Hierarchical MPS-Based Three-Dimensional Geological Structure Reconstruction with Two-Dimensional Image(s)

Abstract

Multiple-point statistics (MPS) is a useful approach to reconstruct three-dimensional models in the macroscopic or microscopic field. Extracting spatial features for three-dimensional reconstruction from two-dimensional training images (TIs), and characterizing non-stationary features with directional ductility are two key issues in MPS simulation. This study presents a step-wise MPS-based three-dimensional structures reconstruction algorithm with the sequential process and hierarchical strategy based on two-dimensional images. An extension method is proposed to construct three-dimensional TIs. With a sequential simulation process, an initial guess at the coarsest scale is simulated, in which hierarchical strategy is used according to the characteristics of TIs. To obtain a more refined realization, an expectation-maximization like iterative process with global optimization is implemented. A concrete example of chondrite micro-structure simulation, in which one scanning electron microscopy (SEM) image of the Heyetang meteorite is used as TI, shows that the presented algorithm can simulate complex non-stationary structures.

Keywords

multiple-point statistics / hierarchical strategy / chondrite / two-dimensional image

References

[1] Barnes C, Shechtman E, Finkelstein A, . Patchmatch: A Randomized Correspondence Algorithm for Structural Image Editing. ACM Transactions on Graphics, 2009, 28: 1-11.

[2] Chen G X, Zhao F, Wang J G, . Regionalized Multiple-Point Stochastic Geological Modeling: A Case from Braided Delta Sedimentary Reservoirs in Qaidam Basin, NW China. Petroleum Exploration and Development, 2015, 42(5): 697-704.

[3] Chen Q Y, Mariethoz G, Liu G, . Locality-Based 3-D Multiple-Point Statistics Reconstruction Using 2-D Geological Cross Sections. Hydrology and Earth System Sciences, 2018, 22(12): 6547-6566.

[4] Comunian A, Giudici M, Landoni L, . Improving Bowen-Ratio Estimates of Evaporation Using a Rejection Criterion and Multiple-Point Statistics. Journal of Hydrology, 2018, 563: 43-50.

[5] Comunian A, Renard P, Straubhaar J. 3D Multiple-Point Statistics Simulation Using 2D Training Images. Computers & Geosciences, 2012, 40: 49-65.

[6] Dimitrakopoulos R, Mustapha H, Gloaguen E. High-Order Statistics of Spatial Random Fields: Exploring Spatial Cumulants for Modeling Complex Non-Gaussian and Non-Linear Phenomena. Mathematical Geosciences, 2009, 42(1): 65-99.

[7] Feng W J, Wu S H, Yin Y S, . A Training Image Evaluation and Selection Method Based on Minimum Data Event Distance for Multiple-Point Geostatistics. Computers & Geosciences, 2017, 104: 35-53.

[8] Gueting N, Caers J, Comunian A, . Reconstruction of Three-Dimensional Aquifer Heterogeneity from Two-Dimensional Geophysical Data. Mathematical Geosciences, 2017, 50(1): 53-75.

[9] Houlding S W. 3D Geoscience Modeling Computer Techniques for Geological Characterization, 1994, Berlin Heidelberg: Springer-Verlag

[10] Hu L Y, Liu Y, Scheepens C, . Multiple-Point Simulation with an Existing Reservoir Model as Training Image. Mathematical Geosciences, 2013, 46(2): 227-240.

[11] Ji L L, Lin M, Jiang W B, . An Improved Method for Reconstructing the Digital Core Model of Heterogeneous Porous Media. Transport in Porous Media, 2017, 121(2): 389-406.

[12] Kaufmann O, Martin T. 3D Geological Modelling from Boreholes, Cross-Sections and Geological Maps, Application over Former Natural Gas Storages in Coal Mines. Computers & Geosciences, 2008, 34(3): 278-290.

