00747-1}, url = {We present a statistical analysis of magnetic fields simulated by the Glatzmaier-Roberts dynamically consistent dynamo model. For four simulations with distinct boundary conditions, means, standard deviations, and probability functions permit an evaluation based on existing statistical paleosecular variation (PSV) models. Although none closely fits the statistical PSV models in all respects, some simulations display characteristics of the statistical PSV models in individual tests. We also find that nonzonal field statistics do not necessarily reflect heat flow conditions at the core-mantle boundary. Multitaper estimates of power and coherence spectra allow analysis of time series of single, or groups of, spherical harmonic coefficients representing the magnetic fields of the dynamo simulations outside the core. Sliding window analyses of both power and coherence spectra from two of the simulations show that a 100 kyr averaging time is necessary to realize stationary statistics of their nondipole fields and that a length of 350 kyr is not long enough to full characterize their dipole fields. Spectral analysis provides new insight into the behavior and interaction of the dominant components of the simulated magnetic fields, the axial dipole and quadrupole. Although we find spectral similarities between several reversals, there is no evidence of signatures that can be conclusively associated with reversals or excursions. We test suggestions that during reversals there is increased coupling between groups of spherical harmonic components. Despite evidence of coupling between antisymmetric and symmetric spherical harmonics in one simulation, we conclude that it is rare and not directly linked to reversals. In contrast to the reversal model of R. T. Merrill and P. L. McFadden, we demonstrate that the geomagnetic power in the dipole part of the dynamo simulations is either relatively constant or fluctuates synchronously with that of the nondipole part and that coupling between antisymmetric and symmetric components occurs when the geomagnetic power is high.

}, keywords = {core, dynamo, geomagnetic-field, harmonic, mantle, models, paleosecular variation, pole, reference fields (regional, global), reversal, reversals, reversals (process,, secular variation, simulation, spectral, stationarity, statistics, theories, time variations-secular and long term, timescale, magnetostratigraphy), transition}, isbn = {1525-2027}, url = {The Earth{\textquoteright}s magnetic field can be subdivided into core and crustal components and we seek to characterize the crustal part through its spatial power spectrum, R-1. We process vector Magsat data to isolate the crustal field and then invert power spectral densities of flight-local components along-track for R-1 following O{\textquoteright}Brien et al. [1999]. Our model, designated LPPC, is accurate up to approximately spherical harmonic degree 45 (lambda = 900 km): this is the resolution limit of our data and suggests that global crustal anomaly maps constructed from vector Magsat data should not contain features with wavelengths less than 900 km. We find continental power spectra to be greater than oceanic ones and attribute this to the relative thicknesses of continental and oceanic crust.

}, keywords = {currents, magnetic-field, model, ocean}, isbn = {0148-0227}, doi = {10.1029/2000jb900437}, url = {We have carried out a detailed paleomagnetic investigation of two stratigraphically overlapping sections from the Scaglia Bianca Formation (similar to 85-89.5 Ma) in the Umbria-Marche area in central Italy. Sampling was conducted over 32 in and 7 in intervals at La Roccaccia and Furlo respectively. After AF cleaning the majority of specimens show the expected normal magnetic field orientation, however a number of specimens are directionally anomalous. Some of these deviant specimens are accompanied by apparent spikes or dips in normalized intensity. A detailed investigation of rock magnetics shows that most of these deviations are not a sign of excursionary geomagnetic field behavior, but rather correspond to specimens with distinct rock magnetic characteristics and are therefore rock magnetic {\textquoteright}noise{\textquoteright}. Such specimens should not be interpreted as records of the geomagnetic field. Our experience suggests that detailed rock magnetic and magnetic fabric analysis should be done on all anomalous directions prior to interpreting them as geomagnetic field behavior. After elimination of rock magnetic noise in the Scaglia Bianca data sets, there is a high degree of agreement in direction and to a lesser extent relative intensity between correlative portions of the two sections. We therefore offer this data set as a robust record of geomagnetic field behavior during the 4.5 Myr interval represented by the La Roccaccia section. A statistical analysis of the relative intensity observations suggests that this period of the Cretaceous Normal Superchron is characterized by a normalized variability in paleointensity (standard deviation about 28\% of the mean value) that is significantly lower than seen during the Oligocene over intervals in which reversals or tiny wiggles occur (typically about 50\%). The directional stability results in virtual geomagnetic pole dispersion compatible with that found in volcanic rocks from around the same latitude and ranging in age from 80 to 110 Ma. (C) 2001 Elsevier Science B.V. All rights reserved.

}, keywords = {anisotropy, Cretaceous, cretaceous magnetic stratigraphy, fabric, geomagnetic-field, gubbio, limestone, magnetic intensity, paleomagnetism, relative paleointensity, section, secular variations, sediments, southern alps, susceptibility}, isbn = {0012-821X}, doi = {10.1016/s0012-821x(01)00354-5}, url = {Magnetic measurements taken by the Orsted satellite during geomagnetic quiet conditions around January 1, 2000 have been used to derive a spherical harmonic model of the Earth{\textquoteright}s magnetic field for epoch 2000.0. The maximum degree and order of the model is 19 for internal, and 2 for external, source fields; however, coefficients above degree 14 may not be robust. Such a detailed model exists for only one previous epoch, 1980. Achieved rms misfit is \< 2 nT for the scalar intensity and \< 3 nT for one of the vector components perpendicular to the magnetic field. For scientific purposes related to the Orsted mission, this model supercedes IGRF 2000.

