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Journal Article
Ziegler, LB, Constable CG, Johnson CL, Tauxe L.  2011.  PADM2M: a penalized maximum likelihood model of the 0-2 Ma palaeomagnetic axial dipole moment. Geophysical Journal International. 184:1069-1089.   10.1111/j.1365-246X.2010.04905.x   AbstractWebsite

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

Johnson, CL, Constable CG.  1996.  Palaeosecular variation recorded by lava flows over the past five million years. Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences. 354:89-141.   10.1098/rsta.1996.0004   AbstractWebsite

We present a new global palaeomagnetic database, comprising lava flows and thin intrusive bodies, suitable for studying palaeosecular variation and the time-averaged field. The database is presented in some detail in the appendix and is available oil-line from the authors. We review palaeosecular variation models to date, emphasizing the assumptions required and the rather arbitrary construction of many of these models, Preliminary studies of the statistical properties of the new database suggest that existing palaeosecular variation models are inadequate to explain the long-term temporal variations in the field. It is increasingly apparent that data distribution and duality are pivotal in determining the characteristics of the secular variation. The work presented here demonstrates the need for revised models of the time-averaged field structure for both normal and reverse polarities before reliable models for palaeosecular variation can be made.

Constable, CG, Tauxe L.  1987.  Paleointensity In The Pelagic Realm - Marine Sediment Data Compared With Archaeomagnetic And Lake Sediment Records. Geophysical Journal of the Royal Astronomical Society. 90:43-59.   10.1111/j.1365-246X.1987.tb00674.x   AbstractWebsite

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

Lawrence, KP, Tauxe L, Staudigel H, Constable CG, Koppers A, McIntosh W, Johnson CL.  2009.  Paleomagnetic field properties at high southern latitude. Geochemistry Geophysics Geosystems. 10   10.1029/2008gc002072   AbstractWebsite

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

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.

Tauxe, L, Constable C, Johnson CL, Koppers AAP, Miller WR, Staudigel H.  2003.  Paleomagnetism of the southwestern USA recorded by 0-5 Ma igneous rocks. Geochemistry Geophysics Geosystems. 4   10.1029/2002gc000343   AbstractWebsite

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

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

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

Constable, CG.  1988.  Parameter-Estimation In Non-Gaussian Noise. Geophysical Journal-Oxford. 94:131-142.   10.1111/j.1365-246X.1988.tb03433.x   AbstractWebsite

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

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

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

Johnson, CL, Constable CG.  1998.  Persistently anomalous Pacific geomagnetic fields. Geophysical Research Letters. 25:1011-1014.   10.1029/98gl50666   AbstractWebsite

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

Tauxe, L, Shaar R, Jonestrask L, Swanson-Hysell NL, Minnett R, Koppers AAP, Constable CG, Jarboe N, Gaastra K, Fairchild L.  2016.  PmagPy: Software package for paleomagnetic data analysis and a bridge to the Magnetics Information Consortium (MagIC) Database. Geochemistry, Geophysics, Geosystems. 17:2450-2463.   10.1002/2016GC006307   Abstract

The Magnetics Information Consortium (MagIC) database provides an archive with a flexible data model for paleomagnetic and rock magnetic data. The PmagPy software package is a cross-platform and open-source set of tools written in Python for the analysis of paleomagnetic data that serves as one interface to MagIC, accommodating various levels of user expertise. PmagPy facilitates thorough documentation of sampling, measurements, data sets, visualization, and interpretation of paleomagnetic and rock magnetic experimental data. Although not the only route into the MagIC database, PmagPy makes preparation of newly published data sets for contribution to MagIC as a byproduct of normal data analysis and allows manipulation as well as reanalysis of data sets downloaded from MagIC with a single software package. The graphical user interface (GUI), Pmag GUI enables use of much of PmagPy's functionality, but the full capabilities of PmagPy extend well beyond that. Over 400 programs and functions can be called from the command line interface mode, or from within the interactive Jupyter notebooks. Use of PmagPy within a notebook allows for documentation of the workflow from the laboratory to the production of each published figure or data table, making research results fully reproducible. The PmagPy design and its development using GitHub accommodates extensions to its capabilities through development of new tools by the user community. Here we describe the PmagPy software package and illustrate the power of data discovery and reuse through a reanalysis of published paleointensity data which illustrates how the effectiveness of selection criteria can be tested.

Clement, BM, Constable CG.  1991.  Polarity Transitions, Excursions and Paleosecular Variation of the Earths Magnetic-Field. Reviews of Geophysics. 29:433-442. AbstractWebsite
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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.