## Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

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

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**Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information.** / Cordua, Knud Skou; Hansen, Thomas Mejer; Mosegaard, Klaus.

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

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*Geophysics*, vol 72, no. 2, pp. H19-H3., 10.1190/geo2011-0170.1

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*Geophysics*,

*72*(2), H19-H3. 10.1190/geo2011-0170.1

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*Geophysics*. 2012, 72(2). H19-H3. Available: 10.1190/geo2011-0170.1

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TY - JOUR

T1 - Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

AU - Cordua,Knud Skou

AU - Hansen,Thomas Mejer

AU - Mosegaard,Klaus

PY - 2012

Y1 - 2012

N2 - We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework for a full-waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included. At the same time we show how temporally and/or spatiallycorrelated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional methods do. Moreover, an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates. The latter may be a key challenge when considering field experiments, which will not be addressed here.

AB - We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework for a full-waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included. At the same time we show how temporally and/or spatiallycorrelated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional methods do. Moreover, an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates. The latter may be a key challenge when considering field experiments, which will not be addressed here.

U2 - 10.1190/geo2011-0170.1

DO - 10.1190/geo2011-0170.1

M3 - Journal article

VL - 72

SP - H19-H3

JO - Geophysics

T2 - Geophysics

JF - Geophysics

SN - 0016-8033

IS - 2

ER -