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Stationarity scores on training images for multipoint geostatistics

Mirowski, Piotr W. and Tetzlaff, Daniel M. and Davies, Roy C. and McCormick, David S. and Williams, Nneka and Signer, Claude (2009) Stationarity scores on training images for multipoint geostatistics. Mathematical Geosciences, 41 (4). pp. 447-474. ISSN 1874-8961.

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This research introduces a novel method to assess the validity of training images used as an input for Multipoint Geostatistics, alternatively called Multiple Point Simulation (MPS). MPS are a family of spatial statistical interpolation algorithms that are used to generate conditional simulations of property fields such as geological facies. They are able to honor absolute “hard” constraints (e.g., borehole data) as well as “soft” constraints (e.g., probability fields derived from seismic data, and rotation and scale). These algorithms require 2D or 3D training images or analogs whose textures represent a spatial arrangement of geological properties that is presumed to be similar to that of a target volume to be modeled. To use the current generation of MPS algorithms, statistically valid training image are required as input. In this context, “statistical validity” includes a requirement of stationarity, so that one can derive from the training image an average template pattern. This research focuses on a practical method to assess stationarity requirements for MPS algorithms, i.e., that statistical density or probability distribution of the quantity shown on the image does not change spatially, and that the image shows repetitive shapes whose orientation and scale are spatially constant. This method employs image-processing techniques based on measures of stationarity of the category distribution, the directional (or orientation) property field and the scale property field of those images. It was successfully tested on a set of two-dimensional images representing geological features and its predictions were compared to actual realizations of MPS algorithms. An extension of the algorithms to 3D images is also proposed. As MPS algorithms are being used increasingly in hydrocarbon reservoir modeling, the methods described should facilitate screening and selection of the input training images.

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Additional Information:© 2008 International Association for Mathematical Geosciences. Received: 5 August 2006 / Accepted: 9 September 2008. Published online: 14 October 2008. The authors wish to thank the Geology and Rock Physics Department of Schlumberger-Doll Research for the support of this project and the NOMAD consortium for geological data. They also thank Romain Prioul, Michael Prange and two anonymous reviewers for helpful advice and reviews of this article.
Funding AgencyGrant Number
Schlumberger-Doll ResearchUNSPECIFIED
Subject Keywords:Stationarity; Orientation; Multi-scale analysis; Multiple point simulation; Training image
Issue or Number:4
Record Number:CaltechAUTHORS:20090727-132510250
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Official Citation:Mirowski, P.W., Tetzlaff, D.M., Davies, R.C. et al. Stationarity Scores on Training Images for Multipoint Geostatistics. Math Geosci 41, 447–474 (2009).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14673
Deposited By: Tony Diaz
Deposited On:07 Aug 2009 23:39
Last Modified:30 Jan 2020 23:41

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