Inversion of gravity anomalies of three-dimensional density interfaces

Abstract

An inversion scheme to trace three-dimensional density interfaces from their gridded gravity anomalies is developed. The scheme requires the gravity anomaly values, profile and station spacings as the input, besides densities of the underlying and overlying materials and the mean or undisturbed depth to the interface. The scheme calculates the initial values of the depths to the interface below the internal grid points, and modifies them iteratively until a best fit is achieved between the observed and calculated anomaly values. The gravity anomalies of the density interface are generated by equating the material below the interface to a series of juxtaposing rectangular blocks, one centered below each of the internal gridded anomaly points. It is assumed that the interface flattens out to its undisturbed depth well ahead of the boundaries of the sampled area. The values of initial thicknesses of the prisms are calculated by equating the anomaly at a station to the algebraic sum of products of vertical gradients of gravity effects of the prisms and their thicknesses. The differences between the observed and calculated anomalies are then used to improve the thicknesses of the prisms by equating these differences to the algebraic sum of the products of the vertical gradients of gravity effects of prisms and increments to their thicknesses. The computer program, named GRAV3DIN coded in FORTRAN 77 and used to invert gravity anomalies of three-dimensional density interfaces, is presented.