Hydraulic Conductivity Field Marginalization in HMC Based Estimation of Piping Zone Boundary

Probabilistic inversion is conducted for the identification of the boundary configuration of a piping zone, which usually develops in soil structures, such as levees. However, the spatially distributing hydraulic conductivity in the soil structure is also unknown and has a significant influence on the estimation of the piping zone. Bayesian inference of both the spatially distributing property, hydraulic conductivity, and the boundary geometry of the piping region become computationally expensive. It is the case even if modern and statistically efficient gradient-based Markov Chain Monte Carlo (MCMC) algorithms called Hamiltonian Monte Carlo (HMC) are implemented. To circumvent this problem, the Bayesian Approximation Error (BAE) approach is employed, by which only the (interesting) piping zone boundary is considered as the target of inversion with the (uninteresting) hydraulic conductivity field fixed. The BAE approach is incorporated into numerical procedures of HMC for boundary estimation in a synthetic steady seepage flow field. Observation data of the hydraulic head and the total outward normal flux at discrete instances in time are numerically prepared. Inversion results are presented with the comparisons of the posterior marginal distributions for the cases with/without the approximation error considered.

Keywords: Inverse problem, Hamiltonian Monte Carlo, Bayesian approximation error, Hydraulic conductivity