Inverse modeling of geochemical and mechanical compaction in sedimentary basins through Polynomial Chaos Expansion

We present an inverse modeling procedure for the estimation of model parameters of sedimentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophysical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likelihood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quantified through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approximations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored.