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2015
Panovska, S, Korte M, Finlay CC, Constable CG.  2015.  Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models. Geophysical Journal International. 202:402-418.   10.1093/gji/ggv137   AbstractWebsite

Characterization of geomagnetic field behaviour on timescales of centuries to millennia is necessary to understand the mechanisms that sustain the geodynamo and drive its evolution. As Holocene paleomagnetic and archeomagnetic data have become more abundant, strategies for regularized inversion of modern field data have been adapted to produce numerous time-varying global field models. We evaluate the effectiveness of several approaches to inversion and data handling, by assessing both global and regional properties of the resulting models. Global Holocene field models cannot resolve Southern hemisphere regional field variations without the use of sediments. A standard data set is used to construct multiple models using two different strategies for relative paleointensity calibration and declination orientation and a selection of starting models in the inversion procedure. When data uncertainties are considered, the results are similar overall regardless of whether we use iterative calibration and reorientation, or co-estimation of the calibration and orientation parameters as part of the inversion procedure. In each case the quality of the starting model used for initial relative paleointensity calibration and declination orientation is crucial and must be based on the best absolute information available. Without adequate initial calibration the morphology of dipole moment variations can be recovered but its absolute value will be correlated with the initial intensity calibrations, an effect that might be mitigated by ensuring an appropriate fit to enough high quality absolute intensity data with low uncertainties. The declination reorientation mainly impacts regional field structure and in the presence of non-zonal fields will result in a non-zero local average. The importance of declination orientation is highlighted by inconsistencies in the West Pacific and Australian sediment records in CALS10k.1b model. Great care must also be taken to assess uncertainties associated with both paleomagnetic and age data and to evaluate the effects of poor data distribution. New consistently allocated uncertainty estimates for sediment paleomagnetic records highlight the importance of adequate uncertainties in the inversion process, as they determine the relative weighting among the data and overall normalized misfit levels which in turn influence the complexity of the inferred field models. Residual distributions suggest that the most appropriate misfit measure is the L-1 norm (minimum absolute deviation) rather than L-2 (least squares), but this seems to have relatively minor impact on the overall results. For future Holocene field modelling we see a need for comprehensive methods to assess uncertainty in individual archeomagnetic data so that these data or models derived from them can be used for reliable initial relative paleointensity calibration and declination orientation in sediments. More work will be needed to assess whether co-estimation or an iterative approach to inversion is more efficient overall. This would be facilitated by realistic and globally consistent data and age uncertainties from the paleomagnetic community.

2011
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.

2008
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.

2006
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.

2003
Korte, M, Constable C.  2003.  Continuous global geomagnetic field models for the past 3000 years. Physics of the Earth and Planetary Interiors. 140:73-89.   10.1016/j.pepi.2003.07.013   AbstractWebsite

Several global geomagnetic field models exist for recent decades, but due to limited data availability models for several centuries to millennia are rare. We present a continuous spherical harmonic model for almost 3 millennia from 1000 B.C. to 1800 A.D., based on a dataset of directional archaeo- and paleomagnetic data and axial dipole constraints. The model, named Continuous Archaeomagnetic and Lake Sediment Geomagnetic Model for the last 3k years (CALS3K.1), can be used to predict both the field and secular variation. Comparisons and tests with synthetic data lead to the conclusion that CALS3K.1 gives a good general, large-scale representation of the geomagnetic field, but lacks small-scale structure due to the limited resolution of the sparse dataset. In future applications the model can be used for comparisons with additional, new data for that time span. For better resolved regions, the agreement of data with CALS3K.1 will provide an idea about the general compatibility of the data with the field and secular variation in that region of the world. For poorly covered regions and time intervals we hope to iteratively improve the model by comparisons with and inclusion of new data. Animations and additional snapshot plots of model predictions as well as the model coefficients and a FORTRAN code to evaluate them for any time can be accessed under http://www.mahi.ucsd.edu/cathy/Holocene/holocene.html. The whole package is also stored in the Earthref digital archive at http://www.earthref.org/... (C) 2003 Elsevier B.V. All rights reserved.