Investigation of generalized Markov chain performance in simulation of discrete variables in a case study

Document Type : Research Article

Authors

1 Sahand university of Technology

2 Assistant Professor, Faculty of Mining Engineering, Sahanad University of Technology, Tabriz, Iran.

3 Associate professor, Faculty of Mining Engineering, Sahanad University of Technology

Abstract

Summary
Geological modeling of heterogeneous facies plays an important role in the detection of stratigraphic uncertainty. In this research, three methods, Indicator kriging (IK), Sequential Indicator Simulation (SIS), and Generalized Coupled Markov Chain (GCMC) were applied to predict geological categories at unknown locations. Then the results of all three methods were compared.
Introduction
There are various methods for estimating and determining the spatial variation of categorical variables using geological data and exploratory wells. One of the best of these methods is geostatistical methods. As new Geostatistical methods, the GCMC algorithm, one of the Markov chain models, has been used in the earth sciences to simulate categorical variables of sedimentary deposits. This method is based on the calculation of transition probability matrixes with respect to the direction and spatial variations between classes. Due to the realistic results and easy implementation, the GCMC method is a suitable tool for the initial predicting and modeling of categorical variables in sedimentary environments.
Methodology and Approaches
In this study, one of the drilling profiles in block C of the Bostanabad Areshtenab limestone deposit was selected for modeling. At this point, three carbonate units can be distinguished from the 5 exploratory boreholes dataset. To build the prediction models, after transforming the coordinates into a stratigraphic coordinates system (unfolding the strata by vertical transformation), the vertical and horizontal variability and continuity structure of the three existing classes were modeled with indicator variograms and transition probabilities. Then the mentioned geostatistical prediction techniques were applied to generate the spatial variability models.
Results and Conclusions
In general, this study suggested the application of three geostatistical prediction methods for constructing realistic subsurface models of the categorical variables. According to the results, the IK result represented the general occurrence trend better. However, the spatial variability structure could not be reflected sufficiently and clearly. Although, in the SIS results fine and subtle variations were reflected, the produced patterns were more scattered. As the result of this study, the GCMC method can reproduce the global statistics, spatial structural functions (transiograms), and more realistic subsurface models, especially with sparse data in sedimentary systems. 

Keywords

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Full Text

پیش‌بینی دقیق زمین‌شناسی و تعیین ناهمگونی‌های زیرسطحی در بسیاری از زمینه­های مهندسی ازجمله مدل‌سازی ذخایر آهکی اهمیت بسزایی دارد و گام مهمی قبل از هر تصمیم مهندسی در مورد برنامه‌های اکتشافی در داخل یا اطراف مناطق مورد نظر است. شناسایی و تفسیر ناهمگنی‌های زیرسطحی به‌ویژه رخساره‌های سنگی، در بازسازی شکل هندسی ذخیره معدنی، در اکتشاف معدن نقشی اساسی دارد [1]. از طرفی به دلیل محدودیت‌های فنی و اقتصادی، برنامه‌های حفاری اکتشافی متراکم و نمونه‌برداری جامع برای اندازه‌گیری خواص متغیرها در منطقه مورد نظر امکان‌پذیر نیست. ازاین‌رو با مدل‌سازی رخساره­ها و تعیین نحوه قرارگیری آن‌ها و شناسایی لایه‌های مختلف، میزان پتانسیل ماده معدنی تخمین زده می‌شود [2]. به همین منظور روش‌های متنوعی برای مدل‌سازی متغیرهای گسسته بخصوص ویژگی‌های رخساره‌های سنگی ارائه‌شده‌اند که از بهترین این روش‌ها می­توان به روش‌های زمین‌آماری اشاره کرد؛ زیرا اجرای روش‌های زمین‌آماری بستر مناسبی را برای ایجاد مدل‌های دقیق و درعین‌حال قابل ارزیابی ازنظر عدم اطمینان فراهم می‌آورد [3]. از روش‌های زمین‌آماری کاربردی در مدل‌سازی متغیرهای گسسته می‌توان به روش‌های شبیه‌سازی شاخص پی‌درپی[i]، شبیه‌سازی چند گوسی[ii]، شبیه‌سازی شیء مبنا[iii]، شبیه‌سازی چندنقطه‌ای[iv]، شبیه‌سازی زنجیره مارکوف[v] و غیره اشاره کرد.


[i] Sequential Indicator Simulation (SIS)

[ii] Pluri-Gaussian Simulation

[iii] Object based modelling

[iv] Multiple Point Simulation (MPS)

[v] Markov Chain (MC)

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Journal of Analytical and Numerical Methods in Mining Engineering
Volume 11, Issue 28
October 2021
Pages 37-50

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History

  • Receive Date: 22 December 2020
  • Revise Date: 25 April 2021
  • Accept Date: 18 May 2021

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