Spherical prism gravity effects by Gauss-Legendre quadrature integration

Satellite-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.