Sensitivity Analysis of a Feedforward Neural Network for Considering Genetic Mechanisms of Kuroko Deposits

Exploration for volcanogenic massive sulfide deposits of the kuroko-type is underway in many places. Clarifying the spatial patterns of the metals in kuroko deposits will be useful for understanding their genetic mechanisms and for future exploration of such types of deposits. This study represents a spatial distribution analysis on the contents of principal metals of kuroko deposits: Cu, Pb, and Zn, in the Hokuroku district, northern Japan, by a feedforward neural network and 1917 sample data at 143 drillhole sites. The network, which consists of three layers, was trained by the principle of SLANS in which the numbers of neurons in the middle layer and training data are changed to improve estimation accuracy. Using the weight coefficients connecting adjacent neurons, sensitivity analysis of the neural network was carried out to identify factors influencing spatial distributions of the three metals. The coordinates depth (z) direction, Bouguer gravity, and specific lithology such as dacite were determined to be influencing factors. The high frequency of the z coordinate signifies that the metal contents differ to a large extent by depth. The sensitivity vector was defined using sensitivity coefficients for x, y, and z coordinates of an estimation point. We determined that the directions of large vectors were different inside and outside of the Hanawa-Ohdate area. This characteristic is considered to originate from the differences in the permeability of fractures that became the paths for rising ore solutions, and the depths that the solutions mixed with sea water.     

New Indices for Characterizing Spatial Models of Ore Deposits by the Use of a Sensitivity Vector and an Influence Factor

Precise spatial estimation of ore grades and impurity contents from sample data limited in amount and location is indispensable to metallic and nonmetallic resource exploration. One of the advantages of using geostatistics for this purpose is that it can incorporate multivariate data into spatial estimation of one variable. However, there are two weak points concerning technical and post-processing problems. First is the difficulty in application to geologic data in which spatial correlations are not clear because of intrinsic nonlinear behavior. Second is the absence of indices to interpret the mechanisms and factors which govern the spatial distribution. To address these problems, a spatial method of modeling based on a feedforward neural network, SLANS, which recognizes the relationship between the data value and location by considering supplementary attributes such as lithology and biostratigraphy, and a sensitivity analysis using this network were developed. These methods were applied to two case studies, genetic mechanisms of kuroko deposits and quality assessment of a limestone mine. The first case study is a spatial analysis of principal metals of kuroko deposits (volcanogenic massive sulfide deposits) in the Hokuroku district, northern Japan. It was clarified that upward and downward sensitivity vectors were distinguished near the deposits inside and outside the tectonic basin, respectively. Sensitivity analysis for the second case study showed a strong effect of crystalline limestone on the important impurity, P₂O₅ contents. Hydrothermal alteration, which could cause leaching and secondary concentration of phosphorus, is considered to have produced this effect.     

Neural Network-Based Estimation of Principal Metal Contents in the Hokuroku District,Northern Japan,for Exploring Kuroko-Type Deposits

The Hokuroku district, extending over 40 × 40 km² in northern Japan, is known to be dominated by kuroko-type massive sulfide deposits that have a genetic relation to submarine volcanic activity. The deposits are hosted in a specific stratigraphic zone of Miocene volcanic rocks. Because kuroko-type deposits are under exploration in several countries, it is important to integrate the geologic and geochemical data that have been accumulated in the Hokuroku district to characterize the distribution of deposits and produce a map of mineral potential. Thus, we collected data on multiple chemical components from 1917 rock cores at 143 drillhole sites and concentrated on components with relatively large amounts of data, which are SiO₂, Al₂O₃, and Fe₂O₃ as major elements and Cu, Pb, and Zn as trace elements. Although frequencies of these data can be approximated by normal or lognormal distributions, spatial correlation structures cannot be extracted from the semivariograms of each component nor from the cross-semivariograms between two components of the major or minor elements. To handle such complexity, a spatial method of modeling content distribution, SLANS, is developed by applying a feedforward neural network. The principle of SLANS is to train a network repeatedly to recognize the relation between the data value and the location and lithology of a sample point. One-hundred outputs for each element are obtained by changing the numbers of neurons in a middle layer from 1 to 10 and sample data used for training from 3 to 12, and finally one output is selected based on the estimation precision of the network which is restricted near the target point. After constructing a geologic distribution model from the geological column classified into 25 rock codes, three-dimensional distributions of Cu, Pb, and Zn contents are estimated over the study area. The content models are considered to be valid because high-content zones are located on the known mine sites and the margins of ancient volcanoes or calderas. Some zones are distributed along strikes of major deep-seated fractures in the district.     

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.     

Characterizing Content Distributions of Impurities in a Limestone Mine Using a Feedforward Neural Network

The factors determining the suitability of limestone for industrial use and its commercial value are the amounts of calcium oxide (CaO) and impurities. From 244 sample points in 18 drillhole sites in a limestone mine, southwestern Japan, data on four impurity elements, SiO₂, Fe₂O₃, MnO, and P₂O₅ were collected. It generally is difficult to estimate spatial distributions of these contents, because most of the limestone bodies in Japan are located in the accretionary complex lithologies of Paleozoic and Mesozoic age. Because the spatial correlations of content data are not clearly shown by variogram analysis, a feedforward neural network was applied to estimate the content distributions. The network structure consists of three layers: input, middle, and output. The input layer has 17 neurons and the output layer four. Three neurons in the input layer correspond with x, y, z coordinates of a sample point and the others are rock types such as crystalline and conglomeratic limestones, and fossil types related to the geologic age of the limestone. Four neurons in the output layer correspond to the amounts of SiO₂, Fe₂O₃, MnO, and P₂O₅. Numbers of neurons in the middle layer and training data differ with each estimation point to avoid the overfitting of the network. We could detect several important characteristics of the three-dimensional content distributions through the network such as a continuity of low content zones of SiO₂ along a Lower Permian fossil zone trending NE-SW, and low-quality zones located in depths shallower than 50 m. The capability of the neural network-based method compared with the geostatistical method is demonstrated from the viewpoints of estimation errors and spatial characteristics of multivariate data. To evaluate the uncertainty of estimates, a method that draws several outputs by changing coordinates slightly from the target point and inputting them to the same trained network is proposed. Uncertainty differs with impurity elements, and is not based on just the spatial arrangement of data points.