Publications

Export 19 results:
Sort by: Author Title Type [ Year  (Desc)]
2018
Cromwell, G, Johnson CL, Tauxe L, Constable CG, Jarboe NA.  2018.  PSV10: A global data set for 0-10 Ma time-averaged field and paleosecular variation studies. Geochemistry Geophysics Geosystems. 19:1533-1558.   10.1002/2017gc007318   AbstractWebsite

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.

2016
Constable, C, Korte M, Panovska S.  2016.  Persistent high paleosecular variation activity in southern hemisphere for at least 10,000 years. Earth and Planetary Science Letters. 453:78-86.   10.1016/j.epsl.2016.08.015   AbstractWebsite

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.

2015
Ziegler, LB, Constable CG.  2015.  Testing the geocentric axial dipole hypothesis using regional paleomagnetic intensity records from 0 to 300 ka. Earth and Planetary Science Letters. 423:48-56.   10.1016/j.epsl.2015.04.022   AbstractWebsite

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.

Brown, MC, Donadini F, Korte M, Nilsson A, Korhonen K, Lodge A, Lengyel SN, Constable CG.  2015.  GEOMAGIA50.v3: 1. general structure and modifications to the archeological and volcanic database. Earth Planets and Space. 67:1-31.   10.1186/s40623-015-0232-0   AbstractWebsite

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'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

Brown, MC, Donadini F, Nilsson A, Panovska S, Frank U, Korhonen K, Schuberth M, Korte M, Constable CG.  2015.  GEOMAGIA50.v3: 2. A new paleomagnetic database for lake and marine sediments. Earth Planets and Space. 67   10.1186/s40623-015-0233-z   AbstractWebsite

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.

2011
Smith-Boughner, LT, Ziegler LB, Constable CG.  2011.  Changing spectrum of geomagnetic intensity variations in a fragmented 12 My sediment record from the Oligocene. Physics of the Earth and Planetary Interiors. 188:260-269.   10.1016/j.pepi.2011.07.011   AbstractWebsite

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.

Korte, M, Constable C.  2011.  Improving geomagnetic field reconstructions for 0-3 ka. Physics of the Earth and Planetary Interiors. 188:247-259.   10.1016/j.pepi.2011.06.017   AbstractWebsite

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'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.

Ziegler, LB, Constable CG.  2011.  Asymmetry in growth and decay of the geomagnetic dipole. Earth and Planetary Science Letters. 312:300-304.   10.1016/j.epsl.2011.10.019   AbstractWebsite

The geodynamo in Earth'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.

Korte, M, Constable C, Donadini F, Holme R.  2011.  Reconstructing the Holocene geomagnetic field. Earth and Planetary Science Letters. 312:497-505.   10.1016/j.epsl.2011.10.031   AbstractWebsite

Knowledge of the Holocene evolution of Earth'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.

Constable, CG.  2011.  Modelling the geomagnetic field from syntheses of paleomagnetic data. Physics of the Earth and Planetary Interiors. 187:109-117.   10.1016/j.pepi.2011.05.004   AbstractWebsite

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'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.

2010
Hulot, G, Finlay CC, Constable CG, Olsen N, Mandea M.  2010.  The Magnetic Field of Planet Earth. Space Science Reviews. 152:159-222.   10.1007/s11214-010-9644-0   AbstractWebsite

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'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'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.

2008
Ziegler, LB, Constable CG, Johnson CL.  2008.  Testing the robustness and limitations of 0-1 Ma absolute paleointensity data. Physics of the Earth and Planetary Interiors. 170:34-45.   10.1016/j.pepi.2008.07.027   AbstractWebsite

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.

2007
Jackson, A, Constable CG, Walker MR, Parker RL.  2007.  Models of Earth's main magnetic field incorporating flux and radial vorticity constraints. Geophysical Journal International. 171:133-144.   10.1111/j.1365-246X.2007.03526.x   AbstractWebsite

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 'null-flux patches' 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.

2006
Lawrence, KP, Constable CG, Johnson CL.  2006.  Paleosecular variation and the average geomagnetic field at +/- 20 degrees latitude. Geochemistry Geophysics Geosystems. 7   10.1029/2005gc001181   AbstractWebsite

[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,'' 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.

2005
Constable, C, Johnson C.  2005.  A paleomagnetic power spectrum. Physics of the Earth and Planetary Interiors. 153:61-73.   10.1016/j.pepi.2005.03.015   AbstractWebsite

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.

2003
Love, JJ, Constable CG.  2003.  Gaussian statistics for palaeomagnetic vectors. Geophysical Journal International. 152:515-565.   10.1046/j.1365-246X.2003.01858.x   AbstractWebsite

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.

1997
RygaardHjalsted, C, Constable CG, Parker RL.  1997.  The influence of correlated crustal signals in modelling the main geomagnetic field. Geophysical Journal International. 130:717-726.   10.1111/j.1365-246X.1997.tb01866.x   AbstractWebsite

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.

Johnson, CL, Constable CG.  1997.  The time-averaged geomagnetic field: global and regional biases for 0-5 Ma. Geophysical Journal International. 131:643-+.   10.1111/j.1365-246X.1997.tb06604.x   AbstractWebsite

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'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'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.

1995
Johnson, CL, Constable CG.  1995.  The Time-Averaged Geomagnetic-Field As Recorded By Lava Flows Over The Past 5 Million-Years. Geophysical Journal International. 122:489-519.   10.1111/j.1365-246X.1995.tb07010.x   AbstractWebsite

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 'far-sided' 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.