Abstract  The decrease of density contrast with depth in sedimentary basins is approximated by an exponential function. The anomaly equation, in frequency domain, of a prismatic model with an exponential density function is derived. The method has been extended to derive the Fourier transforms of the gravity anomalies of the sedimentary basin, wherein the basin is viewed as vertical prisms placed in juxtaposition. The gravity anomalies of the sedimentary basin are obtained by taking the inverse Fourier transforms. Filon’s method has been extended for calculating accurate inverse Fourier transforms. The accuracy of the method has been tested using a synthetic example. A combination of space and frequency domain methods have been developed for inversion of gravity anomalies over the sedimentary basin. The method has been applied to interpret one synthetic profile and one field profile over the Godavari basin. The method developed in this paper to calculate the inverse Fourier transforms yields continuous spectrum with accurate values. The maximum depth deduced from the gravity anomalies is of the same order as the depth encountered to the basement at the Aswaraopeta borewell.