Abstract
The three-dimensional characterization of geological structures is important for determining the distribution of subsurface mineral resources. However, geological structures and geological phenomena have great stochasticity and uncertainty at the microscopic level. Traditional multiple-point geostatistics use mostly three-dimensional conceptual models or two-dimensional sections as training images, while simulations using direct low-dimensional borehole data are lacking. In this paper, we propose a new multiple-point geostatistical method to automatically reconstruct three-dimensional geological models directly from borehole data, which can significantly reduce the complexity of intermediate manual operations. First, the geological structure characteristics in the borehole data are extracted, and then an initial prior model is constructed based on geological constraints. Next, for the non-stationary problem, the mobile local scan approach is proposed to make the simulation nodes scan in a certain range of scaled area to simultaneously achieve the zonal simulation effect and eliminate the discontinuity problem between zonal boundaries. Based on this solution, the whole modeling workflow is designed. Finally, the algorithm is validated using actual plains area geological survey data, compared to other modeling methods, and evaluated for model uncertainty. The results show that the proposed 3D geological modeling method can effectively expose the stratigraphic structural morphology, stratigraphic attributes and overburden relationships. It will provide decision support for resource exploration and reduce exploration costs.
Similar content being viewed by others
References
Alabert, F. G. (1987). Stochastic imaging of spatial distributions using hard and soft information. Stanford University Press.
Ali, M., Abdelhady, A., Abdelmaksoud, A., Darwish, M., & Essa, M. A. (2020). 3D static modeling and petrographic aspects of the Albian/Cenomanian Reservoir, Komombo Basin, Upper Egypt. Natural Resources Research, 29(2), 1259–1281.
Allard, D., Comunian, A., & Renard, P. (2012). Probability aggregation methods in geoscience. Mathematical Geosciences, 44(5), 545–581.
Arpat, G. B., & Caers, J. (2005). A multiple-scale, pattern-based approach to sequential simulation. In Geostatistics Banff 2004 (pp. 255–264). Springer.
Barnes, C., Shechtman, E., Finkelstein, A., & Goldman, D. B. (2009). PatchMatch: A randomized correspondence algorithm for structural image editing. ACM Transactions on Graphics, 28(3), 24.
Caers, J. (2011). Modeling uncertainty in the earth sciences. Wiley.
Caers, J., & Journel, A. G. (1998). Stochastic reservoir simulation using neural networks trained on outcrop data. In SPE annual technical conference and exhibition. Society of Petroleum Engineers.
Calcagno, P., Chiles, J. P., Courrioux, G., & Guillen, A. (2008). Geological modeling from field data and geological knowledge Part I. Modeling method coupling 3D potential-field interpolation and geological rules. Physics of the Earth and Planetary Interiors, 171(1–4), 147–157.
Caumon, G., Tertois, A. L., & Zhang, L. (2007). Elements for stochastic structural perturbation of stratigraphic models. https://doi.org/10.3997/2214-4609.201403041.
Chatterjee, S., Dimitrakopoulos, R., & Mustapha, H. (2012). Dimensional reduction of pattern-based simulation using wavelet analysis. Mathematical Geosciences, 44(3), 343–374.
Chatterjee, S., & Mohanty, M. M. (2015). Automatic cluster selection using gap statistics for pattern-based multi-point geostatistical simulation. Arabian Journal of Geosciences, 8(9), 7691–7704.
Chen, G. X., Zhao, F., Wang, J. G., Zheng, H. J., Yan, Y. Z., Wang, A. P., Li, J. Y., & Hu, Y. P. (2015). Regionalized multiple-point stochastic geological modeling: A case from braided delta sedimentary reservoirs in Qaidam Basin, NW China. Petroleum Exploration and Development, 42(5), 697–704.
Chen, Q., Mariethoz, G., Liu, G., Comunian, A., & Ma, X. (2018). Locality-based 3-D multiple-point statistics reconstruction using 2-D geological cross sections. Hydrology and Earth System Sciences, 22(12), 6547–6566.
Chen, Q. Y., Liu, G., Ma, X. G., Li, X. C., & He, Z. W. (2020). 3D stochastic modeling framework for Quaternary sediments using multiple-point statistics: A case study in Minjiang Estuary area, southeast China. Computers & Geosciences, 136, 104404.
Chen, Q. Y., Liu, G., Ma, X. G., Zhang, J. Q., & Zhang, X. L. (2019). Conditional multiple-point geostatistical simulation for unevenly distributed sample data. Stochastic Environmental Research and Risk Assessment, 33(4–6), 973–987.
Comunian, A., Giudici, M., Landoni, L., & Pugnaghi, S. (2018). Improving Bowen-ratio estimates of evaporation using a rejection criterion and multiple-point statistics. Journal of Hydrology, 563, 43–50.
Comunian, A., Renard, P., & Straubhaar, J. (2012). 3D multiple-point statistics simulation using 2D training images. Computers & Geosciences, 40, 49–65.
