Direct methods for the interpretation of gravity and magnetic field anomalies have been developed and applied to interpret marine geophysical surveys of the Caribbean eastern margin and the Sierra Leone continental shelf. The gravity interpretation programs compute, under certain constraints to remove inherent ambiguity, the space form of the body producing a specified gravity anomaly. The computed body is built up from a set of two-dimensional trapesia thus producing a geologically realistic model. The programs can interpret interfering anomalies, caused by adjacent bodies and anomalies due. to bodies v/ith a known lateral variation in density. The method is based on an equivalent layer technique, the non-linear problem being solved by repeated solution of a linear integral equation, which is approximated by a finite set of linear algebraic equations. The technique has been extended to three dimensional analysis, the source body being built up from a set of rectangular prisms. The magnetic interpretation method is basically similar to the gravity method, but it is necessary to compute the dip of the body magnetisation vector before a solution can be obtained for the body space form. The programs have been used, to interpret a marine gravity survey of the south eastern Caribbean margin. The gravity data is used to determine the possible crustal structure, between points here the structure is known from seismic refraction data. Conclusions are drawn on the generalised crustal structure of the region and on the southward extension of the Lesser Antilles Island arc and the Barbados Ridge. A marine gravity survey of the Sierra Leone Continental Shelf has been interpreted using the programs developed. The space form of the Freetown Complex, a layered gabbroic intrusion, and its extension onto the continental shelf are determined
