Spatial Modeling Techniques for Characterizing Geomaterials: Deterministic vs.Stochastic Modeling for Single-Variable and Multivariate Analyses

Koike Katsuaki

New Frontier Sciences, Graduate School of Science and Technology, Kumamoto University, Japan

More Information

Author Bio:
Katsuaki Koike, E-mail: koike@gpo.kumamoto-u.ac.jp

摘要

- /
- /
- /
- /
- /
- /
Abstract: Sample data in the Earth and environmental sciences are limited in quantity and sampling location and therefore, sophisticated spatial modeling techniques are indispensable for accurate imaging of complicated structures and properties of geomaterials. This paper presents several effective methods that are grouped into two categories depending on the nature of regionalized data used. Type I data originate from plural populations and type II data satisfy the prerequisite of stationarity and have distinct spatial correlations. For the type I data, three methods are shown to be effective and demonstrated to produce plausible results: (1) a spline-based method, (2) a combination of a spline-based method with a stochastic simulation, and (3) a neural network method. Geostatistics proves to be a powerful tool for type II data. Three new approaches of geostatistics are presented with case studies: an application to directional data such as fracture, multi-scale modeling that incorporates a scaling law, and space-time joint analysis for multivariate data. Methods for improving the contribution of such spatial modeling to Earth and environmental sciences are also discussed and future important problems to be solved are summarized.
- geostatistics /
- spline /
- neural network /
- geological modeling /
- mineral resources /
- fracture distribution /
- water environment

HTML全文

Fig. 1. (A) Hohi geothermal region in central Kyushu, Southwest Japan, showing topography, location of wells, and the lengths of the downhole logs used in the study.Depths range from 80 to 3 300 m. (B) Three-dimensional geological model of the Hohi geothermal region constructed using the OPTSIM method and showing the eight main rock types.The topography of the ground surface is shown.V.R.: volcanic rock. (C) Integration of the temperature model, geological model, and large-magnitude fluid flow velocity vectors.The geological model and vectors are overlaid onto the high-temperature zones (>150 ℃).Two ovals circled represent the geothermal reservoirs inferred from the relationship between the temperature and the geological models

下载: 全尺寸图片幻灯片

Fig. 2. (A) Semivariogram constructed from the indicator values, 0 for conductive type and 1 for convective type, assigned to each borehole site depending on the temperature profile in the Hohi geothermal region.(B) Horizontal temperature-distributions estimated by neural kriging at 0 m, -500 m, and -1 000 m levels.Values indicate temperatures retrieved at each borehole site

下载: 全尺寸图片幻灯片

Fig. 3. (A) Distributions of sensitivity vectors for Zn in the Kuroko-mine areas in the Hokuroku District, northern Japan.(B) Distribution of estimation points with large sensitivity vectors.The colors of the points represent the directions of the sensitivity vectors.(C) Schematic model of the occurrence of Kuroko ores, by mixing ore solutions with sea water, for upward vector (left) and downward vector (right)

下载: 全尺寸图片幻灯片

Fig. 4. (A) Topography of the study area (Tono District, central Japan) and the arrangement of 19 sites of deep boreholes ranging 500 to 1 000 m depth.(B) Perspective views showing the distribution pattern of simulated continuous fractures composed of fifty or more facets.(C) Superimposition of the zones of large hydraulic conductivity of more than 10^-5 cm/s onto the continuous simulated fractures

下载: 全尺寸图片幻灯片

Fig. 5. (A) Pore simulation results for different area sizes under conditions of porosity 40% by simulated annealing with scaling laws on size and the spatial correlation of pores.(B) Relationship between the calculation of area size and the maximum connection length of pores from pore simulation results for porosity 40%

下载: 全尺寸图片幻灯片

Fig. 6. Estimated distributions of the concentrations of the nutritive salts NO₂-N and NO₃-N over the Ariake Sea, central Kyushu.MCK and SK denote space-time models by multivariate standardized ordinary cokriging and single variable ordinary kriging

下载: 全尺寸图片幻灯片

Fig. 7. (A) Three-dimensional distribution of the 57 ℃ surface and its relationship to topography over Kyushu Island.(B) Computed 3D temperature distribution at 500 and 900 m depths.Low-temperature zones bounded by the long active faults are circled in the map of 500 m depth

下载: 全尺寸图片幻灯片

参考文献(65)

[1]	Ahmed, S., Marsily, G.D., 1987. Comparison of geostatistical methods for estimating transmissivity using data on transmissivity and specific capacity. Water Resources Research, 23(9): 1717-1737. doi: 10.1029/WR023i009p01717
[2]	Bonnet, E., Bour, O., Odling, N.E., et al., 2001. Scaling of fracture systems in geological media. Reviews of Geophysics, 39(3): 347-383. doi: 10.1029/1999RG000074
[3]	Briggs, I.C., 1974. Machine contouring using minimum curvature. Geophysics, 39(1): 39-48. doi: 10.1190/1.1440410
[4]	Cacas, M.C., Ledoux, E., DeMarsily, G., et al., 1990. Modelling fracture flow with a stochastic discrete fracture network: calibration and validation: 1. The flow model. Water Resources Research, 26(3): 479-489. doi: 10.1029/WR026i003p00491/pdf
[5]	Caers, J., Zhang, T., 2005. Multiple-point geostatistics: a quantitative vehicle for integrating geological analogs into multiple reservoir model. AAPG Memoir, 80: 383-394.
[6]	Casanova, P.G., Alvarez, R., 1985. Splines in geophysics. Geophysics, 50(12): 2831-2848. doi: 10.1190/1.1441903
[7]	Chaplot, V., Darboux, F., Bourennane, H., et al., 2006. Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density. Geomorphology, 77(1-2): 126-141. doi: 10.1016/j.geomorph.2005.12.010
[8]	Chilès, J.P., 1988. Fractal and geostatistical methods for modeling of a fracture network. Mathematical Geology, 20(6): 631-654. doi: 10.1007/BF00890581
[9]	Costa, J.F., Zingano, A.C., Koppe, J.C., 2000. Simulation—an approach to risk analysis in coal mining. Exploration and Mining Geology, 9(1): 43-49. doi: 10.2113/0090043
[10]	Cressie, N., Huang, H., 1999. Classes of nonseparable, spatial-temporal stationary covariance functions. Journal of the American Statistical Association, 94(448): 1330-1340. doi: 10.1080/01621459.1999.10473885
[11]	Daïan, J.F., Fernandes, C.P., Philippi, P.C., et al., 2004.3D reconstitution of porous media from image processing data using a multiscale percolation system. Journal of Petroleum Science & Engineering, 42(1): 15-28. http://www.sciencedirect.com/science/article/pii/S0920410503002031
[12]	de Kemp, E.A., 2000.3-D visualization of structural field data: examples from the Archean Caopatina Formation. Computers & Geosciences, 26 (5): 509-530. http://www.sciencedirect.com/science/article/pii/S0098300499001429
[13]	de Iaco, S., Myers, E.D., Posa, D., 2002. Nonseparable space-time covariance models: some parametric families. Mathematical Geology, 34(1): 23-42. doi: 10.1023/A:1014075310344
[14]	de Iaco, S., Myers, E.D., Posa, D., 2003. The linear coregionalization model and the product-sum space-time variogram. Mathematical Geology, 35(1): 25-38. doi: 10.1023/A:1022425111459
[15]	Dekking, M., Elfeki, A., Kraaikamp, C., et al., 2001. Multi-scale and multi-resolution stochastic modeling of subsurface heterogeneity by tree-indexed Markov Chains. Computational Geosciences, 5(1): 47-60. doi: 10.1023/A:1011610003277
[16]	Gatrell, A., L?y?nen, M., 1998. GIS and health. Taylor & Francis, London, 230.
[17]	Gómez-Hernández, J.J., Srivastava, R.M., 1990. ISIM3D: an ANSI-C three-dimensional multiple indicator conditional simulation program. Computers & Geosciences, 16(4): 395-440. http://dl.acm.org/citation.cfm?id=84572
