Spectral-Element Simulations of Gravity Anomalies for 3D Topography Model

Gravity anomalies including the gravity field and its gradient are governed by the 3D gravitational potential boundary value problem. When the gravity field vector and its gradient tensor are calculated from the gravitational potential boundary based on the integral solution or conventional numerical approaches, they will inevitably lose effectiveness and high accuracy, especially with 3D topography. In this letter, we introduce an efficient and accurate high-order spectral-element approach for simulating 3D gravity anomalies including surface topography. This new method is based on the spectral element technique of hexahedral grids to discretize the 3D Poisson equation of gravitational potential. To solve the gravitational potential variational problem that converted to the boundary value problem, we choose the Gauss-Lobatto-Legendre (GLL) quadrature in all discrete spectral elements, in which the interpolation and quadrature points are the same. A 3D topographic model is used to demonstrate the efficiency, accuracy, and flexibility of the proposed spectral-element approach in forward modeling of gravity anomalies. Numerical results show that our approach can provide an accurate approximation to the gravity field vector and the gravity gradient tensor.