Spectral gravity forward modelling of 3D variable densities using an arbitrary integration radius with application to lunar topographic masses

Spectral gravity forward modelling delivers gravitational fields of mass distributions by evaluating Newton’s integral in the spectral domain. We generalize its spherical harmonic variant to 3D variable densities and to any integration radius. The former is achieved by expressing the density function as an infinite-degree polynomial in the radial direction with polynomial coefficients varying laterally as a bounded function. The latter generalization builds on Molodensky’s truncation coefficients and allows to evaluate gravitational contribution of masses found up to and beyond some integration radius. In a numerical study, we forward-model lunar topographic masses by first assuming constant and then 3D variable density. Our validation with respect to GRAIL-based models shows that the 3D density model yields superior gravitational field compared to the constant density model. Thanks to the efficiency of FFT-based spherical harmonic transforms, the new technique can be employed in high-resolution modelling of topographic potentials. A numerical implementation is made available through CHarm, which is a C/Python library for high-degree spherical harmonic transforms accessible at https://github.com/blazej-bucha/charm.