Three-dimensional analysis of gravity anomalies of sedimentary basins by polygonal prismatic model with a quadratic density function

Abstract

The decrease of density contrast in sedimentary strata may be approximated by a quadratic function. A sedimentary basin may be considered as a number of horizontal polygonal prisms of finite thickness placed one over the other. Equations for the gravity anomaly of ann-sided polygon prism have been derived using a quadratic density function. A method has been developed for inversion of the gravity anomalies using a polygonal prismatic model. An analytical method has been employed for evaluating the necessary derivatives as the computing time by this method is much slower than by a numerical method. Approximate equations have been derived for rapid calculation of the anomalies and derivatives. Efficient computer programs have been developed for calculation of the anomalies and derivatives by an appropriate use of the exact and approximate equations. The depths to the polygon prisms constituting the basin are iteratively adjusted by minimizing the sum of the squares of the differences between the observed and calculated anomalies. These methods have been applied to analyze the Bouguer anomaly map of the Los Angeles basin, California.