An Automated Method of Gravity Interpretation

Abstract

The interpretation of an observed gravity anomaly in terms of an anomalous mass with irregular outline and with uniform density contrast requires the solution of a non-linear problem. It is possible to iterate this non-linear problem by means of a linear approximation, provided some assumption is made about one of the surfaces of the anomalous mass. This paper gives such a method. If there are m observations of a gravity anomaly and if the anomalous mass is assumed to be subdivided into n two-dimensional rectangular blocks (n⩽m) then a set of linear equations can be solved—directly if m=n, and by least squares if m > n—to give a system of blocks of variable density contrast which satisfy, or nearly satisfy in the case of the least squares solution, the observed gravity anomaly. These blocks are then transformed to give blocks of uniform density contrast. Because the gravity effect is non-linear the transformed blocks will not usually satisfy the observed anomaly. It is, therefore, necessary to adjust the model using the same general method. Two computer programs applying respectively to structures with inward dipping contacts and to structures with outward dipping contacts have been developed. The formulae used in the programs apply to two-dimensional structures, but three-dimensional structures are approximated by end corrections.