Publications

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Book
Backus, G, Parker RL, Constable C.  1996.  Foundations of geomagnetism. :xiv,369p.., Cambridge England ; New York: Cambridge University Press AbstractWebsite

The main magnetic field of the Earth is a complex phenomenon. To understand its origins in the fluid of the Earth'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' 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.

Backus, G, Parker RL, Constable C.  2005.  Foundations of geomagnetism. :xiv,369p.., Cambridge ; New York: Cambridge University Press AbstractWebsite
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Book Chapter
Constable, CG.  2007.  Centennial to millennial-scale geomagnetic field variations. Treatise on geophysics. 5( Kono M, Schubert G, Eds.).:337-372., Amsterdam ; Boston: Elsevier Abstract
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Constable, C.  2007.  Dipole moment variation. Encyclopedia of geomagnetism and paleomagnetism. ( Gubbins D, Herrero-Bervera E, Eds.).:159-161., Dordrecht: Springer Abstract
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Constable, CG.  2003.  Geomagnetic Reversals: Rates, Timescales, Preferred Paths, Statistical Models, and Simulations. Earth's core and lower mantle: Fluid mechanics of astrophysics and geophysics. ( Jones CA, Soward AM, Zhang K, Eds.).:77-99., London ; New York: Taylor & Francis Abstract
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Constable, C.  2007.  Geomagnetic temporal spectrum. Encyclopedia of geomagnetism and paleomagnetism. ( Gubbins D, Herrero-Bervera E, Eds.).:353-355., Dordrecht: Springer Abstract
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Constable, C.  2007.  Non-dipole field. Encyclopedia of geomagnetism and paleomagnetism. ( Gubbins D, Herrero-Bervera E, Eds.).:701-704., Dordrecht: Springer Abstract
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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 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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Journal Article
Panovska, S, Constable CG.  2017.  An activity index for geomagnetic paleosecular variation, excursions, and reversals. Geochemistry Geophysics Geosystems. 18:1366-1375.   10.1002/2016gc006668   AbstractWebsite

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.

Gee, JS, Tauxe L, Constable C.  2008.  AMSSpin: A LabVIEW program for measuring the anisotropy of magnetic susceptibility with the Kappabridge KLY-4S. Geochemistry Geophysics Geosystems. 9   10.1029/2008gc001976   AbstractWebsite

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.

Constable, CG, Tauxe L, Parker RL.  1998.  Analysis of 11 Myr of geomagnetic intensity variation. Journal of Geophysical Research-Solid Earth. 103:17735-17748.   10.1029/98jb01519   AbstractWebsite

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.

Constable, CG, Johnson CL.  1999.  Anisotropic paleosecular variation models: implications for geomagnetic field observables. Physics of the Earth and Planetary Interiors. 115:35-51.   10.1016/s0031-9201(99)00065-5   AbstractWebsite

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.

Johnson, CL, Wijbrans JR, Constable CG, Gee J, Staudigel H, Tauxe L, Forjaz VH, Salgueiro M.  1998.  Ar-40/Ar-39 ages and paleomagnetism of Sao Miguel lavas, Azores. Earth and Planetary Science Letters. 160:637-649.   10.1016/s0012-821x(98)00117-4   AbstractWebsite

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.

Genevey, A, Gallet Y, Constable CG, Korte M, Hulot G.  2008.  ArcheoInt: An upgraded compilation of geomagnetic field intensity data for the past ten millennia and its application to the recovery of the past dipole moment. Geochemistry Geophysics Geosystems. 9   10.1029/2007gc001881   AbstractWebsite

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.

Korte, M, Constable CG.  2018.  Archeomagnetic intensity spikes: Global or regional geomagnetic field features? Frontiers in Earth Science. 6   10.3389/feart.2018.00017   AbstractWebsite

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.

McMillan, DG, Constable CG, Parker RL.  2004.  Assessing the dipolar signal in stacked paleointensity records using a statistical error model and geodynamo simulations. Physics of the Earth and Planetary Interiors. 145:37-54.   10.1016/j.pepi.2004.02.011   AbstractWebsite

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.

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.

Avery, MS, Gee JS, Constable CG.  2017.  Asymmetry in growth and decay of the geomagnetic dipole revealed in seafloor magnetization. Earth and Planetary Science Letters. 467:79-88.   10.1016/j.epsl.2017.03.020   AbstractWebsite

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'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.

Constable, C, Tauxe L.  1990.  The Bootstrap for Magnetic Susceptibility Tensors. Journal of Geophysical Research-Solid Earth and Planets. 95:8383-8395.   10.1029/JB095iB06p08383   AbstractWebsite

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.

Constable, C.  1992.  The Bootstrap for Magnetic-Susceptibility Tensors - Reply. Journal of Geophysical Research-Solid Earth. 97:13997-13998.   10.1029/92jb00745   AbstractWebsite
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Tauxe, L, Kylstra N, Constable C.  1991.  Bootstrap Statistics for Paleomagnetic Data. Journal of Geophysical Research-Solid Earth and Planets. 96:11723-11740.   10.1029/91jb00572   AbstractWebsite

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.

Korte, M, Constable CG.  2006.  Centennial to millennial geomagnetic secular variation. Geophysical Journal International. 167:43-52.   10.1111/j.1365-246X.2006.03088.x   AbstractWebsite

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.

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, Genevey A, Constable CG, Frank U, Schnepp E.  2005.  Continuous geomagnetic field models for the past 7 millennia: 1. A new global data compilation. Geochemistry Geophysics Geosystems. 6   10.1029/2004gc000800   AbstractWebsite

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.