Uncertainty quantification of geologic model parameters in 3D gravity inversion by Hessian-informed Markov chain Monte Carlo
Zhouji Liang, Florian Wellmann, Omar Ghattas
Abstract
ABSTRACT 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.