A Segmentation Approach for Stochastic Geological Modeling Using Hidden Markov Random Fields

Stochastic modeling methods and uncertainty quantification are important tools for gaining insight into the geological variability of subsurface structures. Previous attempts at geologic inversion and interpretation can be broadly categorized into geostatistics and process-based modeling. The choice...

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Bibliographic Details
Published in:Mathematical geosciences 2017-02, Vol.49 (2), p.145-177
Main Authors: Wang, Hui, Wellmann, J. Florian, Li, Zhao, Wang, Xiangrong, Liang, Robert Y.
Format: Article
Language:English
Subjects:
Chemistry and Earth Sciences
Computer Science
Earth and Environmental Science
Earth Sciences
Geology
Geophysics
Geotechnical Engineering & Applied Earth Sciences
Heterogeneity
Hydrogeology
Markov analysis
Mathematical analysis
Mathematical models
Physics
Random variables
Segmentation
Statistics for Engineering
Stochastic models
Stochasticity
Uncertainty
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Summary:Stochastic modeling methods and uncertainty quantification are important tools for gaining insight into the geological variability of subsurface structures. Previous attempts at geologic inversion and interpretation can be broadly categorized into geostatistics and process-based modeling. The choice of a suitable modeling technique directly depends on the modeling applications and the available input data. Modern geophysical techniques provide us with regional data sets in two- or three-dimensional spaces with high resolution either directly from sensors or indirectly from geophysical inversion. Existing methods suffer certain drawbacks in producing accurate and precise (with quantified uncertainty) geological models using these data sets. In this work, a stochastic modeling framework is proposed to extract the subsurface heterogeneity from multiple and complementary types of data. Subsurface heterogeneity is considered as the “hidden link” between multiple spatial data sets. Hidden Markov random field models are employed to perform three-dimensional segmentation, which is the representation of the “hidden link”. Finite Gaussian mixture models are adopted to characterize the statistical parameters of multiple data sets. The uncertainties are simulated via a Gibbs sampling process within a Bayesian inference framework. The proposed modeling method is validated and is demonstrated using numerical examples. It is shown that the proposed stochastic modeling framework is a promising tool for three-dimensional segmentation in the field of geological modeling and geophysics.
ISSN:1874-8961
1874-8953
DOI:10.1007/s11004-016-9663-9