S U M M A R YSatellite-measured regional gravity and terrain elevation data are becoming increasingly available for improving our understanding of the geological properties and history of the Earth, Moon, Mars, Venus and other planets. In assessing the geological significance of the existing and growing volumes of these regional data sets, there is great need for computing theoretical anomalous gravity fields from geological models in spherical coordinates. In the present study, we explicitly develop the elegant Gauss-Legendre quadrature formulation for numerically modelling the complete gravity effects (i.e. potential, vector and tensor gradient fields) of the spherical prism. As an application, we investigate the gradient components of the isostatic gravity anomalies that the upcoming Gravity Field and Steady State Ocean Circulation Explorer (GOCE) satellite mission is likely to map over a large tectonically active region of the Middle East centred on Iran.

SUMMARY Regional spherical coordinate observations of the Earth's crustal magnetic field components are becoming increasingly available from shipborne, airborne, and satellite surveys. In assessing the geological significance of these data, theoretical anomalous magnetic fields from geologic models in spherical coordinates need to be evaluated. This study explicitly develops the elegant Gauss–Legendre quadrature formulation for numerically modelling the complete magnetic effects (i.e. potential, vector and tensor gradient fields) of the spherical prism. We also use these results to demonstrate the magnetic effects for the crustal prism and to investigate the crustal magnetic effects at satellite altitudes for a large region of the Middle East centred on Iran.

Summary: CHAMP is recording state-of-the-art magnetic and gravity field observations at altitudes ranging over roughly 300 -550 km. However, anomaly continuation is severely limited by the non-uniqueness of the process and satellite anomaly errors. Indeed, our numerical anomaly simulations from satellite to airborne altitudes show that effective downward continuations of the CHAMP data are restricted to within approximately 50 km of the observation altitudes while upward continuations can be effective over a somewhat larger altitude range. The great unreliability of downward continuation requires that the satellite geopotential observations must be analyzed at satellite altitudes if the anomaly details are to be exploited most fully. Given current anomaly error levels, joint inversion of satellite and nearsurface anomalies is the best approach for implementing satellite geopotential observations for subsurface studies. We demonstrate the power of this approach using a crustal model constrained by joint inversions of near-surface and satellite magnetic and gravity observations for Maud Rise, Antarctica, in the southwestern Indian Ocean. Our modeling suggests that the dominant satellite altitude magnetic anomalies are produced by crustal thickness variations and remanent magnetization of the normal polarity Cretaceous Quiet Zone.

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