}, isbn = {0094-8276}, doi = {10.1029/2000gl011930}, url = {PSVMOD1.0 is a compilation of globally distributed palaeodirectional data from archaeomagnetic artefacts, lava flows, and lake sediments at 24 sites evaluated at 100 year intervals from 1000 BC to AD 1800. We estimate uncertainty in these measures of declination and inclination by comparison with predictions from standard historical models in time-intervals of overlap, and use the 100-year samples and their associated uncertainties to construct a sequence of minimum structure global geomagnetic field models. Global predictions of radial magnetic field at the core mantle boundary (CMB), as well as inclination and declination anomalies at the Earth{\textquoteright}s surface, provide an unprecedented view of geomagnetic secular variations over the past 3000 years, and demonstrate a consistent evolution of the field with time. Resolution of the models is poorest in the Southern Hemisphere, where only six of the 24 sites are located, several with incomplete temporal coverage. Low-flux regions seen in the historical field near the North Pole are poorly resolved, but the Northern Hemisphere flux lobes are clearly visible in the models. These lobes are not fixed in position and intensity, but they only rarely venture into the Pacific hemisphere. The Pacific region is seen to have experienced significant secular variation: a strong negative inclination anomaly in the region, like that seen in 0-5 Ma models, persists from 1000 BC until AD 1000 and then gradually evolves into the smaller positive anomaly seen today. On average bt tween 1000 BC and AD 1800, the non-axial-dipole contribution to the radial magnetic field at the core-mantle boundary is largest in the north-central Pacific, and beneath Central Asia, with clear non-zonal contributions. At the Earth{\textquoteright}s surface, average inclination anomalies are large and negative in the central Pacific, and most positive slightly to the east of Central Africa. Inclination anomalies decrease with increasing latitude. Average declinations are smallest in equatorial regions, again with strong longitudinal variations, largest negative departures are centred over Australia and Eastern Asia. Secular variation at the Earth{\textquoteright}s surface is quantified by standard deviation of inclination and declination about their average values, and at the CMB by standard deviation in radial magnetic field. All three show significant geographical variations, but appear incompatible with the idea that secular variation in the Pacific hemisphere is permanently attenuated by greatly enhanced conductivity in D " beneath the region.

}, keywords = {0-5 ma, 5 myr, averaged paleomagnetic field, directional-data, geomagnetic field, geomagnetic secular variation, lava flows, modelling, palaeomagnetism, palaeosecular variation}, isbn = {1364-503X}, url = {The magnetostratigraphic time scale provides a record of the occurrence of geomagnetic reversals. The temporal distribution of reversals may be modelled as the realization of an inhomogeneous renewal process; i.e., one in which the intensity, lambda(t), or reversal rate is a function of time. Variations in reversal rate occurring on time scales of tens of millions of years an believed to reflect changes in core-mantle boundary conditions influencing the structure of core flow and the field produced by the geodynamo. We present a new estimate for reversal rate variations as a function of time using nonparametric adaptive kernel density estimation and discuss the difficulties in making inferences on the basis of such estimates. Using a technique proposed by Hengartner and Stark (1992a; b; 1995), it is possible to compute confidence bounds on the temporal probability density function for geomagnetic reversals. The method allows the computation of a lower bound on the number of modes required by the observations, thus enabling a test of whether "bumps" are required features of the reversal rate function. Conservative 95\% confidence intervals can then be calculated for the temporal location of a single mode or antimode of the probability density function. Using observations from the time interval 0-158 Ma, it is found that the derivative of the rate function must have changed sign at least once. The timing of this sign change is constrained to be between 152.56 and 22.46 Ma the 95\% confidence level. Confidence bounds are computed for the reversal rate under the assumption that the observed reversals are a realization of an inhomogenous Poisson or other renewal process with an arbitrary monotonically increasing rate function from the end of the Cretaceous Normal Superchron (CNS) to the present, a zero rate during the CNS, and a monotonically decreasing rate function from M29R at 158 Ma to the onset of the CNS. It is unnecessary to invoke more than one sign change in the derivative of the rare function to fit the observations. There is no incompatibility between our results and a recent assertion that there is an asymmetry in average reversal rate prior to and after the CNS, when the CNS is assumed to be a period of zero reversal rate. Neither can we use our results to reject an alternative hypothesis that rates are essentially constant from 158 to 130 Ma, and from 25 Ma to the present. with an intermediate nonstationary segment. (C) 2000 Elsevier Science B.V. All rights reserved.

}, keywords = {100 myr, 15-myr periodicity, earths inner-core, frequency, geomagnetic reversals, magnetic-field reversals, mantle, occurrence, plumes, rates, record, superchron}, isbn = {0031-9201}, doi = {10.1016/s0031-9201(99)00139-9}, url = {The geomagnetic power spectrum R-l is the squared magnetic field in each spherical harmonic degree averaged over a spherical surface. Satellite measurements have given reliable estimates of the spectrum for the part that originates in the core, but above I = 15, where the geomagnetic field arises primarily from crustal magnetization, there is considerable disagreement between various estimates derived from observation. Furthermore, several theoretical models for the spectrum disagree with each other and the data. We have examined observations from a different source, 5000-km-long Project Magnet aeromagnetic survey lines; we make new estimates of the spectrum which overlap with the wavelength interval accessible to the satellites. The usual way the spectrum is derived from observation is to construct a large spherical harmonic decomposition first, then square, weight, and add the Gauss coefficients in each degree, but this method cannot be applied to isolated flight lines. Instead, we apply a statistical technique based on an idea of McLeod and Coleman which relates the geomagnetic spectrum to the power and cross spectra of magnetic field components measured on the survey lines. Power spectra from the 17 aeromagnetic surveys, all of which were conducted over the oceans, are averaged together to improve geographic coverage and reduce variance, and the average spectra are then inverted for the geomagnetic spectrum R-l. Like most of the theoretical models, our spectrum exhibits a maximum, but at a wavelength of 100 km, about a factor of 2 smaller than the closest theoretical prediction. Our spectrum agrees quite well with the most recent estimates based on satellite observations in the range 20 less than or equal to l less than or equal to 50, but above l=50, our values increase slowly, while all the satellite data suggest a sharply rising curve. In this wavelength range we believe our measurements are more trustworthy. Further work is planned to confirm the accuracy of our spectrum when continental survey paths are included.

