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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.

Davies, C, Constable C.  2017.  Geomagnetic spikes on the core-mantle boundary. Nature Communications. 8   10.1038/ncomms15593   AbstractWebsite

Extreme variations of Earth's magnetic field occurred in the Levant region around 1000 BC, when the field intensity rapidly rose and fell by a factor of 2. No coherent link currently exists between this intensity spike and the global field produced by the core geodynamo. Here we show that the Levantine spike must span >60 degrees longitude at Earth's surface if it originates from the core-mantle boundary (CMB). Several low intensity data are incompatible with this geometric bound, though age uncertainties suggest these data could have sampled the field before the spike emerged. Models that best satisfy energetic and geometric constraints produce CMB spikes 8-22 degrees wide, peaking at O(100) mT. We suggest that the Levantine spike reflects an intense CMB flux patch that grew in place before migrating northwest, contributing to growth of the dipole field. Estimates of Ohmic heating suggest that diffusive processes likely govern the ultimate decay of geomagnetic spikes.

Cromwell, G, Tauxe L, Staudigel H, Constable CG, Koppers AAP, Pedersen RB.  2013.  In search of long-term hemispheric asymmetry in the geomagnetic field : Results from high northern latitudes. Geochemistry Geophysics Geosystems. 14:3234-3249.   10.1002/ggge.20174   AbstractWebsite

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

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.

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.

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.

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.

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.

McMillan, DG, Constable CG.  2006.  Limitations in correlation of regional relative geomagnetic paleointensity. Geochemistry Geophysics Geosystems. 7   10.1029/2006gc001350   AbstractWebsite

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

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.

Constable, C, Korte M.  2006.  Is Earth's magnetic field reversing? Earth and Planetary Science Letters. 246:1-16.   10.1016/j.epsl.2006.03.038   AbstractWebsite

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

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.

Korte, M, Constable CG.  2005.  The geomagnetic dipole moment over the last 7000 years - new results from a global model. Earth and Planetary Science Letters. 236:348-358.   10.1016/j.epsl.2004.12.031   AbstractWebsite

Evolution of the geomagnetic field's dipole strength is studied by geomagnetists from global spherical harmonic models and by paleomagnetists using virtual (axial) dipole moments (VDM, VADM). Based on a recently published global model of the past 7000 yr we study whether these three dipole moment descriptions can be considered equivalent, and compare the results to previous global VADM studies and recent global model dipole moments. We conclude that VADM and VDM results averaged over centennial and millennial time scales are systematically higher than the true dipole moment by about 19%. The current dipole decrease is part of a process that has been going on for about 1700 yr. The average rate of decrease is lower than the current one, but has varied significantly so that the current rate cannot be regarded as exceptional. (c) 2005 Elsevier B.V. All rights reserved.

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.

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.