Gravitational attraction of a rectangular prism with depth-dependent density

Abstract

Abstract The gravity effect produced by two and three-dimensional bodies with nonuniform density contrast has been treated by several authors. One of the first attempts in this direction made by Cordell (1973), who developed a method to compute the gravity effect due to a two-dimensional prism whose density decreases exponentially with depth. A different approach was proposed by Murthy and Rao (1979). They extended the line-integral method to obtain the gravity effect for bodies of arbitrary cross-sections, with density contrast varying linearly with depth. Chai and Hinze (1988) have derived a wavenumber-domain approach to compute the gravity effect due to a vertical prism whose density contrast varies exponentially with depth. Recently, Rao (1990) has developed a closed expression of the gravity field produced by an asymmetrical trapezoidal body whose density varies with depth following a quadratic polynomial.