Ground water is a very important underground resource, the principal source of which is thought to be precipitation and underflow from rivers. In general, ground-water level is subject to seasonal fluctuations, and furthermore, the fluctuation pattern varies locally according to the permeability of the aquifer and the distance from the water recharge area. This paper presents a regression analysis method for prediction of the ground-water level.
The autoregressive model constructed from the time-series data can be used to predict future fluctuations. In this paper, we propose that, by extending the theory of the autoregressive model, the multivariate regression model can be related to two kinds of time-series data. This method was applied to specify the relationship between variations of the ground-water level and precipitation in the Kumamoto plain. The optimum multivariate regression models for the nine observation wells, located in the plateau area, at one end of the plain, and in the lowland area, are determined through the value of AIC. The boring data stored in the geotechnical database for the plain are divided into nine groups by the nearest neighborhood method. Assuming that the water level data at each boring site in a group has thesame stochastic structure as the observation-well data in the group, general and regional fluctuation trends in water level under the plain are clearly shown. Furthermore, by using the trend-surface analysis of the water level, seasonal changes of the water-flow pattern are estimated.

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Linear regression analysis based on the theory of probability is used for modeling the relations between multi-variable data. On the other hand, fuzzy linear regression analysis with fuzzy numbers as coefficients of the linear system is proposed to analyze ambiguous relations between various factors affecting the question. By using the fuzzy linear regression analysis, degree of ambiguity of relation between input and output variables can be estimated from the fuzzy regression coefficients. Estimated fuzzy output is expressed as a mean value, and the probable range of the output depends on the value of input data.
In this paper, we propose two applications of the fuzzy regression analysis, i. e., fuzzy multivariateregression model and fuzzy contouring, to examine the potential of fuzzy theory in analysis of subsurface structure. Fuzzy multivariate regression model was applied to the analysis of the relation between variations of ground-water level and precipitation at four observation wells in the Kumamoto plain. For each well, the relative vagueness of correlation between variants was quantified, and the fluctuation model of the ground-water level was constructed. Fuzzy contouring, which fundamentally consists of a polynomial expression, is proposed in order to interpolate values between irregularly distributed data with different populations. As an example, this method is applied to interpolate the supposed N values of data at the same depth in subsurface ground occupied by gravels or by clay. It is clearly shown on the contour maps of N values for the mean values and probable ranges that the probable ranges of N values in the area near to the lithologic boundary are larger than those in other areas of the same soil.

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We explain a procedure to analyze the flow through the network structure on the digital image. The network analysis described in this paper is as follows. First we construct the Pore-Channel (PC) model using the tessellating triangles of the network area. The tessellation procedure was previously explained in Nakano and Fujii (1991b) . For the flow percolating through the network, we calculate the resistance due to channel geometry, and construct the resistor network model. Calculating the net resistance of the network, we can obtain the macroscopic permeability and/or electiric conductivity of the network structure on the image data. We also explain the computer programs for the above procedure.

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An intelligible γ-ray spectra data processing system is developed for instrumental neutron activation analyses. The system works on an ordinary personal computer into which analog-digital converted 4096 channel data are introduced. The functions include automated-peak search and smoothing for peaks and base lines at the same time. Users can set various conditions for the automatic calculation or choose the Kovell method in case many peaks are overlapped. The source list is written in BASIC language which, along with the executable system, is provided for public use.

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Stereographic projection is widely used in mineralogy, structural geology, geophysics and rock mechanics. However, it may be very difficult for the students who have not been learned solid geometry to get the three dimensional image from the stereographic net. Then the author coded the CAI program showing visually both spherical projection and the Wulff's net. This program is applied to the CAI for the paleo-stress fields calculated from the conjugate fault sets.

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