Article

Mathematical Geosciences

, Volume 44, Issue 7, pp 783-803

Open Access This content is freely available online to anyone, anywhere at any time.

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