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

Abstract

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.

Impact of space‐time mesh adaptation on solute transport modeling in porous media

“…We briefly describe here the procedure we employ for model parameter estimation, which is coupled to the adaptive discretization technique described in section 3. We follow the approach proposed by Porta et al . [] and combine the model reduction technique explored in Formaggia et al . [] with a standard Maximum Likelihood parameter estimation framework [ Carrera and Neuman , ].…”

“…Reliability of gPCE surrogate models needs to be carefully assessed. Numerical validation of gPCE models can be performed by comparing full and gPCE model outputs for a number of parameters combinations, randomly selected in the parameter space [e.g., Porta et al ., ]. Global sensitivity analysis and uncertainty quantification. We exploit the gPCE model to obtain a large set of Monte Carlo realizations of the breakthrough curve at a reduced computational cost.…”

“…These are selected on the basis of the functional format of the probability density of the model uncertain parameters. The procedure allows performing multiple evaluations of the system model, which are employed to (a) obtain Maximum Likelihood estimates of model parameters and (b) quantify propagation of parameter uncertainty to target model outputs at a reduced computational cost [ Fajraoui et al ., ; Ciriello et al ., 2013a, b; Oladyshkin et al ., ; Porta et al ., ]. The gPCE strategy can also lead to the analytical evaluation of the variance‐based Sobol sensitivity indices [ Sobol , ; Sudret , ], which quantify the relative contribution of each uncertain model parameter to the total variability of the model output.…”

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

“…In previous contributions we have developed a forward and inverse modeling technique for basin scale compaction under uncertainty [15,16], in a simplified framework in which we assume that compaction mainly takes place along the vertical direction. This allows for a relevant simplification of the model structure which is reduced to a one-dimensional (vertical) setting.…”

“…The sparse grid approximation can then be algebraically post-processed to obtain relevant information for the Uncertainty Quantification analysis, such as statistical moments and Sobol indices of the quantities of interest. Results by [15,16] demonstrate that this approach is very effective for the quantification of uncertainty when the basin has sediments with homogeneous properties, as in such a case the key outputs are typically smooth functions of the model parameters.…”