Harmonic splines for geomagnetic modelling

Shure, Loren; Parker, Robert L.; Backus, George E.

doi:10.1016/0031-9201(82)90003-6

Cited by 215 publications

(141 citation statements)

References 16 publications

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“…It is, however, possible to find a suitable solution by minimization of an objective functional (m) containing two terms, the first Q(m) that corresponds to some measure of the misfit between the observations and the model predictions (d − f (m)), and the second R(m) that measures the complexity of the model (e.g. Shure et al 1982;Gubbins & Bloxham 1985;Gubbins 2004):…”

Section: Inversion Proceduresmentioning

confidence: 99%

Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models

Panovska

Korte

Finlay

et al. 2015

Geophysical Journal International

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S U M M A R YCharacterization 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 timevarying 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...

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Section: Inversion Proceduresmentioning

confidence: 99%

Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models

Panovska

Korte

Finlay

et al. 2015

Geophysical Journal International

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“…VOORHIES (1986), and Huang and Harrison (in preparation) argue that the deviation of the locations of null flux lines obtained by Bloxham and Gubbins are incorrectly calculated and consequently, are unreasonably small; therefore, the conclusion of Bloxham and Gubbins that the frozen flux hypothesis should be rejected is very likely to be misleading. SHURE et al (1982SHURE et al ( , 1985 developed harmonic spline models, using a constraint that minimizes the field roughness at the CMB. Although their model may better represent the core field at the earth's surface, it would certainly filter out the small features of the field at CMB.…”

Section: Pattern Of the Field At The Core Mantle Boundarymentioning

confidence: 99%

“…Since the observations of the magnetic field at the surface are not perfect, in that they have errors and do not cover the Earth uniformly, there are errors in determining the spherical harmonic coefficients which increase with the degree of harmonic. SHURE et al (1982) investigated functions which were smooth in some sense at the core-mantle boundary but which fitted the surface data to within some specified accuracy. They showed that the power within the lower degrees of harmonic for their smooth function was very similar to the power obtained from the normal spherical harmonic analysis, whereas at higher degrees, their smooth functions gave lower power.…”

Section: Introductionmentioning

confidence: 99%

Rates of change of the Earth's magnetic field measured by recent analyses.

Harrison

Huang

1990

J. geomagn. geoelec

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The availability of accurate representations of the Earth's magnetic field for the past 25 years allows us to study the typical rates of change of the field as a function of the degree of the spherical harmonic. It is shown that there is a general increase in the relative rate of change as the degree of harmonic is increased. The analysis was only carried out to degree eight harmonics, because knowledge of the rate of change of the higher degrees is poor. If the projected rate of change continues in the same manner for higher degrees, then it is predicted that harmonics of, say, degree 14 will change at a rate of about 6% per year. This will mean that it should be easy to determine whether harmonics higher than degree fourteen originate in the core or whether they are caused by crustal magnetization. Although westward drift of the field does not necessarily tell us about motions of the core fluid at the core mantle boundary, it is probably true that these motions depend on the same parameters as those used to determine the westward drift. Since the westward drift depends on the longitudinal gradient of the component of field under consideration, it generally depends more on the higher orders of harmonic within each degree than on the lower orders, all other things being equal. In fact, not all other things are equal, because it is shown that in general the power in the higher orders of harmonic is less than the power in the lower orders. Another important factor in determining longitudinal motions is that it is the field at the core mantle boundary which is important, not the field at the Earth's surface. This results in the higher degrees being relatively more important than at the surface of the Earth. But because of the longitudinal differentiation, it turns out that in order to determine a major portion of the longitudinal drift it is necessary to have information about harmonics up to about degree 20. Therefore, with knowledge only of degrees eight or less, we really know rather little about longitudinal motions. Evidence for secular acceleration was found. Not surprisingly, the average rate of secular acceleration

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“…For the last four of the anomaly fields, we used the method of depleted basis harmonic splines Shure et al, 1982) to downward continue, using satellite data alone and jointly modeling the satellite and EPB data (Whaler, 1994;Langel and Whaler, 1996). The method is described in detail in Langel and Hinze (1998, chapter 5).…”

Section: Correlationmentioning

confidence: 99%

Compatibility of high-altitude aeromagnetic and satellite-altitude magnetic anomalies over Canada

et al. 2002

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Results from equivalent-source distributions derived jointly from high-altitude (average 4 km) aeromagnetic and Magsat-derived (average 400 km) magnetic anomalies over Canada indicate that long-wavelength components (500–2500 km) in these fields are extremely compatible with one another (with a correlation coefficient of 0.95). The jointly estimated anomaly field at the earth's surface can be used as a long-wavelength adjustment surface for regional near-surface magnetic anomaly compilations and in assessing the performance of other downward-continuation techniques. Because near-surface anomalies are not available over all regions of the world, we compare the jointly estimated anomaly field to the results of two different downward-continuation techniques: the evaluation of anomalies at the earth's surface from spherical harmonic coefficients derived from satellite-altitude data and the use of downward-continuation methods based on harmonic splines. Numerical and visual comparisons of these downward- continued fields with the jointly estimated anomaly field from the equivalent-source method indicate they are well correlated and could provide a useful method of deriving long-wavelength leveling surfaces for regional and worldwide magnetic anomaly maps.

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Harmonic splines for geomagnetic modelling

Cited by 215 publications

References 16 publications

Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models

Limitations in paleomagnetic data and modelling techniques and their impact on Holocene geomagnetic field models

Rates of change of the Earth's magnetic field measured by recent analyses.

Compatibility of high-altitude aeromagnetic and satellite-altitude magnetic anomalies over Canada

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