Evaluation of interpolation accuracy of neural kriging with application totemperature-distribution analysis

An interpolation method based on a multilayer neural network (MNN), has bee n 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 tr aining of MNN is used to modify connection weights between nodes located in different layers by a simulated annealing algorithm (one of the optimizati on algorithms of the network). In this process, three types of errors are c onsidered: differences in values, semivariograms, and gradients between sam ple data and outputs from the trained network. The training is continued un til the summation of these errors converges to an acceptably small value. B ecause the MNN trained by this learning criterion can estimate a value at a n arbitrary location, this method is a form of kriging and termed Neural Kr iging (NK). In order to evaluate the effectiveness of NK, a problem on rest oration ability of a defined reference surface from randomly chosen discret e data was prepared. Two types of surfaces, whose semivariograms are expres sed 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, t he interpolation errors of NK were shown to be smaller than both those of o rdinary MNN and ordinal kriging. NK can also produce a contour map in consi deration of gradient constraints. Furthermore, NK was applied to distributi on analysis of subsurface temperatures using geothermal investigation loggi ngs of the Hohi area in southwest Japan. In spite of the restricted quantit y of sample data, the interpolation results revealed high temperature zones and convection patterns of hydrothermal fluids. NK is regarded as an inter polation method with high accuracy that can be used for regionalized variab les with any structure of spatial correlation.