Cui, Z. S., Chen, Q. Y., Liu, G., Ma, X. G., & Que, X. (2021a). Multiple-point geostatistical simulation based on conditional conduction probability. Stochastic Environmental Research and Risk Assessment, 35(7), 1355–1368.
Cui, Z. S., Chen, Q. Y., Liu, G., Mariethoz, G., & Ma, X. G. (2021b). Hybrid parallel framework for multiple-point geostatistics on Tianhe-2: A robust solution for large-scale simulation. Computers & Geosciences, 157, 104923.
Deutsch, C. V. (1992). Annealing techniques applied to reservoir modeling and the integration of geological and engineering (well test) data. Thesis, Stanford University.
Eskandari, K., & Srinivasan, S. (2007). Growthsim—a multiple point framework for pattern simulation. In EAGE conference on petroleum geostatistics (pp. cp-32-00006). European Association of Geoscientists & Engineers.
Fabian, V. (1997). Simulated annealing simulated. Computers & Mathematics with Applications, 33(1–2), 81–94.
Ferrer, R., Emery, X., Maleki, M., & Navarro, F. (2021). Modeling the uncertainty in the layout of geological units by implicit boundary simulation accounting for a preexisting interpretive geological model. Natural Resources Research, 30, 1–23.
Goovaerts, P. (1997). Geostatistics for natural resources evaluation. Oxford University Press on Demand.
Guardiano, F. B., & Srivastava, R. M. (1993). Multivariate geostatistics: Beyond bivariate moments. In Geostatistics Troia’92 (pp. 133–144). Springer.
Guo, J. T., Dai, X. W., Liu, C. J., Wu, L. X., Li, C. L., & Li, F. D. (2021a). An implicit cutting method for 3D geological body model. Geomatics and Information Science of Wuhan University, 46(11), 1766–1773.
Guo, J. T., Wang, J. M., Wu, L. X., Liu, C. Z., Li, C. L., Li, F. D., Lin, M., Jessell, M. W., Li, P. Y., Dai, X. W., & Tang, J. R. (2020). Explicit-implicit-integrated 3-D geological modeling approach: A case study of the Xianyan Demolition Volcano (Fujian, China). Tectonophysics, 795, 228648.
Guo, J. T., Wang, X. L., Wang, J. M., Dai, X. W., Wu, L. X., Li, C. L., Li, F. D., Liu, S. J., & Jessell, M. W. (2021b). Three-dimensional geological modeling and spatial analysis from geotechnical borehole data using an implicit surface and marching tetrahedra algorithm. Engineering Geology, 284, 106047.
Honarkhah, M., & Caers, J. (2010). Stochastic simulation of patterns using distance-based pattern modeling. Mathematical Geosciences, 42(5), 487–517.
Hou, W., Liu, H., Zheng, T., Shen, W., & Xiao, F. (2021). Hierarchical MPS-based three-dimensional geological structure reconstruction with two-dimensional image(s). Journal of Earth Science, 32(2), 455–467.
Hu, L., Liu, Y., Scheepens, C., Shultz, A., & Thompson, R. (2014). Multiple-point simulation with an existing reservoir model as training image. Mathematical Geosciences, 46(2), 227–240.
Jessell, M., Ogarko, V., de Rose, Y., Lindsay, M., Joshi, R., Piechocka, A., Grose, L., de la Varga, M., Ailleres, L., & Pirot, G. (2021). Automated geological map deconstruction for 3D model construction using map2loop 1.0 and map2model 1.0. Geoscientific Model Development, 14(8), 5063–5092.
Kentwell, D., Bloom, L., & Comber, G. (1999). Geostatistical conditional fractal simulation with irregularly spaced data. Mathematics and Computers in Simulation, 48(4–6), 447–456.
Lantuéjoul, C. (2001). Geostatistical simulation: Models and algorithms. Springer.
Mariethoz, G., & Caers, J. (2014). Multiple-point geostatistics: Stochastic modeling with training images. Wiley.
Mariethoz, G., & Renard, P. (2010). Reconstruction of incomplete data sets or images using direct sampling. Mathematical Geosciences, 42(3), 245–268.
Mariethoz, G., Renard, P., & Straubhaar, J. (2010). The direct sampling method to perform multiple-point geostatistical simulations. Water Resources Research. https://doi.org/10.1029/2008wr007621
Matheron, G., Beucher, H., de Fouquet, C., Galli, A., Guerillot, D., & Ravenne, C. (1987). Conditional simulation of the geometry of fluvio-deltaic reservoirs. In SPE annual technical conference and exhibition. OnePetro.
Mirmehdi, M. (2008). Handbook of texture analysis. Imperial College Press.
Okabe, H., & Blunt, M. J. (2004). Prediction of permeability for porous media reconstructed using multiple-point statistics. Physical Review E, 70(6), 066135.
