A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information

Katrine Lange, Jan Frydendall, Knud Skou Cordua, Thomas Mejer Hansen, Yulia Melnikova, Klaus Mosegaard

Research output: Contribution to journalJournal articleResearchpeer-review

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.
Original languageEnglish
JournalMathematical Geosciences
Volume44
Issue number7
Pages (from-to)783-803
ISSN1874-8961
DOIs
Publication statusPublished - 2012

Keywords

  • Geostatistics
  • Multiple point statistics
  • Training image
  • Maximum a posteriori solution

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