Improving Filtersim Simulation Algorithm of Multiple-Point Geostatistics Using New Training Image Based Adaptive Filters and Supervised Hard Data Conditioning

Document Type : Research Article

Authors

1 Digital Signal Processing Lab, electrical & Computer Department, Isfahan University of Technology

2 Mining Engineering Department, , Isfahan University of Technology

10.29252/anm.8.15.55

Abstract

Summary
Simulations based on Multiple-point statistics (MPS) form a class of newly developed techniques that have received great attention in recent years and are mainly used to map spatial complexity and heterogeneity of geological phenomenon.  One of the most commonly used pattern based multiple-point geostatistical simulation algorithm is called Filtersim. In the conventional Filtersim algorithm, the detected patterns in training images are transformed into filter score space using a fixed number of filters that are neither dependent on the training images nor on the characteristics of patterns extracted from them. Through using principal component analysis in current study, a set of new filters are designed in such a way to include most structural information specific to the governing training image resulting in the selection of closer patterns in the filter score space. Comparing the results of applying our proposed filters to that of conventional Filtersim algorithm shows a significant improvement in recovering expected shapes and structural continuity in the final simulated realizations.
 
Introduction
MPS simulation is capable of reproducing complex geological patterns that cannot be modeled by two-point statistics moments such as variograms. One of the commonly used pattern-based approach, FILTERSIM, introduces filters to summarize high dimensional patterns into a filter score space. Then, it classifies the patterns into a limited number of classes. FILTERSIM uses six predefined filters, which are not specific to the Training Image. The aim of current research is to introduce new improvements to the initial FILTERSIM technique through defining new adaptive filters.
 
Methodology and Approaches
In contrast to original FILTERSIM method, our approach uses some filters which are designed specifically for any given Training Image using PCA analysis. In addition, our approach uses a combination of raster path and random partitioning methods in the course of simulation. The raster path approach results in simulations showing a good continuity of the patterns. The random partitioning is a new feature that allows better simulated realizations as compared to the straightforward use of the raster path.
 
 
Results and Conclusions
The newly proposed approach have been tested on some training images and the results have been compared with previous pattern-based algorithms. Through visual inspection and some discrepancy measures it is shown that the simulated realizations obtained by our approach are much closer to the training image than those obtained with the other methods. In particular, the continuity of the patterns is better preserved with the proposed method.

Keywords

Main Subjects

References

[1]      Honarkhah, M, (2011) Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling, Caers, J., Department of Energy Resources Engineering, Stanford University.
[2]      Strebelle,S. (2002). Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics, Mathematical Geology, 34(1), 1-21.
[3]      Mariethoz G, Renard P, Caers J (2010) Bayesian inverse problem and optimization with iterative spatial resampling. Water Resour Res 46.
[4]      Zhang, T.( 2006). Filter-based Training Pattern classification for spatial Pattern simulation , Switzer,P., The Department of Geological and Environmental Sciences, Stanford University.
[5]      Wua ,J. , Boucherb, A., Zhang, T.( 2008) , A SGeMS code for pattern simulation of continuous and categorical variables: FILTERSIM, Computers & Geosciences, 34(1) ,1863–1876,
[6]      Wua ,J. , Zhang, T., Journel, A. (2008), Fast FILTERSIM Simulation with Score-based Distance, Math Geosci, 40(1) , 773–788.
[7]      Mariethoz, G. , Caers, J.(2015) , Multiple-point geostatistics, John Wiley & Sons, Ltd, USA.
[8]      Carvalho PRM, Costa JFCL, Rasera LG, Varella LES (2016) Geostatistical facies simulation with geometric patterns of a petroleum reservoir. Stoch Environ Res Risk Assess:1-18. doi: 10.1007/s00477–016–1243–5
[9]      Zhang T, Du Y, Li B, Zhang A (2017) Stochastic reconstruction of spatial data using LLE and MPS. Stoch Environ Res Risk Assess:1-14.
[10]      Zhang T, Du Y, Huang T, Yang J, Lu F, Li X (2016) Reconstruction of porous media using ISOMAP-based MPS. Stoch Environ Res Risk Assess. 30(1):395–412.
[11]      Wu, J.(2007), 4D Seismic and Multiple-Point Pattern Data Integration Using Geostatistics, Journel, A.G. Department of Energy Resources Engineering, Stanford University.
[12]      Burc,G.,Caers,J.(2004) , A Multiple-scale, Pattern-based Approach to Sequential Simulation, springer, Quantitative Geology and Geostatistics, 14(1), 255-264.
[13]      Zhang, T., Switzer, P., Journel, A.,(2006) , Filter-Based Classification of Training Image Pattern for Spatial Simulation, Mathematical Geology, 38(1), 63-80.
[14]      Duda, R., Hart, P., Seork,D., ( 2001). Pattern Classification, the Electrical Engineering Department at San Jose State University, San Jose, California.
[15]      Shannon, C.E.,(1948) A Mathematical Theory of Communication. Bell System Technical Journal, 27(1) 379-423.
[16]      Cover TM., Thomas JA.,( 1991). Elements of information theory. Wiley, New York.
[17]      Tibshirani, R., G. Walther, and T. Hastie. Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B. Vol. 63, Part 2, 2001, pp. 411–423.
[18]      Maimon O. and Rokach L., (Ed). 2010, Data Mining and Knowledge Discovery Handbook, Second Edition, Springer
Journal of Analytical and Numerical Methods in Mining Engineering
Volume 8, Issue 15
May 2018
Pages 55-67

Files

History

  • Receive Date: 13 February 2016
  • Revise Date: 24 August 2018
  • Accept Date: 05 March 2018

Share

How to cite

Statistics