[18]	Heriawan, M.N., Koike, K., 2008a. Identifying spatial heterogeneity of coal resource quality in a multilayer coal deposit by multivariate geostatistics. International Journal of Coal Geology, 73(3-4): 307-330. doi: 10.1016/j.coal.2007.07.005
[19]	Heriawan, M.N., Koike, K., 2008b. Uncertainty assessment of coal tonnage by spatial modeling of seam structure and coal quality. International Journal of Coal Geology, 76(3): 217-226. doi: 10.1016/j.coal.2008.07.014
[20]	Journel, A.G., 1989. Fundamentals of geostatistics in five lessons: short course in geology, Vol. 8. American Geophysical Union, 40, Washington D.C. .
[21]	Kay, M., Dimitrakopoulos, R., 2000. Integrated interpolation methods for geophysical data: applications to mineral exploration. Natural Resources Research, 9(1): 53-63. http://www.ingentaconnect.com/content/klu/narr/2000/00000009/00000001/00224167
[22]	Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P., 1983. Optimization by simulated annealing. Science, 4598: 671-680. http://www.zhangqiaokeyan.com/open-access_resources_thesis/0100057209782.html
[23]	Koike, K., Gu, B., Ohmi, M., 1998a. Three-dimensional distribution analysis of phosphorus content of limestone through a combination of geostatistics and artificial neural network. Nonrenewable Resources, 7(3): 197-210. doi: 10.1007/BF02767670
[24]	Koike, K., Shiraishi, Y., Verdeja, E., et al., 1998b. Three-dimensional interpolation and lithofacies analysis of granular composition data for earthquake-engineering characterization of shallow soil. Mathematical Geology, 30(6): 733-759. doi: 10.1023/A:1022473320050
[25]	Koike, K., Matsuda, S., Gu, B., 2001a. Evaluation of interpolation accuracy of neural kriging with application to temperature-distribution analysis. Mathematical Geology, 33(4): 421-448. doi: 10.1023/A:1011084812324
[26]	Koike, K., Sakamoto, H., Ohmi, M., 2001b. Detection and hydrologic modeling of aquifers in unconsolidated alluvial plains through combination of borehole data sets: a case study of the Arao area, Southwest Japan. Engineering Geology, 62(4): 301-317. doi: 10.1016/S0013-7952(01)00031-X
[27]	Koike, K., Matsuda, S., Suzuki, T., et al., 2002. Neural network-based estimation of principal metal contents in the Hokuroku district, northern Japan, for exploring Kuroko-type deposits. Natural Resources Research, 11(2): 135-156. doi: 10.1023/A:1015520204066
[28]	Koike, K., Fujiyoshi, H., 2003. Spatial modeling of pore distribution in porous media using geostatistics for detecting hydraulic property. In: Saito, T., Murata, S., eds., Environmental rock engineering. A.A. Balkema Publishers, Lisse, 259-264.
[29]	Koike, K., Matsuda, S., 2005. Spatial modeling of discontinuous geological attributes with geotechnical applications. Engineering Geology, 78(1-2): 143-161. doi: 10.1016/j.enggeo.2004.12.004
[30]	Koike, K., Ichikawa, Y., 2006. Spatial correlation structures of fracture systems for identifying a scaling law and modeling fracture distributions. Computers & Geosciences, 32(8): 1079-1095. http://www.sciencedirect.com/science/article/pii/S0098300406000318
[31]	Koike, K., Matsuda, S., 2006. New indices for characterizing spatial models of ore deposits by the use of a sensitivity vector and influence factor. Mathematical Geology, 38(5): 541-564. doi: 10.1007/s11004-006-9030-3
[32]	Koike, K., Liu, C., 2007. Spatial modeling method considering scaling-law with application to pore simulation in porous media. Geoinformatics, 18(3): 159-175 (in Japanese with English abstract).