}, keywords = {anomalies, core, main geomagnetic-field, models, paleosecular variation, pole, vector}, isbn = {0148-0227}, doi = {10.1029/1999jb900302}, url = {We present a family of statistical models for paleosecular variation (PSV) of the geomagnetic field that are compatible with paleodirectional and paleointensity variations in lava flows sampling the last 5 Ma, and explore what paleomagnetic observables might be used to discriminate among the various family members. We distinguish statistical models with axial anisotropy, which provide a suitable description for an earth with homogeneous boundary conditions at the core-mantle interface from those with more general anisotropy corresponding to geographically heterogeneous boundary conditions. The models revise and extend earlier ones, which are themselves descendants of CP88, devised by Constable and Parker [Constable, C.G., Parker, R.L., 1988. Statistics of the geomagnetic secular variation for the past 5 m.y. J. Geophys, Res. 93, 11569-11581]. In CP88, secular variation is described by statistical variability of each Gauss coefficient in a spherical harmonic description of the geomagnetic field, with each coefficient treated as a normally distributed random variable: the Gauss coefficients of the non-dipole part of the field exhibit isotropic variability, and the variances are derived from the present field spatial power spectrum. The dipole terms have a special status in CP88, with a non-zero mean for the axial-dipole, and lower variance than predicted from the spatial power spectrum. All non-dipole terms have zero mean except the axial-quadrupole. CP88 is untenable for two reasons: it fails to predict the observed geographic dependence of directional variability in the magnetic field, and it grossly underpredicts the variance in paleointensity data. The new models incorporate large variance in the axial-dipole, and in the non-axial-quadrupole Gauss coefficients, g1/2: and h1/2:. The resulting variance in paleomagnetic observables depends only on latitude (zonal models), unless the variance in h1/2: is different from that in g1/2 (non-zonal models). Non-zonal (longitudinal) variations in PSV, such as the flux lobes seen in the historical magnetic field, are simulated using the non-zonal models. Both the zonal and non-zonal models fit summary statistics of the present dataset. We investigate the influence of persistent non-zonal influences in PSV on various paleomagnetic observables. It is shown that virtual geomagnetic pole (VGP) dispersion is rather insensitive to longitudinal variations in structure of PSV, and that inclination dispersion has the potential to be more informative given the right site distribution. There is also the possibility of using paleointensity and geographic variations in the frequency of occurrence of excursional directions to identify appropriate PSV models. (C) 1999 Elsevier Science B.V. All rights reserved.

}, keywords = {earths magnetic-field, geometry, inner-core, intensity, lava, lava flows, paleointensity, paleosecular variation, records, reversals, secular variation, time, virtual geomagnetic pole}, isbn = {0031-9201}, doi = {10.1016/s0031-9201(99)00065-5}, url = {We have conducted a detailed exploratory analysis of an II million year long almost continuous record of relative geomagnetic paleointensity from a sediment core acquired on Deep Sea Drilling Project Leg 73, at Site 522 in the South Atlantic. We assess the quality of the paleointensity record using spectral methods and conclude that the relative intensity record is minimally influenced by climate variations. Isothermal remanence is shown to be the most effective normalizer for these data, although both susceptibility and anhysteretic remanence are also adequate. Statistical analysis shows that the paleointensity variations follow a gamma distribution, and are compatible with predictions from modified paleosecular variation models and global absolute paleointensity data. When subdivided by polarity interval, the variability in paleointensity is proportional to the average, and further, the average is weakly correlated with interval length. Spectral estimates for times from 28.77 until 22.74 Ma, when the reversal rate is about 4 Myr(-1), are compatible with a Poisson model in which the spectrum of intensity variations is dominated by the reversal process in the frequency range 1-50 Mgr(-1) In contrast, between 34.7 and 29.4 Ma, when the reversal rate is about 1.6 Myr(-1), the spectra indicate a different secular variation regime. The magnetic field is stronger, and more variable, and a strong peak in the spectrum occurs at about 8 Myr(-1). This peak magi be a reflection of the same signal as recorded by the small variations known as tiny wiggles seen in marine magnetic anomaly profiles.

}, keywords = {drilling project site-522, field, models, paleointensity, paleosecular variation, pole, relative}, doi = {10.1029/98jb01519}, url = {We present new Ar-40/Ar-39 ages and paleomagnetic data for Sao Miguel island, Azores. Paleomagnetic samples were obtained for 34 flows and one dike; successful mean paleomagnetic directions were obtained for 28 of these 35 sites. Ar-40/Ar-39 age determinations on 12 flows from the Nordeste complex were attempted successfully: ages obtained are between 0.78 Ma and 0.88 Ma, in contrast to published K-Ar ages of 1 Ma to 4 Ma. Our radiometric ages are consistent with the reverse polarity paleomagnetic field directions, and indicate that the entire exposed part of the Nordeste complex is of a late Matuyama age. The duration of volcanism across Sao Miguel is significantly less than previously believed, which has important implications for regional melt generation processes, and temporal sampling of the geomagnetic field. Observed stable isotope and trace element trends across the island can be explained, at least in part, by communication between different magma source regions at depth. The Ar-40/Ar-39 ages indicate that our normal polarity paleomagnetic data sample at least 0.1 Myr (0-0.1 Ma) and up to 0.78 Myr (0-0.78 Ma) of paleosecular variation and our reverse polarity data sample approximately 0.1 Myr (0.78-0.88 Ma) of paleosecular variation. Our results demonstrate that precise radiometric dating of numerous flows sampled is essential to accurate inferences of long-term geomagnetic field behavior. Negative inclination anomalies are observed for both the normal and reverse polarity time-averaged field. Within the data uncertainties, normal and reverse polarity field directions are antipodal, but the reverse polarity field shows a significant deviation from a geocentric axial dipole direction. (C) 1998 Elsevier Science B.V. All rights reserved.

}, keywords = {absolute age, Ar-40/Ar-39, Azores, enriched mantle, flows, geomagnetic-field, magnetic field, paleomagnetism, secular variations}, isbn = {0012-821X}, doi = {10.1016/s0012-821x(98)00117-4}, url = {A new average geomagnetic field model for the past 3kyr (ALS3K) helps bridge a large temporal sampling gap between historical models and more traditional paleomagnetic studies spanning the last 5 Myr. A quasi-static feature seen historically in the central Pacific has the opposite sign in ALS3K; its structure is similar to, but of larger amplitude than, that in the time-averaged geomagnetic field for the last 5 Myr. Anomalous geomagnetic fields exist beneath the Pacific over timescales ranging from 10(2)-10(6) years. It is unlikely that bias over such long time scales arises from electromagnetic screening, but conceivable that the Lorentz force is influenced by long wavelength thermal variations and/or localized regions of increased electrical conductivity (associated with compositional anomalies and possibly partial melt). This is consistent with recent seismic observations of the lower mantle.

