A Multivariate Geometric Equivalent Transformation (MGET) Method for Efficient Kernel Function Calculation in the Inversion of Gravity Data With Undulating Observation Surface

The observation surface of gravity data is often undulating, and the density inversion efficiency of gravity data is seriously reduced due to the low computational efficiency of the kernel function when the undulating surface is considered, which makes it impossible to apply to the detailed inversion of large-scale data. We proposed a multivariate geometric equivalent transformation (MGET) method to rapidly compute the kernel matrix with an undulating observation surface for improving density inversion efficiency. We first build the equivalence relation of the kernel function for different grid nodes, grid cells, and adjacent layers with a structured hexahedron mesh, which reduces the computation time and the number of kernel function, and can significantly improve the density inversion efficiency of gravity data. Tests show that the kernel matrices computed by the MGET method are accurate and efficient, and the computational efficiency of the kernel function is improved by more than ten times, and the density inversion can be performed efficiently and quickly. Finally, we apply the MGET method to real gravity data from Harbin City, China, to obtain the fault distribution and trends. This will contribute to future city construction planning.