Efficient parallelization of geostatistical inversion using the quasi-linear approach

Hydraulic conductivity is a key parameter for the simulation of groundwater flow and transport. Typically, it is highly variable in space and difficult to determine by direct methods. The most common approach is to infer hydraulic-conductivity values from measurements of dependent quantities, such as hydraulic head and concentration. In geostatistical inversion, the parameters are estimated as continuous, spatially auto-correlated fields, the most likely values of which are obtained by conditioning on the indirect data. In order to identify small-scaled features, a fine three-dimensional discretization of the domain is needed. This leads to high computational demands in the solution of the forward problem and the calculation of sensitivities. In realistic three-dimensional settings with many measurements parallel computing becomes mandatory. present study, we investigate how parallelization of the quasi-linear geostatistical approach of inversion can be made most efficient. We suggest a two-level approach of parallelization, in which the computational domain is subdivided and the evaluation of sensitivities is also parallelized. We analyze how these two levels of parallelization should be balanced to optimally exploit a given number of computing nodes.