Zhouji Liang, Florian Wellmann

Geological modeling has been widely adopted to investigate underground geometries. However, modeling processes inevitably have uncertainties due to scarcity of data, measurement errors, and simplification of modeling methods. Recent developments in geomodeling methods have introduced a Bayesian framework to constrain the model uncertainties by considering additional geophysical data into 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 utilize derivative information. Hence, we introduce an approach to efficiently evaluate second-order derivatives in geological modeling and introduce 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-Hasting and Hamiltonian Monte Carlo, on a synthetic three-layer geological model. Our experiment demonstrates that superior performance is achieved by the gpCN, which has the potential to be generalized to more complex models.