Earth, Planets and Space (Apr 2017)
Utility of Slepian basis functions for modeling near-surface and satellite magnetic anomalies of the Australian lithosphere
Abstract
Abstract The utility of frequency- and space-limited spherical harmonic Slepian basis functions for magnetic anomaly modeling over restricted spherical patches of the Earth was investigated using combined near-surface scalar and CHAMP satellite vector observations from Australia and adjacent marine areas. In particular, Slepian spherical harmonic models up to degree 360 were studied for modeling anomaly features of 1° (~111 km) and longer over a 25°-radius cap centered on Australia. Relative to the roughly 130,000 coefficients required for global spherical harmonic modeling, less than 5% of this number of coefficients is sufficient for effective localized Slepian modeling. Slepian coefficients have maximum power over the spherical cap and may be exploited for estimating the magnetic anomaly vectors and gradients to all orders within the working precision of the observations. The Earth cap modeled by Slepian coefficients is also more efficient in accommodating local crustal constraints from drilling and other geological and geophysical studies for interpreting the associated magnetic anomaly data registered in spherical coordinates. In general, Slepian spherical harmonic modeling is well suited for combining spectrally diverse compilations of near-surface and satellite magnetic observations over any spatially restricted spherical cap of the Earth or other planetary body. Graphical Abstract The utility of frequency- and space-limited Slepian spherical harmonic basis functions up to degree 360 was studied for modeling near-surface scalar and CHAMP satellite magnetic anomalies of 1° (~111 km) and longer over a 25°-radius cap centered on Australia. Slepian spherical harmonic modeling is well suited for combining spectrally divorce compilations of near-surface and satellite magnetic observations. It is also very efficient for updating global spherical harmonic models for new regional data and providing perspectives on how magnetic lithospheric anomalies vary up to satellite altitudes that are not available from standard upward and downward anomaly continuations. For example, Map A shows the Australians magnetic anomaly estimates at 10 km altitude from the Slepian model jointly constrained by near-surface and CHAMP satellite magnetic observations that minimize the differences between Maps B and C of upward continued near-surface and downward continued CHAMP data, respectively. Map D, on the other hand, shows the Slepian model estimates at 275 km altitude that minimize differences between Maps E and F of downward continued CHAMP and upward continued near-surface data, respectively. Any continuous, however, is not unique and subject to measurement and modeling errors so that its interpretation at location lacking observations requires considerable care.
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