1 Center for Energy Resources Engineering, Center, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark4 CERE – Center for Energy Ressources Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark5 Department of Informatics and Mathematical Modeling, Technical University of Denmark6 National Space Institute, Technical University of Denmark
During the last decade multiple-point statistics has become in-creasingly popular as a tool for incorporating complex prior infor-mation when solving inverse problems in geosciences. A variety of methods have been proposed but often the implementation of these is not straightforward. One of these methods is the recently proposed Frequency Matching method to compute the maximum a posteriori model of an inverse problem where multiple-point statistics, learned from a training image, is used to formulate a closed form expression for an a priori probability density function. This paper discusses aspects of the implementation of the Fre-quency Matching method and the techniques adopted to make it com-putationally feasible also for large-scale inverse problems. The source code is publicly available at GitHub and this paper also provides an example of how to apply the Frequency Matching method to a linear inverse problem.
Multiple-points statistics; Training image; A priori in- formation; Maximum a posteriori model