A novel algorithm and software for efficient global gravimetric forward modeling in the spherical coordinate system

Abstract

We present a novel algorithm and complementary software for the global gravimetric forward modeling that accommodates masses with complex shapes and density distributions defined in the frame of spherical coordinates. Traditional gravimetric forward modeling techniques often face significant challenges when dealing with irregularly shaped bodies and complex density variations, leading to high computational costs and long processing times. To address these practical limitations, we introduce an innovative algorithm that divides the 3-D mass-density body into spherical concentric rings with equal intervals in the radial direction, while discretizing the latitudinal and longitudinal directions into a grid with equal intervals. After discretization, we assume that each spherical volumetric mass ring has a laterally varying density and constant upper and lower bounds. Based on this approach, the gravitational field at any point outside the Earth is evaluated as the sum of the gravitational contributions generated by each concentric ring. This discretization allows applying the Fast Fourier Transform (FFT) technique to drastically improve computational efficiency of the spherical harmonic analysis and synthesis. Numerical results are validated against corresponding solutions obtained using the tesseroid method in the spatial domain. The comparison of results reassures a high accuracy of proposed method, with relative differences between results obtained from both methods less than 1 % and 4 % for the gravitational attraction and gradient respectively, while significantly improving the numerical efficiency. When modelling the gravitational field quantities of very complex structures by means of their geometry and density distribution, such as the Earth's crustal density structure, the numerical efficiency improved several orders of magnitude.