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

Publication: Research - peer-review › Journal article – Annual report year: 2012

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**A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information.** / Lange, Katrine; Frydendall, Jan; Cordua, Knud Skou; Hansen, Thomas Mejer; Melnikova, Yulia; Mosegaard, Klaus.

Publication: Research - peer-review › Journal article – Annual report year: 2012

### Harvard

*Mathematical Geosciences*, vol 44, no. 7, pp. 783-803., 10.1007/s11004-012-9417-2

### APA

*Mathematical Geosciences*,

*44*(7), 783-803. 10.1007/s11004-012-9417-2

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*Mathematical Geosciences*. 2012, 44(7). 783-803. Available: 10.1007/s11004-012-9417-2

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### Bibtex

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### RIS

TY - JOUR

T1 - A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information

A1 - Lange,Katrine

A1 - Frydendall,Jan

A1 - Cordua,Knud Skou

A1 - Hansen,Thomas Mejer

A1 - Melnikova,Yulia

A1 - Mosegaard,Klaus

AU - Lange,Katrine

AU - Frydendall,Jan

AU - Cordua,Knud Skou

AU - Hansen,Thomas Mejer

AU - Melnikova,Yulia

AU - Mosegaard,Klaus

PB - Springer Netherlands

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Geostatistics

KW - Multiple point statistics

KW - Training image

KW - Maximum a posteriori solution

U2 - 10.1007/s11004-012-9417-2

DO - 10.1007/s11004-012-9417-2

JO - Mathematical Geosciences

JF - Mathematical Geosciences

SN - 1874-8961

IS - 7

VL - 44

SP - 783

EP - 803

ER -