}, keywords = {core-mantle boundary, earths core}, isbn = {0094-8276}, doi = {10.1029/98gl50666}, url = {Algorithms used in geomagnetic main-field modelling have for the most part treated the noise in the field measurements as if it were white. A major component of the noise consists of the field due to magnetization in the crust and it has been realized for some time that such signals are highly correlated at satellite altitude. Hence approximation by white noise, while of undoubted utility, is of unknown validity. Langel, Estes \& Sabaka (1989) were the first to evaluate the influence of correlations in the crustal magnetic field on main-field models. In this paper we study two plausible statistical models for the crustal magnetization described by Jackson (1994), in which the magnetization is a realization of a stationary, isotropic, random process. At a typical satellite altitude the associated fields exhibit significant correlation over ranges as great as 15 degrees or more, which introduces off-diagonal elements into the covariance matrix, elements that have usually been neglected in modelling procedures. Dealing with a full covariance matrix for a large data set would present a formidable computational challenge, brit fortunately most of the entries in the covariance matrix are so small that they can be replaced by zeros. The resultant matrix comprises only about 3 per cent non-zero entries and thus we can take advantage of efficient sparse matrix techniques to solve the numerical system. We construct several main-field models based on vertical-component data from a selected 5 degrees by 5 degrees data set derived from the Magsat mission. Models with and without off-diagonal terms are compared. For one of the two Jackson crustal models, k(3), we find significant changes in the main-field coefficients, with maximum discrepancies near degree 11 of about 27 per cent. The second crustal spectrum gives rise to much smaller effects for the data set used here, because the correlation lengths are typically shorter than the data spacing. k(4) also significantly underpredicts the observed magnetic spectrum around degree 15. We conclude that there is no difficulty in computing main-field models that include off-diagonal terms in the covariance matrix when sparse matrix techniques are employed; we find that there may be important effects in the computed models, particularly if we wish to make full use of dense data sets. Until a definitive crustal field spectrum has been determined, the precise size of the effect remains uncertain. Obtaining such a statistical model should be a high priority in preparation for the analysis of future low-noise satellite data.

}, keywords = {core-mantle boundary, crustal magnetization, geomagnetism, magnetic-field, magsat data}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.1997.tb01866.x}, url = {The frozen-flux hypothesis for the Earth{\textquoteright}s liquid core assumes that convective terms dominate diffusive terms in the induction equation governing the behaviour of the magnetic field at the surface of the core. While highly plausible on the basis of estimates of physical parameters, the hypothesis has been questioned in recent work by Bloxham, Gubbins \& Jackson (1989) who find it to be inconsistent with their field models for most of the century. To study this question we improve the method of Constable, Parker \& Stark (1993), which tests the consistency of magnetic observations with the hypothesis by constructing simple, flux-conserving core-field models fitting the data at pairs of epochs. We introduce a new approach that fixes the patch configurations at each of the two epochs before inversion, so that each configuration is consistent with its respective data set but possesses the same patch topology. We expand upon the inversion algorithm, using quadratic programming to maintain the proper flux sign within patches; the modelling calculations are also extended to include data types that depend non-linearly on the model. Every test of a hypothesis depends on the characterization of the observational uncertainties; we undertake a thorough review of this question. For main-field models, the primary source of uncertainty comes from the crustal field. We base our analysis on one of Jackson{\textquoteright}s (1994) statistical models of the crustal magnetization, adjusted to bring it into better conformity with our data set. The noise model permits us to take into account the correlations between the measurements and requires that a different weighting be given to horizontal and vertical components. It also indicates that the observations should be fit more closely than has been the practice heretofore. We apply the revised method to Magsat data from 1980 and survey and observatory data from 1915.5, two data sets believed to be particularly difficult to reconcile with the frozen-flux hypothesis. We compute a pair of simple, flux-conserving models that fit the averaged data from each epoch. We therefore conclude that present knowledge of the geomagnetic fields of 1980 and 1915.5 is consistent with the frozen-flux hypothesis.

}, keywords = {algorithm, core-mantle boundary, crustal magnetization, geomagnetic variation, geomagnetic-field, inversion, magnetic-field, magsat data}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.1997.tb01566.x}, url = {Palaeodirectional data from lava flows and marine sediments provide information about the long-term structure and variability in the geomagnetic held. We present a detailed analysis of the internal consistency and reliability of global compilations of sediment and lava-flow data. Time-averaged field models are constructed for normal and reverse polarity periods for the past 5 Ma, using the combined data sets. Non-zonal models are required to satisfy the lava-flow data, but not those from sediments alone. This is in part because the sediment data are much noisier than those from lavas, but is also a consequence of the site distributions and the way that inclination data sample the geomagnetic field generated in the Earth{\textquoteright}s core. Different average held configurations for normal and reverse polarity periods are consistent with the palaeomagnetic directions; however, the differences are insignificant relative to the uncertainty in the average field models. Thus previous inferences of non-antipodal normal and reverse polarity field geometries will need to be re-examined using recently collected high-quality palaeomagnetic data. Our new models indicate that current global sediment and lava-flow data sets combined do not permit the unambiguous detection of northern hemisphere flux lobes in the 0-5 Ma time-averaged field, highlighting the need for the collection of additional high-latitude palaeomagnetic data. Anomalous time-averaged held structure is seen in the Pacific hemisphere centred just south of Hawaii. The location of the anomaly coincides with heterogeneities in the lower mantle inferred from seismological data. The seismic observations can be partly explained by lateral temperature variations; however, they also suggest the presence of lateral compositional variations and/or the presence of partial melt. The role of such heterogeneities in influencing the geomagnetic held observed at the Earth{\textquoteright}s surface remains an unresolved issue, requiring higher-resolution time-averaged geomagnetic field models, along with the integration of future results from seismology, mineral physics and numerical simulations.

