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Tauxe, L, Constable C, Stokking L, Badgley C.  1990.  Use of Anisotropy to Determine the Origin of Characteristic Remanence in the Siwalik Red Beds of Northern Pakistan. Journal of Geophysical Research-Solid Earth and Planets. 95:4391-4404.   10.1029/JB095iB04p04391   AbstractWebsite

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.

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Constable, C, Tauxe L.  1996.  Towards absolute calibration of sedimentary paleointensity records. Earth and Planetary Science Letters. 143:269-274.   10.1016/0012-821x(96)00128-8   AbstractWebsite

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.

Amit, H, Korte M, Aubert J, Constable C, Hulot G.  2011.  The time-dependence of intense archeomagnetic flux patches. Journal of Geophysical Research-Solid Earth. 116   10.1029/2011jb008538   AbstractWebsite

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' 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.

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.

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.

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.

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.

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Buffett, BA, Ziegler L, Constable CG.  2013.  A stochastic model for palaeomagnetic field variations. Geophysical Journal International. 195:86-97.   10.1093/gji/ggt218   AbstractWebsite

Regeneration of the Earth'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'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.

Constable, CG, Parker RL.  1988.  Statistics of the Geomagntic Seculariation for the Past 5-MY. Journal of Geophysical Research-Solid Earth and Planets. 93:11569-11581.   10.1029/JB093iB10p11569   AbstractWebsite

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 g1 and axial quadrupole g2 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 g11 and h11 and of the magnitude of the axial dipole are all about 10% of the present-day g1 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.

McMillan, DG, Constable CG, Parker RL, Glatzmaier GA.  2001.  A statistical analysis of magnetic fields from some geodynamo simulations. Geochemistry Geophysics Geosystems. 2:art.no.-2000GC000130. AbstractWebsite

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.

Avery, MS, Constable CG, Davies CJ, Gubbins D.  2019.  Spectral methods for analyzing energy balances in geodynamo simulations. Physics of the Earth and Planetary Interiors. 286:127-137.   10.1016/j.pepi.2018.10.002   AbstractWebsite

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.

Smith-Boughner, LT, Constable CG.  2012.  Spectral estimation for geophysical time-series with inconvenient gaps. Geophysical Journal International. 190:1404-1422.   10.1111/j.1365-246X.2012.05594.x   AbstractWebsite

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.

Korte, M, Constable CG.  2008.  Spatial and temporal resolution of millennial scale geomagnetic field models. Advances in Space Research. 41:57-69.   10.1016/j.asr.2007.03.094   AbstractWebsite

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'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.

Constable, CG, Parker RL.  1988.  Smoothing, Splines And Smoothing Splines - Their Application In Geomagnetism. Journal of Computational Physics. 78:493-508.   10.1016/0021-9991(88)90062-9   AbstractWebsite

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.

Constable, C.  1990.  A Simple Statistical-Model For Geomagnetic Reversals. Journal of Geophysical Research-Solid Earth and Planets. 95:4587-4596.   10.1029/JB095iB04p04587   AbstractWebsite

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.

Korte, M, Constable S, Constable C.  2003.  Separation of external magnetic signal for induction studies. First CHAMP mission results for gravity, magnetic and atmospheric studies. ( Reigber C, Luehr H, Schwintzer P, Eds.).:315-320., Berlin: Springer Abstract
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Davies, CJ, Constable CG.  2018.  Searching for geomagnetic spikes in numerical dynamo simulations. Earth and Planetary Science Letters. 504:72-83.   10.1016/j.epsl.2018.09.037   AbstractWebsite

We use numerical dynamo simulations to investigate rapid changes in geomagnetic field intensity. The work is motivated by paleomagnetic observations of 'geomagnetic spikes', 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'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'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 'extremal events', defined as the maximum intensity difference between consecutive time points, at each location on a 2 degrees latitude-longitude grid at Earth'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.

Ribaudo, JT, Constable CG, Parker RL.  2012.  Scripted finite element tools for global electromagnetic induction studies. Geophysical Journal International. 188:435-446.   10.1111/j.1365-246X.2011.05255.x   AbstractWebsite

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.

Constable, CG, Constable SC.  2004.  Satellite magnetic field measurements: applications in studying the deep earth. The state of the planet : frontiers and challenges in geophysics. ( Sparks RSJ, Hawkesworth CJ, Eds.).:147-160., Washington, DCS.l.: American Geophysical Union ;International Union of Geodesy and Geophysics   10.1029/150GM13   Abstract
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Korte, M, Constable CG, Parker RL.  2002.  Revised magnetic power spectrum of the oceanic crust. Journal of Geophysical Research-Solid Earth. 107   10.1029/2001jb001389   AbstractWebsite

[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'Brien et al. [1999] to obtain a new, improved estimate of the crustal geomagnetic power spectrum. O'Brien et al. '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.

Cromwell, G, Constable CG, Staudigel H, Tauxe L, Gans P.  2013.  Revised and updated paleomagnetic results from Costa Rica. Geochemistry Geophysics Geosystems. 14:3379-3388.   10.1002/ggge.20199   AbstractWebsite

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.

Korte, M, Brown MC, Gunnarson SR, Nilsson A, Panovska S, Wardinski I, Constable CG.  2019.  Refining Holocene geochronologies using palaeomagnetic records. Quaternary Geochronology. 50:47-74.   10.1016/j.quageo.2018.11.004   AbstractWebsite

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.

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.

Johnson, CL, Constable CG, Tauxe L, Barendregt R, Brown LL, Coe RS, Layer P, Mejia V, Opdyke ND, Singer BS, Staudigel H, Stone DB.  2008.  Recent investigations of the 0-5 Ma geomagnetic field recorded by lava flows. Geochemistry Geophysics Geosystems. 9   10.1029/2007gc001696   AbstractWebsite

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.

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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.