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 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.
Highlights
The confirmation of lithospheric components in low Earth orbiting satellite magnetic observations spawned numerous investigations showing the enhanced interpretational utility of combined satellite and near-surface magnetic anomaly data (e.g., Hildenbrand et al 1996; Langel and Hinze 1998; von Frese et al 1999; Ravat et al 2002; Kim et al 2004; Hinze et al 2013)
The performance of our regional degree 360 joint Slepian spherical harmonic model S360 is summarized in Table 1, where the strong correlation coefficients (CC > 0.9) show the Slepian model predictions are in good phase agreement with the near-surface and satellite data
This study demonstrated the utility of localized Slepian basis functions to model near-surface low-pass-filtered total intensity and selected CHAMP satellite vector magnetic anomalies over a 25°-radius cap centered on Australia
Summary
The confirmation of lithospheric components in low Earth orbiting satellite magnetic observations spawned numerous investigations showing the enhanced interpretational utility of combined satellite and near-surface magnetic anomaly data (e.g., Hildenbrand et al 1996; Langel and Hinze 1998; von Frese et al 1999; Ravat et al 2002; Kim et al 2004; Hinze et al 2013). The shorter-wavelength near-surface anomalies from terrestrial, shipborne, and airborne magnetic surveys provide important constraints to augment lithospheric studies of the satellite magnetic data. The near-surface data, on the other hand, commonly suffer from corrupted longer-wavelength components due to measurement errors and non-uniform survey coverage so that satellite observations yield important regional anomaly constraints for lithospheric analysis
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