}, keywords = {anomalies, core-mantle boundary, dynamo, earths magnetic-field, geomagnetism, inner-core, lava flows, palaeomagnetism, paleomagnetic field, reversals, secular variation, time-averaged field, velocity structure}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.1997.tb06604.x}, url = {Using relative paleointensity estimates derived from twelve globally distributed pelagic sediment cores, we assess whether they record a signal consistent with that expected from a dominant geocentric axial dipole, The cores span the Matuyama-Brunhes boundary and we normalize the observations by supposing that at the time the direction reverses the intensity low reflects only the non-axial-dipole contribution to the field. We further assume that this non-axial-dipole contribution to the field is invariant with geographic location. From absolute paleointensity compilations we estimate its size to be about 7.5 mu T; this supplies the calibration for the axial dipole signal away from the extreme low in intensity, The data predict the dipole field variation with latitude with similar accuracy to that observed in absolute paleointensity records, and show similar behavior when transformed to virtual axial dipole moments.

}, keywords = {calibration, cores, geomagnetic-field intensity, magnetic intensity, natural remanent magnetization, pacific, paleomagnetism, sediments}, isbn = {0012-821X}, doi = {10.1016/0012-821x(96)00128-8}, url = {We present a new global palaeomagnetic database, comprising lava flows and thin intrusive bodies, suitable for studying palaeosecular variation and the time-averaged field. The database is presented in some detail in the appendix and is available oil-line from the authors. We review palaeosecular variation models to date, emphasizing the assumptions required and the rather arbitrary construction of many of these models, Preliminary studies of the statistical properties of the new database suggest that existing palaeosecular variation models are inadequate to explain the long-term temporal variations in the field. It is increasingly apparent that data distribution and duality are pivotal in determining the characteristics of the secular variation. The work presented here demonstrates the need for revised models of the time-averaged field structure for both normal and reverse polarities before reliable models for palaeosecular variation can be made.

}, keywords = {averaged paleomagnetic field, geomagnetic reversal paths, geometry, mantle, myr, paleosecular, secular variation, sediments, variation}, doi = {10.1098/rsta.1996.0004}, url = {The main magnetic field of the Earth is a complex phenomenon. To understand its origins in the fluid of the Earth{\textquoteright}s core, and how it changes in time requires a variety of mathematical and physical tools. This book presents the foundations of geomagnetism, in detail and developed from first principles. The book is based on George Backus{\textquoteright} courses for graduate students at the University of California, San Diego. The material is mathematically rigorous, but is logically developed and has consistent notation, making it accessible to a broad range of readers. The book starts with an overview of the phenomena of interest in geomagnetism, and then goes on to deal with the phenomena in detail, building the necessary techniques in a thorough and consistent manner. Students and researchers will find this book to be an invaluable resource in the appreciation of the mathematical and physical foundations of geomagnetism.

}, keywords = {Geomagnetism.}, isbn = {0521410061 (hardback)}, url = {http://www.loc.gov/catdir/toc/cam023/95044208.htmlhttp://www.loc.gov/catdir/description/cam027/95044208.htmlhttp://www.worldcat.org/oclc/33333582}, author = {Backus, George and Parker, Robert L. and Constable, Catherine} } @article {21456, title = {The Time-Averaged Geomagnetic-Field As Recorded By Lava Flows Over The Past 5 Million-Years}, journal = {Geophysical Journal International}, volume = {122}, number = {2}, year = {1995}, note = {n/a}, month = {Aug}, pages = {489-519}, type = {Article}, abstract = {A recently compiled lava flow data base spanning the last 5 million years is used to investigate properties of the time-averaged geomagnetic field. More than 90 per cent of the power in the palaeofield can be accounted for by a geocentric axial dipole; however, there are significant second-order structures in the held. Declination and inclination anomalies for the new data base indicate that the main second-order signal is the {\textquoteright}far-sided{\textquoteright} effect, and there is also evidence for non-zonal structure. VGP (virtual geomagnetic pole) latitude distributions indicate that, over the last 5 million years, normal and reverse polarity morphologies are different, and that any changes in the normal polarity field morphology are undetectable, given the present data distribution. Regularized non-linear inversions of the palaeomagnetic directions support all these observations. We test the hypothesis that zonal models for the time-averaged field are adequate to describe the data and find that they are not. Non-zonal models are needed to fit the data to within the required tolerance level. Normal and reverse polarity held models obtained are significantly different. Field models obtained for the Brunhes epoch data alone are much smoother than those obtained from combining an the normal polarity data; simulations indicate that these differences can be explained by the less extensive data distribution for the Brunhes epoch. The field model for all of the normal polarity data (LN1) contains features observed in the historical field maps, although the details differ. LN1 suggests that, although the two northern hemisphere flux lobes observed in the historical field are stationary to a first-order approximation, they do show changes in position and amplitude. A. third, less pronounced flux lobe is observed in LN1 over central Europe. The lack of structure ih the southern hemisphere is due in part to the paucity of data. Jackknife estimates of the field models for different subsets of the data suggest that a few sites contribute significant structure to the final field models. More conservative estimates of the time-averaged field morphology are obtained by removing these sites.

}, keywords = {anomalies, core-mantle boundary, earths magnetic-field, field, geomagnetism, inversion, models, palaeosecular variation, paleomagnetic field, paleomagnetism, secular variation, time-averaged}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.1995.tb07010.x}, url = {Hydraulic piston coring operations at Deep Sea Drillng Project site 522 in the South Atlantic retrieved an unusually continuous section of late Eocene to late Oligocene pelagic sediments, which we sampled at 3-4 cm intervals (approximately 3-5 kyr). Natural remanent magnetization demagnetization studies indicate a well-behaved remanence. Various rock magnetic procedures strongly suggest the magnetic carrier is dominated by pseudo-single domain magnetite appropriate for recording relative intensity variations of the paleomagnetic field. Nine zones of unusually low relative paleointensity were identified within the 2 my Chron C12R interval. Seven can be typified by a approximately 20-40 kyr interval of low field intensity accompanied by apparently random, low-amplitude, short-duration directional fluctuations. The other two are of approximately equal duration and intensity but exhibit an orderly progression of directional changes that result in well-defined virtual geomagnetic pole (VGP) paths confined along a preferred meridian of approximately 70-90-degrees-W longitude. We propose that both styles occur when the main dipole term diminishes significantly but that the former result when undimished {\textquoteright}{\textquoteright}normal{\textquoteright}{\textquoteright} secular variation is continuous during the period of low axial dipole moment. We propose that the other two lows in relative paleointensity, along with one reversal record, reflect a field structure of low axial dipole moment dominated by a low-degree nonzonal spherical harmonic term. Alternatively, the confined VGP paths could be an artifact of heavy remanence smoothing between nonantipodal, semistable transitional geomagnetic pole positions. Geographical control of VGP paths, particularly along approximately 70-90-degrees-W longitude, has recently been noted for much younger reversals. The site 522 record may indicate that the underlying cause of this phenomenon was present at 32 Ma. We compare our C12R record of paleointensity lows with C12R marine magnetic anomaly {\textquoteright}{\textquoteright}tiny wiggles{\textquoteright}{\textquoteright}. These data appear to indicate that C12R tiny wiggles resulted from periods of low geomagnetic field intensity that were sometimes accompanied by directional excursions.

