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Stochastic simulation of spatially correlated geo-processes

Mathematical Geology

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DOI: 10.1007/BF00893018

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Abstract

In this study, developments in the theory of stochastic simulation are discussed. The unifying element is the notion of Radon projection in Euclidean spaces. This notion provides a natural way of reconstructing the real process from a corresponding process observable on a reduced dimensionality space, where analysis is theoretically easier and computationally tractable. Within this framework, the concept of space transformation is defined and several of its properties, which are of significant importance within the context of spatially correlated processes, are explored. The turning bands operator is shown to follow from this. This strengthens considerably the theoretical background of the geostatistical method of simulation, and some new results are obtained in both the space and frequency domains. The inverse problem is solved generally and the applicability of the method is extended to anisotropic as well as integrated processes. Some ill-posed problems of the inverse operator are discussed. Effects of the measurement error and impulses at origin are examined. Important features of the simulated process as described by geomechanical laws, the morphology of the deposit, etc., may be incorporated in the analysis. The simulation may become a model-dependent procedure and this, in turn, may provide numerical solutions to spatial-temporal geologic models. Because the spatial simu??lation may be technically reduced to unidimensional simulations, various techniques of generating one-dimensional realizations are reviewed. To link theory and practice, an example is computed in detail. ?? 1987 International Association for Mathematical Geology.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Stochastic simulation of spatially correlated geo-processes
Series title:
Mathematical Geology
DOI:
10.1007/BF00893018
Volume
19
Issue:
8
Year Published:
1987
Language:
English
Publisher location:
Kluwer Academic Publishers-Plenum Publishers
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
807
Last page:
831
Number of Pages:
25