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

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.      

Seismic response control using electromagnetic inertial mass dampers

This paper presents a new type of electromagnetic damper with rotating inertial mass that has been developed to control the vibrations of structures subjected to earthquakes. The electromagnetic inertial mass damper (EIMD) consists of a ball screw that converts axial oscillation of the rod end into rotational motion of the internal flywheel and an electric generator that is turned by the rotation of the inner rod. The EIMD is able to generate a large inertial force created by the rotating flywheel and a variable damping force developed by the electric generator. Device performance tests of reduced‐scale and full‐scale EIMDs were undertaken to verify the basic characteristics of the damper and the validity of the derived theoretical formulae. Shaking table tests of a three‐story structure with EIMDs and earthquake response analyses of a building with EIMDs were conducted to demonstrate the seismic response control performance of the EIMD. The EIMD is able to reduce story drifts as well as accelerations and surpasses conventional types of dampers in reducing acceleration responses. Copyright © 2013 John Wiley & Sons, Ltd.     

Three-Dimensional Interpolation and Lithofacies Analysis of Granular Composition Data for Earthquake-Engineering Characterization of Shallow Soil

In Japan, many major cities are located on tectonic basins which are surrounded by faults and underlain by soft alluvial materials. Because these areas are subject to earthquake damages, it is important to determine their seismic engineering characteristics. Geotechnical databases which contain many borehole logs are useful information sources for this type of analysis. Each datum stored in the database has a value or an attribute, and its location is irregular in both horizontal and vertical directions. A new interpolation method based on the optimization principle is proposed here to deal with such three-dimensionally distributed data. Susceptibility of unconsolidated ground to liquefaction is known to be related to the content of loose and saturated sand. The mixture ratio of several soil types in a deposit, i.e., granular composition, is strongly influenced by the sedimentary environment. There are two numerical methods: the optimization principle method (OPM) used to determine three-dimensional distribution of granular composition and the model used to evaluate liquefaction. The application of the proposed methods to two locations in Japan indicated that the zones with high susceptibility to liquefaction were indeed those that had suffered from liquefaction during past earthquakes.     

Radon concentrations in soil gas,considering radioactive equilibrium conditions with application to estimating fault-zone geometry

A calculation method for determining the amount of Rn isotopes and daughter products at the start of measurement (CRAS) is proposed as a more accurate means of estimating the initial Rn concentration in soil gas. The CRAS utilizes the decay law between ²²²Rn and ²²⁰Rn isotopes and the daughter products ²¹⁸Po and ²¹⁶Po, and is applicable to α-scintillation counter measurements. As Rn is both inert and chemically stable, it is useful for fault investigation based on the soil gas geochemistry. However, the total number of α particles emitted by the decay of Rn has generally been considered to be proportional to the initial Rn concentration, without considering the gas condition with respect to radioactive equilibrium. The CRAS method is shown to be effective to derive Rn concentration for soil gases under both nonequilibrium conditions, in which the total number of decays increases with time, and equilibrium conditions, which are typical of normal soil under low gas flux. The CRAS method in conjunction with finite difference method simulation is applied to the analysis of two active fault areas in Japan, and it is demonstrated that this combination could detect the sharp rises in ²²²Rn concentrations associated with faults. The method also allows the determination of fault geometry near the surface based on the asymmetry variation of the Rn concentration distribution when coupled with a numerical simulation of ²²²Rn transport. The results for the new method as applied to the two case studies are consistent with the data collected from the geological survey. It implies that the CRAS method is suitable for investigating the fault system and interstitial gas mobility through fractures. The present analyses have also demonstrated that high Rn concentrations require the recent and repeated accumulation of ²²²Rn parents (²³⁰Th and ²²⁶Ra) in fault gouges through deep gas release during fault movement.     

Evaluation of Interpolation Accuracy of Neural Kriging with Application to Temperature-Distribution Analysis

An interpolation method based on a multilayer neural network (MNN), has been examined and tested for the data of irregular sample locations. The main advantage of MNN is in that it can deal with geoscience data with nonlinear behavior and extract characteristics from complex and noisy images. The training of MNN is used to modify connection weights between nodes located in different layers by a simulated annealing algorithm (one of the optimization algorithms of the network). In this process, three types of errors are considered: differences in values, semivariograms, and gradients between sample data and outputs from the trained network. The training is continued until the summation of these errors converges to an acceptably small value. Because the MNN trained by this learning criterion can estimate a value at an arbitrary location, this method is a form of kriging and termed Neural Kriging (NK). In order to evaluate the effectiveness of NK, a problem on restoration ability of a defined reference surface from randomly chosen discrete data was prepared. Two types of surfaces, whose semivariograms are expressed by isotropic spherical and geometric anisotropic gaussian models, were examined in this problem. Though the interpolation accuracy depended on the arrangement pattern of the sample locations for the same number of data, the interpolation errors of NK were shown to be smaller than both those of ordinary MNN and ordinal kriging. NK can also produce a contour map in consideration of gradient constraints. Furthermore, NK was applied to distribution analysis of subsurface temperatures using geothermal investigation loggings of the Hohi area in southwest Japan. In spite of the restricted quantity of sample data, the interpolation results revealed high temperature zones and convection patterns of hydrothermal fluids. NK is regarded as an interpolation method with high accuracy that can be used for regionalized variables with any structure of spatial correlation.     