}, keywords = {depositional remanent magnetization, excursion, identification, matuyama, paleointensity, polarity intervals, profiles, record, reversal, sediments}, isbn = {0148-0227}, doi = {10.1029/93jb02019}, url = {Techniques for modelling the geomagnetic field at the surface of Earth{\textquoteright}s core often penalize contributions at high spherical harmonic degrees to reduce the effect of mapping crustal fields into the resulting field model at the core-mantle boundary (CMB). Ambiguity in separating the observed field into crustal and core contributions makes it difficult to assign error bounds to core field models, and this makes it hard to test hypotheses that involve pointwise values of the core field. The frozen-flux hypothesis, namely that convective terms dominate diffusive terms in the magnetic-induction equation, requires that the magnetic flux through every patch on the core surrounded by a zero contour of the radial magnetic field remains constant, although the shapes, areas and locations (but not the topology) of these patches may change with time. Field models exactly satisfying the conditions necessary for the hypothesis have not yet been constructed for the early part of this century. We show that such models must exist, so testing the frozen-flux hypothesis becomes the question of whether the models satisfying it are geophysically unsatisfactory on other grounds, for example because they are implausibly rough or complicated. We introduce an algorithm to construct plausible fleld models satisfying the hypothesis, and present such models for epochs 1945.5 and 1980. Our algorithm is based on a new parametrization of the field in terms of its radial component B(r) at the CMB. The model consists of values of B(r) at a finite set of points on the CMB, together with a rule for interpolating the values to other points. The interpolation rule takes the specified points to be the vertices of a spherical triangle tessellation of the CMB, with B(r) varying linearly in the gnomonic projections of the spherical triangles onto planar triangles in the planes tangent to the centroids of the spherical triangles. This parametrization of B(r) provides a direct means of constraining the integral invariants required by the frozen-flux hypothesis. Using this parametrization, we have constructed field models satisfying the frozen-flux hypothesis for epochs 1945.5 and 1980, while fitting observatory and survey data for 1945.5 and Magsat data for 1980. We use the better constrained 1980 CMB field model as a reference for 1945.5: we minimize the departure of the 1945.5 CMB field model from a regularized 1980 CMB field model, while constraining the 1945.5 model to have the same null-flux curves and flux through those curves as the 1980 model. The locations, areas and shapes of the curves are allowed to change. The resulting 1945.5 CMB field model is nearly as smooth as that for 1980, fits the data adequately, and satisfies the conditions necessary for the frozen-flux hypothesis.

}, keywords = {core mantle boundary, earths magnetic-field, frozen-flux model, geomagnetic field, inference, magsat data, motions, secular variation, top}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.1993.tb00897.x}, url = {PALAEOMAGNETIC records provide information about the behaviour of the geomagnetic field during reversals1,2. Existing records are incompatible with transitional field configurations that are either entirely dipolar or entirely zonal (dependent only on latitude)3,4. Recent compilations5-8 have indicated that the transitional paths of virtual geomagnetic poles (VGPs) for the past few reversals are located preferentially within two antipodal longitudinal bands, suggesting that simple but non-zonal field configurations dominate during reversals. Here I point out that one of the longitudinal bands coincides with that expected from the reversal of a non-axial-dipole field exactly like that present today; the other requires only a sign change in the non-axial-dipole terms of today{\textquoteright}s field. Evidence for persistent non-zonal contributions to the field has generally9-13 (but not always14,15) been regarded as not statistically significant in the light of poor data distributions. I show here that a non-zonal bias, similar to that observed in reversal data, is evident in data on secular variation of the field over the past 5 Myr, even after normalization according to site locations. These results suggest that the time-averaged field does indeed contain persistent (but not constant) non-zonal contributions.

}, keywords = {averaged paleomagnetic field, dynamo, polarity transition}, isbn = {0028-0836}, doi = {10.1038/358230a0}, url = {The magnetization of long cores of sedimentary material is often measured in a pass-through magnetometer, whose output is the convolution of the desired function with the broad impulse response of the system. Because of inevitable measurement noise and the inherent poor conditioning of the inverse problem, any attempt to estimate the true magnetization function from the observations must avoid unnecessary amplification of small-scale features which would otherwise dominate the model with deceptively large undulations. We propose the construction of the smoothest possible magnetization model satisfying the measured data to within the observational error. By means of a cubic spline basis in the representations of both the unknown magnetization and the empirically measured response, we facilitate the imposition of maximum smoothness on the unknown magnetization. For our purposes, the smoothest model is the one with the smallest 2-norm of the second derivative, the same criterion used in the construction of cubic spline interpolators. The approach is tested on a marine core that was subsequently sectioned and measured in centimetre-sized individual specimens, with highly satisfactory results. An empirical estimate of the resolution of the method indicates a three-fold improvement in the processed record over the original signal. We illuminate the behaviour of the numerical scheme by showing the relation between our smoothness-maximizing procedure and a more conventional filtering approach. Our solution can indeed be approximated by convolution with a special set of weights, although the approximation may be poor near the ends of the core. In an idealized system we study the question of convergence of the deconvolution process, by whether the model magnetization approaches the true one when the experimental error and other system parameters are held constant, while the spacing between observations is allowed to become arbitrarily small. We find our procedure does in fact converge (under certain conditions) but only at a logarithmic rate. This suggests that further significant improvement in resolution cannot be achieved by increased measurement density or enhanced observational accuracy.

