Kernel method for gravity forward simulation in implicit probabilistic geologic modeling

Gravity is one of the most widely used geophysical data types in subsurface exploration. In the recent developments of stochastic geologic modeling, gravity data serve as an additional constraint to the model construction. The gravity data can be included in the modeling process as the likelihood function in a probabilistic joint inversion framework and allow the quantification of uncertainty in geologic modeling directly. A fast but also precise forward gravity simulation is essential to the success of the probabilistic inversion. Hence, we have developed a gravity kernel method, which is based on the widely adopted analytical solution on a discretized grid. As opposed to a globally refined regular mesh, we construct local tensor grids for individual gravity receivers, respecting the gravimeter locations and the local sensitivities. The kernel method is efficient in terms of computing and memory use for mesh-free implicit geologic modeling approaches. This design makes the method well suited for many-query applications, such as Bayesian machine learning using gradient information calculated from automatic differentiation. Optimal grid design without knowing the underlying geometry is not straightforward before evaluating the model. Therefore, we further provide a novel perspective on a refinement strategy for the kernel method based on the sensitivity of the cell to the corresponding receiver. Numerical results are presented and found superior performance compared to the conventional spatial convolution method.