Surrogate-Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High-Dimensional Inverse Problem by Use of Smooth Local Parameterization

Abstract

This paper introduces an efficient surrogate model with the aim of accelerating joint estimation of subsurface geological properties and relative permeability parameters for high-dimensional inversion problems. We fully replace the high-fidelity model with a set of subdomain linear models through integrating model linearization with smooth local parameterization where the Gaussian geological parameters and non-Gaussian facies indicators are locally parameterized. These subdomain linear models with smooth local parameterization, referred to as SLM-SLP, are constructed in each subdomain individually using only a few high-fidelity model simulations. An adaptive scheme, that is, weighting smooth local parameterization (WSLP), is introduced as well to mitigate the negative effects of inappropriate domain decomposition schemes by adaptively optimizing the domain decomposition strategy. The computational advantages of the proposed algorithm are demonstrated on a synthetic non-Gaussian facies model and a real-world high-dimensional Gaussian model. The amount of computational cost has been drastically reduced while reasonable accuracy remains. Specifically, SLM-SLP only needs 220 fidelity simulations to optimize 302 parameters. Compared to ensemble smoother with multiple data assimilation (ES-MDA), SLM-SLP effectively and efficiently mitigates the ensemble collapse problem in the course of uncertain quantification.