[33]	Koike, K., Liu, C., Masoud, A.A., et al., 2009. Large-scale modeling of 3D fracture distributions for hydrogeological characterization. Proceedings iamg09. Stanford Univ., CA, USA.
[34]	Liu, C., Koike, K., 2007. Extending multivariate space-time geostatistics for environmental data analysis. Mathematical Geology, 39(3): 289-305. doi: 10.1007/s11004-007-9085-9
[35]	Long, J.C.S., Gilmour, P., Witherspoon, P.A., 1985. A model for steady fluid flow in random three-dimensional networks of disc-shaped fractures. Water Resources Research, 21(8): 1105-1115. doi: 10.1029/WR021i008p01105
[36]	Lu, S., Molz, F.J., Liu, H.H., 2003. An efficient, three-dimensional, anisotropic, fractional Brownian motion and truncated fractional Levy motion simulation algorithm based on successive random additions. Computers & Geosciences, 29(1): 15-25. http://www.sciencedirect.com/science/article/pii/S0098300402000730
[37]	Magnussen, S., N?sset, E., Wulder, M.A., 2007. Efficient multiresolution spatial predictions for large data arrays. Remote Sensing of Environment, 109(4): 451-463. doi: 10.1016/j.rse.2007.01.018
[38]	Masoud, A.A., Koike, K., 2009. Spatial quality modeling of the Kaolin resources integrating GIS and geostatistics. Proc. MMIJ Annual Meeting (2009), Vol. I: 125-126.
[39]	Matías, J.M., Vaamonde, A., Taboada, J., et al., 2004. Support vector machines and gradient boosting for graphical estimation of a slate deposit. Stochastic Environmental Research and Risk Assessment, 18(5): 309-323. doi: 10.1007/s00477-004-0185-5
[40]	Matsuda, S., Koike, K., 2003. Sensitivity analysis of a feedforward neural network for considering genetic mechanisms of Kuroko deposits. Natural Resources Research, 12(4): 291-301. doi: 10.1023/B:NARR.0000007807.14126.a2
[41]	Merwade, V., 2009. Effect of spatial trends on interpolation of river bathymetry. Journal of Hydrology, 371(1-4): 169-181. doi: 10.1016/j.jhydrol.2009.03.026
[42]	Mitasova, H., Mitas, L., 1993. Interpolation by regularized spline with tension: I. theory and implementation. Mathematical Geology, 25(6): 641-655. doi: 10.1007/BF00893171
[43]	Palmer, D.J., H?ck, B.K., Kimberley, M.O., et al., 2009. Comparison of spatial prediction techniques for developing Pinus radiata productivity surfaces across New Zealand. Forest Ecology and Management, 258(9): 2046-2055. doi: 10.1016/j.foreco.2009.07.057
[44]	Pardo-Igúzquiza, E., Dowd, P.A., 2002. FACTOR2D: a computer program for factorial cokriging. Computers & Geosciences, 28(8): 857-875. http://www.sciencedirect.com/science/article/pii/S0098300402000031
[45]	Pardo-Igúzquiza, E., Atkinson, P.M., 2007. Modelling the semivariograms and cross-semivariograms required in downscaling cokriging by numerical convolution-deconvolution. Computers & Geosciences, 33(10): 1273-1284. doi: 10.1016/j.cageo.2007.05.004
[46]	Rizzo, D.M., Dougherty, D.E., 1994. Characterization of aquifer properties using artificial neural networks: neural kriging. Water Resources Research, 30 (2): 483-497. doi: 10.1029/93WR02477
[47]	Robinson, T.P., Metternicht, G., 2005. Comparing the performance of techniques to improve the quality of yield maps. Agricultural Systems, 85(1): 19-41. doi: 10.1016/j.agsy.2004.07.010
[48]	Robinson, T.P., Metternicht, G., 2006. Testing the performance of spatial interpolation techniques for mapping soil properties. Computers and Electronics in Agriculture, 50(2): 97-108. doi: 10.1016/j.compag.2005.07.003
[49]	Saepuloh, A., Koike, K., 2009. Detailed mapping of pyroclastic flow deposits by SAR data processing for an active volcano in the Torrid zone. In: Proceeding of International Conference on Earth and Space Sciences and Engineering 2009 (ICESSE 2009). Tokyo, Japan, 270-274.
