Organisers: Marie-Colette van Lieshout (CWI), Kathrin Smetana (University of Twente)

Svetlana Dubinkina (CWI)

Bayesian approach to elliptic inverse problems

Predicting the amount of gas or oil extracted from a subsurface reservoir depends on the soil properties such as porosity and permeability. These properties, however, are highly uncertain due to the lack of measurements. Therefore decreasing these uncertainties is of a great importance.

Mathematically speaking, permeability can be represented by a random process, which in turn leads to a random partial differential equation. The solution of such a partial differential equation, for example pressure, is only partially observed and, moreover, contaminated with measurement errors. Therefore, instead of a well-posed forward problem of finding pressure from certain permeability, we are faced with an ill-posed inverse problem of finding uncertain random process from a few pressure measurements. We develop a Bayesian method for inverse problems, that is both general and computationally affordable.