}, keywords = {magnetization, paleomagnetic cores, spline deconvolution}, isbn = {0956-540X}, doi = {10.1111/j.1365-246X.1991.tb05693.x}, url = {The power and utility of paleomagnetic analyses stem largely from the ability to quantify such parameters as the degree of rotation of a rock body, or the orientation of an anisotropy axis. Until recently, estimates for uncertainty in these paleomagnetically determined parameters derived from assumptions concerning the underlying parametric distribution functions of the data. In many geologically important situations, the commonly used parametric distribution functions fail to model the data adequately and the uncertainty estimates so obtained are unreliable. Such essentials as the test for common mean require data sets consistent with a spherically symmetric underlying distribution; their application in inappropriate circumstances can result in flawed interpretations. Moreover, the almost universally used approximation for a cone of 95\% confidence for the mean of a sample drawn from a Fisher distribution is quite biased even for moderate dispersions (kappa = 25). The availability of inexpensive, powerful computers makes possible the empirical estimation of confidence regions by means of data resampling techniques such as the bootstrap. These resampling schemes replace analytical solutions with repeated simple calculations. We describe a bootstrap approach for the calculation of uncertainties for means or principal directions of paleomagnetic data. The method is tested on means of simulated Fisher distributions with known parameters and is found to be reliable for data sets with more than about 25 elements. Because a Fisher distribution is not assumed, the approach is applicable to a wide range of paleomagnetic data and can be used equally well on directions or associated virtual poles. We also illustrate bootstrap techniques for the discrimination of directions and for the fold test which enable the use of these powerful tests on the wider range of data sets commonly obtained in paleomagnetic investigations.

}, keywords = {bingham distribution, confidence-regions, directional-data, rotation, sediments, sphere}, isbn = {0148-0227}, doi = {10.1029/91jb00572}, url = {In studies of the anisotropy of susceptibility or remanence of paleomagnetic samples it is conventional to specify the anisotropy in terms of the parameters of the anisotropy ellipsoids, namely the directions of the principal axes of the ellipsoid and their associated eigenvalues. Confidence intervals for these parameters have in the past often been estimated by using a linearization scheme to propagate the effect of small changes through the eigenvalue decomposition. The validity of these approximations is explored using a Monte-Carlo simulation from measurements that are presumed normally distributed, showing that there are circumstances in which the linearization scheme gives confidence intervals that are much too small. Q-Q plots indicate that the common assumption that the noise in the measurements is Gaussian does not always hold. Because of these shortcomings in the conventional technique we propose using a bootstrap resampling scheme to find empirically the distribution of uncertainties in the results. Confidence intervals for the eigenvalues are found directly from their empirical distributions. For the principal axes, approximate elliptical regions of confidence on the unit sphere are parameterized in terms of the Kent or FB5 distribution. The number of modes observed in the distribution of eigenvalues obtained by bootstrapping is used to classify the shape of the susceptibility ellipsoid as spherical, oblate, prolate or triaxial. The empirical nature of the bootstrap technique allows the extension of the analysis of uncertainties to parameters derived from the principal susceptibilities, such as percentage anisotropy or shape factor.

}, isbn = {0148-0227}, doi = {10.1029/JB095iB06p08383}, url = {The diversity of paleomagnetic records of geomagnetic reversals now available indicate that the field configuration during transitions cannot be adequtely described by simple zonal or standing field models. A new model described here is based on statistical properties inferred from the present field and is capable of simulating field transitions like those observed. Some insight is obtained into what one can hope to learn from paleomagnetic records. In particular, it is crucial that the effects of smoothing in the remanence acquisition process be separated from true geomagnetic field behavior. This might enable us to determine the time constants associated with the dominant field configuration during a reversal.

}, isbn = {0148-0227}, doi = {10.1029/JB095iB04p04587}, url = {It is often difficult or impossible to determine the origin of the characteristic remanent magnetization of red beds from the bulk remanence alone. However, anisotropy of remanence or susceptibility is strongly controlled by the statistical alignment of hematite grains; this in turn may reflect the development of the magnetic fabric of the sediment over time, so the shape of the anisotropy ellipsoid may provide clues to the origin of remanence. In this work, we make a study of the anisotropy of magnetic susceptibility (AMS) in Siwalik red beds of Miocene age from northern Pakistan. Comparison of the results with detailed petrographic studies and other information suggests that advanced soil development leads to the destruction of primary fabrics and often with it, a coherent magnetization. Furthermore, it should be possible to use AMS fabric information to quantify the degree of pedogenesis in these Miocene soils. We attempted to determine the anisotropy of isothermal remanence (AIR) but found AMS to be the technique of choice because of apparent changes in coercivity during AIR experiments. We interpret the AIR data as resulting from metastable domains in hematite grains which change domain state during the AIR experiment.

}, isbn = {0148-0227}, doi = {10.1029/JB095iB04p04391}, url = {We discuss the use of smoothing splines (SS) and least squares splines (LSS) in nonparametric regression on geomagnetic data. The distinction between smoothing splines and least squares splines is outlined, and it is suggested that in most cases the smoothing spline is, a preferable function estimate. However, when large data sets are involved, the smoothing spline may require a prohibitive amount of computation; the alternative often put forward when moderate or heavy smoothing is -desired is the least squares spline. This may not be capable of modeling the data adequately since the smoothness of the resulting function can be controlled only by the number and position of the knots. The computational efficiency of the least squares spline may be retained and its principal disadvantage overcome, by adding a penalty term in the square of the second derivative to the minimized functional. We call this modified form a penalized least squares spline, (denoted by PS throughout this work), and illustrate its use in the removal of secular trends in long observatory records of geomagnetic field components. We may compare the effects of smoothing splines, least squares splines, and penalized least squares splines by treating them as equivalent variable-kernel smoothers. As Silverman has shown, the kernel associated with the smoothing spline is symmetric and is highly localized with small negative sidelobes. The kernel for the least squares spline with the same fit to the data has large oscillatory sidelobes that extend far from the central region; it can be asymmetric even in the middle of the interval. For large numbers of data the penalized least squares spline can achieve essentially identical performance to that of a smoothing spline, but at a greatly reduced computational cost. The penalized spline estimation technique has potential widespread applicability in the analysis of geomagnetic and paleomagnetic data. It may be used for the removal of long term trends in data, when either the trend or the residual is of interest.