[50]	Sahimi, M., Mehrabi, A.R., 1999. Percolation and flow in geological formations: upscaling from microscopic to megascopic scales. Physica A, 266(1-4): 136-152. doi: 10.1016/S0378-4371(98)00586-X
[51]	Sahimi, M., 2000. Fractal-wavelet neural-network approach to characterization and upscaling of fractured reservoirs. Computers & Geosciences, 26(8): 877-905. doi: 10.5555/351914.351917
[52]	Salu, Y., Tilton, J., 1993. Classification of miltispectal image data by the binary diamond neural network and by nonparametric, pixel-by-pixel-methods. IEEE Transactions on Geoscience & Remote Sensing, 31(3): 606-617. http://ci.nii.ac.jp/naid/30019684845
[53]	Samanta, B., Ganguli, R., Bandopadhyay, S., 2005. Comparing the predictive performance of neural networks with ordinary kriging in a bauxite deposit. Transactions of the Institutions of Mining and Metallurgy, Section A: Mining Technology, 114(3): A129-A139. doi: 10.1179/037178405X53980
[54]	Solomon, S., Qin, D., Manning, M., et al., eds., 2007. Climate change 2007—the physical science basis, contribution of working group I to the fourth assessment report of the IPCC. Cambridge University Press, New York, 996.
[55]	Strebelle, S., 2002. Conditional simulation of complex geological structures using multiple-point statistics. Mathematical Geology, 34(1): 1-21. doi: 10.1023/A:1014009426274
[56]	Sun, Y., Kang, S., Li, F., et al., 2009. Comparison of interpolation methods for depth to groundwater and its temporal and spatial variations in the Minqin oasis of Northwest China. Environmental Modelling & Software, 24(10): 1163-1170. http://www.cabdirect.org/abstracts/20133063655.html
[57]	Tadakuma, N., Koike, K., Asaue, H., 2010.3D temperature modeling over Kyushu Island (SW Japan) and its characterization from geological structures. Proceedings World Geothermal Congress 2010, Bali, Indonesia. Paper Number 1539.
[58]	Teng, Y., Koike, K., 2007. Three-dimensional imaging of a geothermal system using temperature and geological models derived from a well-log dataset. Geothermics, 36(6): 518-538. doi: 10.1016/j.geothermics.2007.07.006
[59]	Tran, N.H., Chen, Z., Rahman, S.S., 2006. Integrated conditional global optimisation for discrete fracture network modeling. Computers & Geosciences, 32(1): 17-27.
[60]	van der Meer, F., 1994. Sequential indicator conditional simulation and indicator kriging applied to discrimination of dolomitization in GER 63-channel imaging spectrometer data. Nonrenewable Resources, 3(2): 146-164. doi: 10.1007/BF02286439
[61]	Weissmann, G.S., Carle, S.F., Fogg, G.E., 1999. Three-dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics. Water Resources Research, 35: 1761-1770. doi: 10.1029/1999WR900048
[62]	Wolf, D.J., Withers, K.D., Burnaman, M.D., 1994. Integration of well and seismic data using geostatistics. In: Yarus, J.M., Chambers, R.L., eds., Stochastic modeling and geostatistics. AAPG, Tulsa, 177-199.
[63]	Yamamoto, J.K., 2005. Correcting the smoothing effect of ordinary kriging estimates. Mathematical Geology, 37(1): 69-94. doi: 10.1007/s11004-005-8748-7
[64]	Zimmerman, D., Pavlik, C., Ruggles, A., et al., 1999. An experimental comparison of ordinary and universal kriging and inverse distance weighting. Mathematical Geology, 31(4): 375-390. doi: 10.1023/A:1007586507433
[65]	Zhu, H., Journel, A., 1993. Formatting and integrating soft data: stochastic imaging via the Markov-Bayes algorithm. In: Soares A., ed., Geostatistics Toria'92. Kluwer Academic Publishers, 1-12.