Florian Wellmann

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.

Geologic modeling has been widely adopted to investigate underground structures. However, modeling processes inevitably have uncertainties due to scarcity of data, measurement errors, and simplification of the modeling method. Recent developments in geomodeling methods have introduced a Bayesian framework to constrain the model uncertainties by considering the additional geophysical data in the modeling procedure. Markov chain Monte Carlo (MCMC) methods are normally used as tools to solve the Bayesian inference problem. To achieve a more efficient posterior exploration, advances in MCMC methods use derivative information. Hence, we introduce an approach to efficiently evaluate second-order derivatives in geologic modeling and adopt a Hessian-informed MCMC method, the generalized preconditioned Crank-Nicolson (gpCN), as a tool to solve the 3D model-based gravity Bayesian inversion problem. The result is compared with two other widely applied MCMC methods, random-walk Metropolis–Hastings and Hamiltonian Monte Carlo, on a synthetic geologic model and a realistic structural model of the Kevitsa deposit. Our experiment demonstrates that superior performance is achieved by the gpCN compared with the other two state-of-the-art sampling methods. This indicates the potential of the proposed method to be generalized to more complex models.