}, isbn = {0021-9991}, doi = {10.1016/0021-9991(88)90062-9}, url = {A new statistical model is proposed for the geomagnetic secular variation over the past 5 m.y. Unlike previous models, which have concentrated upon particular kinds of paleomagnetic observables, such as VGP or field direction, the new model provides a general probability density function from which the statistical distribution of any set of paleomagnetic measurements can be deduced. The spatial power spectrum of the present-day nondipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is our model of the nondipole field. Assuming that this characterization holds for the fields of the past, we can combine it with an arbitrary statistical description of the dipole. We compute the corresponding probability density functions and cumulative distribution functions for declination and inclination that would be observed at any site on the surface of the Earth. Global paleomagnetic data spanning the past 5 m.y. are used to constrain the free parameters of the model, i.e., those giving the dipole part of the field. The final model has these properties: (1) with two exceptions, each Gauss coefficient is independently normally distributed with zero mean and standard deviation for the nondipole terms commensurate with a white source at the core surface; (2) the exceptions are the axial dipole g_{1}^{} and axial quadrupole g_{2}^{} terms; the axial dipole distribution is bimodal and symmetric, resembling a combination of two normal distributions with centers close to the present-day value and its sign-reversed counterpart; (3) the standard deviations of the nonaxial dipole terms g_{1}^{1} and h_{1}^{1} and of the magnitude of the axial dipole are all about 10\% of the present-day g_{1}^{} component; and (4) the axial quadrupole reverses sign with the axial dipole and has a mean magnitude of 6\% of its mean magnitude. The advantage of a model specified in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, capable of simultaneously satisfying many known properties of the field. Predictions about any measured field elements may be made to see if they satisfy the available data.

Least squares (LS) estimation of model parameters is widely used in geophysics. If the data errors are Gaussian and independent the LS estimators will be maximum likelihood (ML) estimators and will be unbiased and of minimum variance. However, if the noise is not Gaussian, e.g. if the data are contaminated by extreme outliers, LS fitting will result in parameter estimates which may be biased or grossly inaccurate. When the probability distribution of the errors is known it is possible, using the maximum likelihood method, to obtain consistent and efficient (minimum variance) estimates of parameters. In some cases the distribution of the noise may be determined empirically, and the resulting distribution used in the ML estimation. A procedure for doing this is described here. Hourly values of geomagnetic observatory data are used to illustrate the technique. These data sets contain a number of periodic components, whose amplitudes and phases are geophysically interesting. Geomagnetic storms and other phenomena in the record make the noise distribution long-tailed, asymmetric and variable with location. Using an iterative procedure, one can model the form of these distributions using smoothing splines. For these data ML estimation yields quite different results from standard robust and LS procedures. The technique has the potential for widespread application to other problems involving the recovery of a known form of signal from non-Gaussian noise.

}, isbn = {0952-4592}, doi = {10.1111/j.1365-246X.1988.tb03433.x}, url = {The inversion of electromagnetic sounding data does not yield a unique solution, but inevitably a single model to interpret the observations is sought. We recommend that this model be as simple, or smooth, as possible, in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models. To obtain smooth models, the nonlinear forward problem is linearized about a starting model in the usual way, but it is then solved explicitly for the desired model rather than for a model correction. By parameterizing the model in terms of its first or second derivative with depth, the minimum norm solution yields the smoothest possible model. Rather than fitting the experimental data as well as possible (which maximizes the roughness of the model), the smoothest model which fits the data to within an expected tolerance is sought. A practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models, resulting in a stable and rapidly convergent algorithm. The inversion of both magnetotelluric and Schlumberger sounding field data, and a joint magnetotelluric-resistivity inversion, demonstrate the method and show it to have practical application.

}, isbn = {0016-8033}, doi = {10.1190/1.1442303}, url = {Four box cores collected from the Ontong{\textemdash}Java plateau during the Eurydice expedition have been used to make relative geomagnetic palaeo-intensity measurements. Rock magnetic measurements on the sediments show that they are characterized by a uniform magnetic mineralogy, and that they are suitable for relative intensity estimates. These are obtained by normalizing the NRM by an ARM imparted in a low DC bias field. the palaeoceanographic event known as the preservation spike is used to establish a crude time-scale for the record so that it may be compared with other data from the same region, and also with global palaeointensity estimates. the marine sediment data are quite similar to Australian intensity data from lake sediments and archaeomagnetic sources, but as might be expected exhibit some obvious differences from the global record.

}, isbn = {0016-8009}, doi = {10.1111/j.1365-246X.1987.tb00674.x}, url = {Two north-eastern Australian volcanic crater lake cores have been used to obtain relative intensity estimates for the geomagnetic field. ARM imparted in a low DC bias field has been used as a normalizing parameter. The intensity fluctuations in the two lakes are in excellent agreement with each other and with south-eastern Australian archaeointensity data over their coeval time spans. This strongly suggests that the same sources are influencing the geomagnetic secular variation throughout eastern Australia at this time. The relative intensity records go back to about 14000yr BP thereby extending currently available recent Australian intensity records by some 7000 yr.

}, isbn = {0016-8009}, doi = {10.1111/j.1365-246X.1985.tb01354.x}, url = {Secular variation records have been obtained from cores from Lakes Barrine and Eacham, two north-eastern Australian volcanic crater lakes. The results from several cores have been stratigraphically correlated and then stacked and smoothed. The chronology provided by radiocarbon dating indicates that the Lake Eacham sequence spans the last 5700 calendar years. The time-scale for the Lake Barrine record is less well constrained but it appears to cover about 1600 to 16200 yr BP.VGP paths for the sites show two periods of anticlockwise motion between about 5710 and 3980 BP and 10500 and 8800 BP. These times correspond to periods of anticlockwise motion in south-eastern Australian records (Barton \& McElhinny) and Argentine records (Creer et al.), to within the uncertainties of the assigned time-scales.

}, isbn = {0016-8009}, doi = {10.1111/j.1365-246X.1985.tb01353.x}, url = {