Efficient 3D large-scale forward-modeling and inversion of gravitational fields in spherical coordinates with application to lunar mascons

A novel efficient forward modeling algorithm of gravitational fields in spherical coordinates is developed for 3D large-scale gravity inversion problems. 3D Gauss-Legendre quadrature (GLQ) is used to calculate the gravitational fields of mass distributions discretized into tesseroids. Equivalence relations in the kernel matrix of the forward-modeling are exploited to decrease storage and computation time. The numerical investigations demonstrate that the computation time of the proposed algorithm is reduced by approximately two orders of magnitude, and the memory requirement is reduced by <i>N</i><i>^'_l</i> times compared with the traditional GLQ method, where <i>N</i><i>^'_l</i> is the number of model elements in the longitudinal direction. These significant improvements in computational efficiency and storage make it possible to calculate and store the dense Jacobian matrix in 3D large-scale gravity inversions. The equivalence relations could be equally applied to the Taylor series method or combined with the adaptive discretization to ensure high accuracies.