Correlation-driven direct sampling method for geostatistical simulation and training image evaluation

Chen Zuo, Zhibin Pan, Zhaoqi Gao, and Jinghuai Gao
Phys. Rev. E 99, 053310 – Published 29 May 2019

Abstract

Multiple-point geostatistics (MPS) is a competitive algorithm that produces a set of geologically realistic models. Viewing a training image (TI) as a prior model, MPS extracts patterns from the TI and reproduces patterns which are compatible with the hard data (HD). However, two challenges within the MPS framework are the geologically complex simulation and the TI evaluation. With the objective to achieve a high-quality simulation, we explore a way to address these two issues. First, correlation-driven direct sampling (CDS) is proposed to realize geostatistical simulation. We introduce the correlation-driven distance as a measure of similarity between two patterns. The weights in our distance measurement are derived by the concepts of the ellipse, correlation coefficient, Gaussian function, and affine transformation. Second, we fulfill TI evaluation on the basis of the consistency between TI and HD. Inspired by CDS, the minimum correlation-driven distance (MCD) is proposed to improve the evaluation accuracy. We suggest a conditioning pattern extraction history strategy to speed up the evaluation program. Third, the local consistency is presented to address nonstationarity. The program automatically divides the simulation domain into several subareas. A two-dimensional (2D) channelized reservoir image and a three-dimensional (3D) rock image are used to validate our proposed method. In comparison with previous methods, CDS yields better simulation quality. The further applications include a set of 2D TI evaluations and a 3D simulation domain segmentation. MCD exhibits sensible evaluation accuracy, excellent computational efficiency, and the ability to deal with nonstationarity.

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  • Received 16 October 2018
  • Revised 29 April 2019

DOI:https://doi.org/10.1103/PhysRevE.99.053310

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Chen Zuo, Zhibin Pan*, Zhaoqi Gao, and Jinghuai Gao

  • School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China

  • *zbpan@mail.xjtu.edu.cn

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Issue

Vol. 99, Iss. 5 — May 2019

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