[13] Lessenger, M., Gladczenko, T., Hardt, J., et al., 2019. Facies-Calibrated Petrophysical and Geocellular Property Modeling Using Data Analytics and Multi-Point Statistics in the Delaware Basin. SPE/AAPG/SEG Unconventional Resources Technology Conference, July 2019, Denver. https://doi.org/10.15530/urtec-2019-421

[14] Li J Q, Zhang P F, Lu S F, . Scale-Dependent Nature of Porosity and Pore Size Distribution in Lacustrine Shales: An Investigation by BIB-SEM and X-Ray CT Methods. Journal of Earth Science, 2019, 30(4): 823-833.

[15] Li Y, Teng Q Z, He X H, . Super-Dimension-Based Three-Dimensional Nonstationary Porous Medium Reconstruction from Single Two-Dimensional Image. Journal of Petroleum Science and Engineering, 2019, 174: 968-983.

[16] Ma B J, Wu S G, Mi L J, . Mixed Carbonate-Siliciclastic Deposits in a Channel Complex in the Northern South China Sea. Journal of Earth Science, 2018, 29(3): 707-720.

[17] Mariethoz G, Caers J. Multiple-Point Geostatistics, 2014, Chichester: John Wiley & Sons

[18] Mariethoz G, Renard P, Straubhaar J. The Direct Sampling Method to Perform Multiple-Point Geostatistical Simulations. Water Resources Research, 2010, 46(11): W11536

[19] Mohammadmoradi P Institute of Petroleum Engineering University of Tehran Iran Rasaeii M, . Reconstruction of Non-Stationary Complex Spatial Structures by a Novel Filter-Based Multi Scale Mps Algorithm. Open Transactions on Geosciences, 2014, 2014 2 60-71.

[20] Pyrcz M J, Deutsch C V. Geostatistical Reservoir Modeling, 2014, Oxford: Oxford University Press

[21] Shen W, Hu S, Lin Y, . Chemical and Petrologic Study of the Heyetang Meteorite. Chinese Journal of Polar Research, 2013, 25(4): 386-393. in Chinese wtih English Abstract)

[22] Song W H, Yao J, Ma J S, . Pore-Scale Numerical Investigation into the Impacts of the Spatial and Pore-Size Distributions of Organic Matter on Shale Gas Flow and Their Implications on Multiscale Characterisation. Fuel, 2018, 216: 707-721.

[23] Strebelle S. Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics. Mathematical Geology, 2002, 34(1): 1-21.

[24] Tahmasebi P, Hezarkhani A, Sahimi M. Multiple-Point Geostatistical Modeling Based on the Cross-Correlation Functions. Computational Geosciences, 2012, 16(3): 779-797.

[25] Tahmasebi P, Sahimi M. Reconstruction of Three-Dimensional Porous Media Using a Single Thin Section. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 2012, 85(6): 066709

[26] Tahmasebi P, Sahimi M. Reconstruction of Nonstationary Disordered Materials and Media: Watershed Transform and Cross-Correlation Function. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 2015, 91 3 032401

[27] Tang Y W, Atkinson P M, Zhang J X. Downscaling Remotely Sensed Imagery Using Area-to-Point Cokriging and Multiple-Point Geostatistical Simulation. ISPRS Journal of Photogrammetry and Remote Sensing, 2015, 101: 174-185.

[28] Western A W, Blöschl G, Grayson R B. Toward Capturing Hydrologically Significant Connectivity in Spatial Patterns. Water Resources Research, 2001, 37(1): 83-97.

[29] Yang L, Hou W S, Cui C J, . GOSIM: a Multi-Scale Iterative Multiple-Point Statistics Algorithm with Global Optimization. Computers & Geosciences, 2016, 89 57-70.

[30] Zhang T F, Gelman A, Laronga R. Structure- and Texture-Based Fullbore Image Reconstruction. Mathematical Geosciences, 2017, 49(2): 195-215.

[31] Zhang W B, Duan T Z, Liu Z Q, . Application of Multi-Point Geostatistics in Deep-Water Turbidity Channel Simulation: a Case Study of Plutonio Oilfield in Angola. Petroleum Exploration and Development, 2016, 43(3): 443-450.

[32] Zhou Z C, Mei L F, Shi H S, . Evolution of Low-Angle Normal Faults in the Enping Sag, the Northern South China Sea: Lateral Growth and Vertical Rotation. Journal of Earth Science, 2019, 30(6): 1326-1340.