Geostatistical Modeling of Ore Grade Distribution from Geomorphic Characterization in a Laterite Nickel Deposit

Due to growing consumption of nickel (Ni) in a range of industries, the demand for Ni has increased rapidly around the world. This trend requires a more precise estimation of available Ni grade deposits and an identification of factors controlling the grade distribution. To achieve these requirements, this study applies geostatistical techniques to spatial modeling of the Ni grade in a laterite Ni deposit, with reference to geomorphic features such as slope gradient and the thickness of limonite and saprolite zones. The Sorowako area in Sulawesi Island, Indonesia, was chosen as a case study area because it has a representative laterite Ni deposit with large reserves. Chemical content data from drillhole cores at 294 points were used for the analysis. The slope gradient was found to have a remarkable correlation with the thickness of the limonite zone, but there was no correlation between the thickness of the limonite and the saprolite zones above the bedrock. One important feature was a general correlation between the thickness of the saprolite zone and the maximum Ni grade in this zone: the grade increases with the thickness of the zone. Co-kriging was adopted to incorporate this correlation into estimating the maximum Ni grade in the saprolite zone. As a result, the maximum Ni grade in the saprolite zone tends to be high mainly in areas of slight slope. The Ni accumulation at this topographic feature probably originates from deep weathering by groundwater infiltrating through well-developed rock fractures.     

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

In addition to spatial distribution of groundwater-flow parameters, aquifer properties of location and shape are also significant for assessing groundwater resources because they strongly affect water flow. We present a selection of geologic data suitable for aquifer analysis, a mathematical method of processing them, and a combination of several maps produced by it. The data used in the analysis are typically obtained by borehole investigation. Our targets are the areas underlain by geologic bodies with different ages and lithologies; the spatial correlation structures of geologic data over the areas tend to change locally. The processing method should be a versatile one that is applicable to areas where geostatistical stationarity is not satisfied. The aquifer analysis consistent with that requirement consists of two steps: the first is the transformation of screen locations, locations of sand and gravel layers, and resistivity by electric logging into indicator values, and the second is three-dimensional interpolation of these using the optimization principle method to produce three kinds of distribution models. A stochastic simulation is also used for modeling the resistivity distribution. The three distribution models are integrated to generate a value for evaluating the possibility of aquifer existence. A case study of an alluvial coastal plain, situated in southwest Japan, describes an aquifer model that contains three permeable layers. Each layer has about 10-m thickness and is lens shaped. To confirm the validity of the model, we have drilled two wells that reached one of the middle and bottom permeable layers, observing the water level change. Low correlation of the temporal changes of levels between the wells indicates that the two layers are hydrologically independent of each other. Additionally, groundwater-flow patterns have been estimated by transforming the simulation model parameter into hydraulic conductivity through a simple function and using a finite difference method for flow analysis. The procedure proposed by this study can be applied to other areas by changing the weights assigned to each geologic and geotechnical factor in the generation of the coefficient for aquifer existence, considering the reliability of each factor and hydrologic properties of study area.     

Application of Magnetotelluric (MT) Resistivity to Imaging of Regional Three-Dimensional Geologic Structures and Groundwater Systems

Widespread definition of a groundwater system in three dimensions is necessary for the management and maintenance of groundwater resources. A magnetotelluric (MT) survey can be an effective geophysical prospecting method for imaging regional geological structures by measuring both shallow and deep resistivity. To demonstrate the capability of an MT survey to characterize a groundwater system, the Kumamoto area of central Kyushu in southwestern Japan was selected as a case study site because of its rich groundwater resources. Three-dimensional (3D) MT resistivity structure to a depth of 5?km was modeled by 1D inversion analysis of raw MT data and 3D interpolation of the resultant resistivity column data by the optimization principle method. Consequently, both deep and shallow aquifers were detected. A high-resistivity zone appears at depths between 500 and 2,000?m between the Futagawa?CHinagu faults and the Usuki?CYatsushiro tectonic line, which supports the existence of an aquiclude under the aquifer. The most important characteristic inferred from the 3D resistivity model is that the deep groundwater system below a depth of 1,000?m has two main flow paths. One path is likely to be through porous rocks because the low resistivity zone is regarded as tuff with sand and gravel, and the other flow path is interpreted to be through fractured zones along the Hinagu faults. Hence, the path and direction of the groundwater flows are probably controlled by geologic structures and the configuration of the active faults. These findings support the effectiveness of the MT method for investigating groundwater systems.     

Introduction to the Special Issue on the “Mathematical Geology for Resource Exploration” Session at IGC32

Natural Resources Research -     

Hydrogeologic-structure and groundwater-movement imaging in tideland using electrical sounding resistivity: a case study on the Ariake Sea coast, southwest Japan

Groundwater flow exerts a crucial control on the boundary between the sea and freshwater and is thus a key factor for preserving groundwater resources and preventing seawater intrusion in coastal areas. Although it is highly probable that geological faults in coastal areas affect groundwater flow patterns, the effect has not been described yet in detail. This study is aimed at detecting and imaging groundwater flow and its temporal change around a fault in a coastal area through resistivity and chargeability distributions using electrical sounding. The Okoshiki area in central Kyushu, southwest Japan, was selected as a case study area, because of the presence of Kamiouda Fault. The measurements were conducted along six lines of both parallel and perpendicular orientations to the coastline. A feature suggesting a fault zone was evident on two lines. Through the temporal change of resistivity, movement and mixing processes of the seawater and freshwater during the ebb, low and flood tides were interpreted. A conceptual model of the processes was constructed in which a fault zone and the configuration of bedrock are dominant elements by acting as a selective path and a barrier to the groundwater flow, respectively.