, Volume 44, Issue 7, pp 783803
A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information
 Katrine LangeAffiliated withCenter for Energy Resources Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark Email author
 , Jan FrydendallAffiliated withCenter for Energy Resources Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark
 , Knud Skou CorduaAffiliated withCenter for Energy Resources Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark
 , Thomas Mejer HansenAffiliated withCenter for Energy Resources Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark
 , Yulia MelnikovaAffiliated withCenter for Energy Resources Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark
 , Klaus MosegaardAffiliated withCenter for Energy Resources Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark
Abstract
The frequency matching method defines a closed form expression for a complex prior that quantifies the higher order statistics of a proposed solution model to an inverse problem. While existing solution methods to inverse problems are capable of sampling the solution space while taking into account arbitrarily complex a priori information defined by sample algorithms, it is not possible to directly compute the maximum a posteriori model, as the prior probability of a solution model cannot be expressed. We demonstrate how the frequency matching method enables us to compute the maximum a posteriori solution model to an inverse problem by using a priori information based on multiple point statistics learned from training images. We demonstrate the applicability of the suggested method on a synthetic tomographic crosshole inverse problem.
Keywords
Geostatistics Multiple point statistics Training image Maximum a posteriori solution Title
 A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Mathematical Geosciences
Volume 44, Issue 7 , pp 783803
 Cover Date
 201210
 DOI
 10.1007/s1100401294172
 Print ISSN
 18748961
 Online ISSN
 18748953
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Geostatistics
 Multiple point statistics
 Training image
 Maximum a posteriori solution
 Industry Sectors
 Authors

 Katrine Lange ^{(1)}
 Jan Frydendall ^{(1)}
 Knud Skou Cordua ^{(1)}
 Thomas Mejer Hansen ^{(1)}
 Yulia Melnikova ^{(1)}
 Klaus Mosegaard ^{(1)}
 Author Affiliations

 1. Center for Energy Resources Engineering, Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800, Kongens Lyngby, Denmark