Gravity kernel method for implicit geological modeling

Gravity is one of the most widely used geophysical data types in subsurface exploration. In the recent developments of stochastic geological modeling, gravity data serves as an additional constraint to the modeling construction and can be included in the modeling process as the likelihood function in a Bayesian workflow. A fast but also precise forward gravity simulation is key to the success of the geological modeling inverse problem.

In this study, we present 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 each sensor, respecting the gravimeter locations and the local sensitivities. The kernel method is efficient in terms of both computing and memory use for meshless implicit geological modeling approaches. This design makes the method well suited for many-query applications like Bayesian machine learning using gradient information calculated from Automatic Differentiation (AD). 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. Synthetic results are presented and show superior performance compared to the traditional spatial convolution method.