Computational algorithm for the continuation of potential fields towards gravitating masses

P. N. Vabishchevich

Numerical methods and programming, Tome 25 (2024) no. 1, pp. 1-9

Résumé

The continuation of potential fields from the Earth's surface into the depths is the most important problem in gravity exploration. Based on the solution of such a problem, the location of gravity field anomalies is identified. The solution of the integral equation of the first kind with the application of some regularization procedures is often used for the approximate solution of the problem of the continuation of potential fields. A similar approach is used in our work when the continued field is represented as a simple layer potential or its vertical derivative. The density of the equivalent simple layer potential is positive (negative) for positive (negative) density anomalies, provided that the surface of the equivalent simple layer potential contains all of the anomalies. The consideration of this property is a key feature of the proposed calculation algorithm for continuation of potential fields with respect to anomalies. The determination of the non-negative density of the simple layer potential is based on the NNLS (Non-Negative Least Squares) method. The efficiency of the developed computational algorithm is illustrated by calculating two-dimensional problems.

Détail

Keywords: anomalous gravitational field, method of integral equations, simple layer potential, method of least squares.