The gravity anomaly of two‐dimensional sources with continuous density distribution and bounded by continuous surfaces

Abstract

The gravity anomaly of a complicated two‐dimensional (2-D) source having arbitrary surfaces and density varying in either horizontal or vertical direction is calculated using a combination of closed form solutions and numerical integration. The surfaces and density can be defined by continuous or piecewise continuous two‐dimensional functions in the integration interval. For example, the anomalies for intrusions or folded sedimentary units, having an arbitrary density in the horizontal direction and a polynomial density distribution in the vertical direction, can be calculated using surfaces represented by functions of the horizontal dimension. When modeling dipping layered intrusions or sedimentary beds the surfaces are represented by functions of the vertical dimension in which case the density can be an arbitrary function of depth and a polynome function of horizontal coordinate. The accuracy of the method is defined by the user. The method gives simple and general equations to calculate anomalies of complicated sources which have no closed form solution, thus reducing the number of algorithms needed in interpretation programs.