Pakyuz-Charrier, E., Giraud, J., Ogarko, V., Lindsay, M., & Jessell, M. (2018). Drillhole uncertainty propagation for three-dimensional geological modeling using Monte Carlo. Tectonophysics, 747, 16–39.
Pourfard, M., Abdollahifard, M. J., Faez, K., Motamedi, S. A., & Hosseinian, T. (2017). PCTO-SIM: Multiple-point geostatistical modeling using parallel conditional texture optimization. Computers & Geosciences, 102, 116–138.
Qin, Y. Z., Liu, L. M., & Wu, W. C. (2021). Machine learning-based 3D modeling of mineral prospectivity mapping in the Anqing Orefield, Eastern China. Natural Resources Research, 30(5), 3099–3120.
Srivastava, R. (1992). Reservoir characterization with probability field simulation. In SPE annual technical conference and exhibition. OnePetro.
Straubhaar, J., Renard, P., Mariethoz, G., Froidevaux, R., & Besson, O. (2011). An improved parallel multiple-point algorithm using a list approach. Mathematical Geosciences, 43(3), 305–328.
Strebelle, S. (2002). Conditional simulation of complex geological structures using multiple-point statistics. Mathematical Geology, 34(1), 1–21.
Tahmasebi, P., Hezarkhani, A., & Sahimi, M. (2012). Multiple-point geostatistical modeling based on the cross-correlation functions. Computational Geosciences, 16(3), 779–797.
Tahmasebi, P., & Sahimi, M. (2015). Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function. Physical Review E, 91(3), 032401.
Tahmasebi, P., Sahimi, M., & Caers, J. (2014). MS-CCSIM: Accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space. Computers & Geosciences, 67, 75–88.
Turner, R. J., Mansour, M. M., Dearden, R., Dochartaigh, B. E. O., & Hughes, A. G. (2015). Improved understanding of groundwater flow in complex superficial deposits using three-dimensional geological-framework and groundwater models: An example from Glasgow, Scotland (UK). Hydrogeology Journal, 23(3), 493–506.
Wang, L. X., Yin, Y. S., Wang, H., Zhang, C. M., Feng, W. J., Liu, Z. K., Wang, P. G., Cheng, L. F., & Liu, J. (2021). A method of reconstructing 3D model from 2D geological cross-section based on self-adaptive spatial sampling: A case study of Cretaceous McMurray reservoirs in a block of Canada. Petroleum Exploration and Development, 48(2), 407–420.
Wang, L. X., Yin, Y. S., Zhang, C. M., Feng, W. J., Li, G. Y., Chen, Q. Y., & Chen, M. (2022). A MPS-based novel method of reconstructing 3D reservoir models from 2D images using seismic constraints. Journal of Petroleum Science and Engineering, 209, 109974.
Wellmann, J. F., & Regenauer-Lieb, K. (2012). Uncertainties have a meaning: Information entropy as a quality measure for 3-D geological models. Tectonophysics, 526, 207–216.
Wycisk, P., Hubert, T., Gossel, W., & Neumann, C. (2009). High-resolution 3D spatial modeling of complex geological structures for an environmental risk assessment of abundant mining and industrial megasites. Computers & Geosciences, 35(1), 165–182.
Xie, Q., Xu, J. P., Yuan, Y. D., & Niu, C. (2020). Quantitative analysis for the reconstruction of porous media using multiple-point statistics. Geofluids, 2020, 8844968.
Yang, L., Achtziger-Zupancic, P., & Caers, J. (2021). 3D modeling of large-scale geological structures by linear combinations of implicit functions: Application to a large banded iron formation. Natural Resources Research, 30(5), 3139–3163.
Yang, L., Hou, W. S., Cui, C. J., & Cui, J. (2016). GOSIM: A multi-scale iterative multiple-point statistics algorithm with global optimization. Computers & Geosciences, 89, 57–70.
Zhang, T., Du, Y., Huang, T., & Li, X. (2016). Stochastic simulation of geological data using isometric mapping and multiple-point geostatistics with data incorporation. Journal of Applied Geophysics, 125, 14–25.
Zhang, T. F., Switzer, P., & Journel, A. (2006). Filter-based classification of training image patterns for spatial simulation. Mathematical Geology, 38(1), 63–80.
Acknowledgments
This research was financially supported by the National Natural Science Foundation of China (Nos. 42172327 and 41671404), the Fundamental Research Funds for the Central Universities (N2201022), and China Geological Survey Projects (DD20190416). We are very grateful to the editor and two anonymous reviewers for their insightful comments and suggestions, which led to the improvement of the manuscript.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Rights and permissions
About this article
Cite this article
Guo, J., Wang, Z., Li, C. et al. Multiple-Point Geostatistics-Based Three-Dimensional Automatic Geological Modeling and Uncertainty Analysis for Borehole Data. Nat Resour Res 31, 2347–2367 (2022). https://doi.org/10.1007/s11053-022-10071-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11053-022-10071-6