A finite element method for computation of the regional gravity anomaly

A regional gravity anomaly, based on element shape functions used in finite element analysis, is developed. The regional gravity is approximated by a weighted sum of discrete gravity values at eight stations coinciding with the eight nodes of a second-order or at twelve stations coinciding with the twelve nodes of a third-order isoparametric element superimposing the map space. The computations are carried out on a reference space with the shape functions acting as weighting factors, and subsequently translated to the real map space. In this technique, no observed gravity data lying inside the survey area enter into the regional computation. Tests on the gravity field in Harris County, Texas, a well known hydrocarbon prospect during the 1940s, and the Klamath Mountains and the Cascade Range in California confirmed the efficacy of this method.