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

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

摘要

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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

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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

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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

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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)

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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

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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%

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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

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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

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