Gradual deformation and iterative calibration of gaussian-related stochastic models

This paper describes a new method for gradually deforming realizations of Gaussian-related stochastic models while preserving their spatial variability. This method consists in building a stochastic process whose state space is the ensemble of the realizations of a spatial stochastic model. In parti...

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Bibliographic Details
Published inMathematical geology Vol. 32; no. 1; pp. 87 - 108
Main Author HU, L. Y
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 2000
Springer Nature B.V
Subjects
Algorithms
Deformation
Earth sciences
Earth, ocean, space
Exact sciences and technology
Hydrocarbons
Mathematical models
Sedimentary rocks
Stochastic models
Stochastic processes
Stratigraphy
Studies
geostatistics
stochastic models
mathematical methods
optimization
permeability
deformation
wells
spatial variations
pressure
petroleum
calibration
heterogeneity
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Summary:This paper describes a new method for gradually deforming realizations of Gaussian-related stochastic models while preserving their spatial variability. This method consists in building a stochastic process whose state space is the ensemble of the realizations of a spatial stochastic model. In particular, a stochastic process, built by combining independent Gaussian random functions, is proposed to perform the gradual deformation of realizations. Then, the gradual deformation algorithm is coupled with an optimization algorithm to calibrate realizations of stochastic models to nonlinear data. The method is applied to calibrate a continuous and a discrete synthetic permeability fields to well-test pressure data. The examples illustrate the efficiency of the proposed method. Furthermore, we present some extensions of this method (multidimensional gradual deformation, gradual deformation with respect to structural parameters, and local gradual deformation) that are useful in practice. Although the method described in this paper is operational only in the Gaussian framework (e.g., lognormal model, truncated Gaussian model, etc.), the idea of gradually deforming realizations through a stochastic process remains general and therefore promising even for calibrating non-Gaussian models.[PUBLICATION ABSTRACT]
ISSN:0882-8121
1874-8961
1573-8868
1874-8953
DOI:10.1023/A:1007506918588