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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.

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.

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.

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
Korte, M, Donadini F, Constable CG.  2009.  Geomagnetic field for 0-3 ka: 2. A new series of time-varying global models. Geochemistry Geophysics Geosystems. 10   10.1029/2008gc002297   AbstractWebsite

Steadily increasing numbers of archeomagnetic and paleomagnetic data for the Holocene have allowed development of temporally continuous global spherical harmonic models of the geomagnetic field extending present and historical global descriptions of magnetic field evolution. The current work uses various subsets of improved data compilations, details of which are given in a companion paper by Donadini et al. (2009), and minor modifications of standard modeling strategies (using temporally and spatially regularized inversion of the data and cubic spline parameterizations for temporal variations) to produce five models with enhanced spatial and temporal resolution for 0-3 ka. Spurious end effects present in earlier models are eliminated by enforcing large-scale agreement with the gufm1 historical model for 1650-1990 A.D. and by extending the model range to accommodate data older than 3 ka. Age errors are not considered as a contribution to data uncertainties but are included along with data uncertainties in an investigation of statistical uncertainty estimates for the models using parametric bootstrap resampling techniques. We find common features but also significant differences among the various models, indicating intrinsic uncertainties in global models based on the currently available Holocene data. Model CALS3k.3 based on all available archeomagnetic and sediment data, without a priori quality selection, currently constitutes the best global representation of the past field. The new models have slightly higher dipole moments than our previous models. Virtual axial dipole moments (VADMs) calculated directly from the data are in good agreement with all corresponding model predictions of VADMs. These are always higher than the spherical harmonic dipole moment, indicating the limitations of using VADMs as a measure of geomagnetic dipole moments.

Korte, M, Constable CG.  2006.  On the use of calibrated relative paleointensity records to improve millennial-scale geomagnetic field models. Geochemistry Geophysics Geosystems. 7   10.1029/2006gc001368   AbstractWebsite

[ 1] Current millennial-scale time-varying global geomagnetic field models suffer from a lack of intensity data compared to directional data, because only thermoremanently magnetized material can provide absolute information about the past field strength. The number of archeomagnetic artifacts that can provide such data diminishes rapidly prior to 3000 B. C. Sediment cores provide time series of declination and inclination and of variations of magnetization: the latter can reflect relative geomagnetic field variations if suitably normalized. We propose a calibration technique based on predictions from global models and use the CALS7K. 2 model to calibrate relative paleointensity records from 22 globally distributed locations and assess whether they reflect actual field variations. All except a few contain useful information for 0 to 7 ka and could be used to improve the existing models. Using synthetic data from a numerical dynamo simulation, we show that with the existing directional data the distribution of intensity data has an important influence on model quality. Intensity data from a broad range of latitudes seem particularly important. This study opens the possibility of extending global time-varying geomagnetic field models further back in time than the current 7 kyr interval.

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

The aperiodic nature of geomagnetic field variations, both in intensity and direction, can aid in dating archaeological artefacts, volcanic rocks, and sediment records that carry a palaeomagnetic signal. The success of palaeomagnetic dating relies upon our knowledge of past field variations at specific locations. Regional archaeo- and palaeomagnetic reference curves and predictions from global geomagnetic field models provide our best description of field variations through the Holocene. State-of-the-art palaeomagnetic laboratory practices and accurate independent age controls are prerequisites for deriving reliable reference curves and models from archaeological, volcanic, and sedimentary palaeomagnetic data. In this review paper we give an overview of these prerequisites and the available reference curves and models, discuss techniques for palaeomagnetic dating, and outline its limitations. In particular, palaeomagnetic dating on its own cannot give unique results, but rather serves to refine or confirm ages obtained by other methods. Owing to the non-uniform character of magnetic field variations in different regions, care is required when choosing a palaeomagnetic dating curve, so that the distance between the dating curve and the record to be dated is not too large. Accurate reporting and incorporation of new, independently dated archaeo- and palaeomagnetic results into databases will help to improve reference curves and global models for all regions on Earth.

Korte, M, Constable 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.

Korte, M, Constable C.  2011.  Improving geomagnetic field reconstructions for 0-3 ka. Physics of the Earth and Planetary Interiors. 188:247-259.   10.1016/j.pepi.2011.06.017   AbstractWebsite

Global geomagnetic field reconstructions on millennial time scales can be based on comprehensive paleomagnetic data compilations but, especially for older data, these still suffer from limitations in data quality and age controls as well as poor temporal and spatial coverage. Here we present updated global models for the time interval 0-3 ka where additions to the data basis mainly impact the South-East Asian, Alaskan, and Siberian regions. We summarize recent progress in millennial scale modelling, documenting the cumulative results from incremental modifications to the standard algorithms used to produce regularized time-varying spherical harmonic models spanning 1000 BC to 1990 AD: from 1590 to 1990 AD gauss coefficients from the historical gufm1 model supplement the paleomagnetic information; in addition to absolute paleointensities, calibrated relative paleointensity data from sediments are now routinely included; iterative data rejection and recalibration of relative intensity records from sediments ensure stable results; bootstrap experiments to generate uncertainty estimates for the model take account of uncertainties in both age and magnetic elements and additionally assess the impact of sampling in both time and space. Based on averaged results from bootstrap experiments, taking account of data and age uncertainties, we distinguish more conservative model estimates CALS3k.nb representing robust field structure at the core-mantle boundary from relatively high resolution models CALS3k.n for model versions n = 3 and 4. We assess the impact of newly available data and modifications to the modelling method by comparing the previous CALS3k.3, the new CALS3k.4, and the conservative new model, CALS3k.4b. We conclude that with presently available data it is not feasible to produce a model that is equally suitable for relatively high-resolution field predictions at Earth's surface and robust reconstruction of field evolution, avoiding spurious structure, at the core-mantle boundary (CMB). We presently consider CALS3k.4 the best high resolution model and recommend the more conservative lower resolution version for studies of field evolution at the CMB. (C) 2011 Elsevier B.V. All rights reserved.

