High-accuracy gravity field and gravity gradient forward modelling based on 3D vertex-centered finite-element algorithm

Gravity anomalies generated by density non-uniformity are governed by the 3D Poisson equation. Most existing forward methods for such anomalies rely on integral techniques and cell-centered numerical approaches. Once the gravitational potential is calculated, these numerical schemes will inevitably lose high accuracy. To alleviate this problem, an accurate and efficient high-order vertex-centered finite-element scheme for simulating 3D gravity anomalies is presented. Firstly, the forward algorithm is formulated through the vertex-centered finite element with hexahedral meshes. The biconjugate gradient stabilized algorithm can solve the linear equation system combined with an incomplete LU factorization (ILU-BICSSTAB). Secondly, a high-degree Lagrange interpolating scheme is applied to achieve the first-derivate and second-derivate gravitational potential. Finally, a 3D cubic density model is used to test the accuracy of the vertex-centered finite-element algorithm, and thin vertical rectangular prisms and real example for flexibility. All numerical results indicate that our high-order vertex-centered finite-element method can provide an accurate approximation for the gravity field vector and the gravity gradient tensor. Meanwhile, compared to the cell-centered numerical algorithm, the high-order vertex-centered finite element scheme exhibits higher efficiency and accuracy in simulating 3D gravity anomalies.