General 2D gravity inversion with density contrast varying with depth

An algorithm is presented for computing the gravitational attraction of a two-dimensional polygon whose density is a polynomial function of depth. The contribution of each side and its partial derivatives with respect to the vertex coordinates are expressed analytically, and they contain only powers of the z-coordinates and the same logarithm and arctangent terms used with homogeneous polygons; thus, both direct and inverse calculations can be efficiently performed. A variant using rectangular blocks permits also to handle lateral density changes.

The case of an exponential density-depth function is covered by a series expansion, and bounds of error are given in order to select the proper number of terms.

In the application to a real case, the determination of the basement of a deep sedimentary basin serves to compare the performance of different density-depth estimates.