Korte, M, Constable CG, Parker RL.  2002.  Revised magnetic power spectrum of the oceanic crust. Journal of Geophysical Research-Solid Earth. 107   10.1029/2001jb001389   AbstractWebsite

[1] The magnetic field originating within the Earth can be divided into core and crustal components, which can be characterized by the geomagnetic power spectrum. While the core spectrum is determined quite well by satellite studies, models of the shorter wavelength crustal spectrum disagree considerably. We reexamine aeromagnetic data used by O'Brien et al. [1999] to obtain a new, improved estimate of the crustal geomagnetic power spectrum. O'Brien et al. 's model somewhat failed to give a satisfactory connection between the longer-wavelength satellite studies and a reliable crustal model. We show that this was caused by an inadequate processing step that aimed to remove external variations from the data. We moreover attempt to bound the long-wavelength part of the spectrum using constraints of monotonicity in the correlation of the magnetization. However, this proves to be a weak constraint. Reversing the process, though, we are able to evaluate the correlation function using the reliable part of our geomagnetic spectrum. Thus we can obtain a sensible estimate for the long-wavelength part of the spectrum that is not well constrained by the data. Our new model shows better agreement with earlier satellite studies and can be considered reliable in the spherical harmonic degree range l = 30 to 1200.

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.

Korte, M, Constable CG.  2005.  Continuous geomagnetic field models for the past 7 millennia: 2. CALS7K. Geochemistry Geophysics Geosystems. 6   10.1029/2004gc000801   AbstractWebsite

We present two continuous global geomagnetic field models for recent millennia: CALS3K.2, covering the past 3000 years, and CALS7K.2, covering 7000 years from 5000 BC to 1950 AD. The models were determined by regularized least squares inversion of archeomagnetic and paleomagnetic data using spherical harmonics in space and cubic B splines in time. They are derived from a greatly increased number of paleomagnetic directional data, compared to previous efforts, and for the first time a significant amount of archeointensity data is used in this kind of global model, allowing the determination of evolution of geomagnetic dipole strength. While data accuracy and dating uncertainties remain a limitation, reliable low-resolution global models can be obtained. The results agree well with previous results from virtual axial dipole moment (VADM) studies from archeomagnetic intensity data apart from a systematic offset in strength. A comparison of model predictions with the previous 3000 year model, CALS3K.1, gives general agreement but also some significant differences particularly for the early epochs. The new models suggest that the prominent two northern hemisphere flux lobes are more stationary than CALS3K.1 implied, extending considerably the time span of stationary flux lobes observed in historical models. Between 5000 BC and 2000 BC there are time intervals of weak dipole moment where dipole power is exceeded by low-degree nondipole power at the core-mantle boundary.

Korte, M, Constable C, Donadini F, Holme R.  2011.  Reconstructing the Holocene geomagnetic field. Earth and Planetary Science Letters. 312:497-505.   10.1016/j.epsl.2011.10.031   AbstractWebsite

Knowledge of the Holocene evolution of Earth's magnetic field is important for understanding geodynamo processes in the core, is necessary for studying long-term solar-terrestrial relationships, and can provide useful age constraints for archeologicaland stratigraphic applications. Continuous time-varying global field models based on archeo- and paleomagnetic data are useful tools in this regard. We use a comprehensive data compilation and recently refined modelling strategies to produce CALS10k.1b, the first time-varying spherical harmonic geomagnetic field model spanning 10 ky. The model is an average obtained from bootstrap sampling to take account of uncertainties in magnetic components and ages in the data (and hence has version number 1b instead of 1). This model shows less spatial and temporal resolution than earlier versions for 0-3 ka, and particularly aims to provide a robust representation of the large-scale field at the core-mantle boundary (CMB). We discuss the geomagnetic dipole evolution and changes in Holocene magnetic field morphology at the CMB as shown by the new reconstruction. The results are compatible with earlier models (CALS3k.3 and CALS3k.4) for 0-3 ka, but reveal some clear deficiencies in the 0-7 ka CALS7K.2 model prior to 3 ka. CALS10k.1b is able to resolve mobile and structurally-evolving high latitude radial field flux lobes at the CMB in both hemispheres, as well as persistent non-zonal structure, in the 10 ky average. Contributions to the average field from time-varying structures in the equatorial Indonesian-Australian region are particularly striking. (C) 2011 Elsevier B.V. All rights reserved.

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 The whole package is also stored in the Earthref digital archive at (C) 2003 Elsevier B.V. All rights reserved.