We have presented the process of geologic mapping in mathematical formulae, and constructed the software system CIGMA. Input data are composed of numerical data and relationship data. Numerical data show the coordinate of point, and strike and dip of the stratum. Relationship data show the structural relationship between two strata. Though these types of data are independently processed in this system, input data for geologic mapping should be essentially observed in the field. Observed data have been accumulated in the outcrop database, The CIGMA system is one of the softwares to which the outcrop database can be applied.

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Hazard zonation maps for slope failure are widely utilized for diverse people who have various view points.Digitizing of data is indispensable to transformation of data and their expression for such multi-purpose use.
The grade of“danger”which is expressed by probabilities on the map may strongly depend on time interval and spatial extent of the spot.Therefore, probabilistic data on the map should be expressed with the parameter of time T in addition to the position x and y.This may be possible by using the change in terms of time for physical deteriorating of the slope.
Considering that source data are insufficient and the algorithm to construct probability values from them have not been established, reliability of the probability value may be relative low. Therefore, it may be effective to express it by fuzzy number.
To realize these multi-purpose hazard map, a management system which are charge of transformation and expression of data are required with data base.

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In most cases, geological and geotechnical investigation data are irregularly distributed in horizontal and vertical directions. Therefore proper choice of an automatic contouring method is required to reveal diverse subsurface structures. Many contouring methods have been proposed so far, which can be classified into two categories regarding their principles. The first method is a global fit algorithm termed approximation. The usual global algorithm is a trend surface analysis, which reveals a regional trend in sample (or measured) data through the weighted least squares method. In this method, weighting coefficients are assigned to each data point according to the statistical property of sample data. The second method is a local fit algorithm termed interpolation, which constructs a curved surface passing through or very near to every sample value. The second method can be subdivided into two groups in consideration of the population of sample data.
This paper examines several interpolation methods suitable for the sample data which are originated from a single population and therefore satisfy the geological homogeneity. The moving average method, the optimization principle method, kriging, and the optimization principle method combined with kriging were chosen and applied to the reconstruction problem of the defined forthorder polynomial using irregularly spaced sample data. It was revealed that the optimization principle method gives the smallest interpolation error among those methods. The goodness of the interpolation result by the optimization principle method was also judged through two interpolation criterion calculated from the interpolated grid data: the smoothness of curved surface and the error of semivariogram. Furthermore, the interpolation error was found to have a correlation with the total values of three factors, namely, the distance between grid point and data point, the angular distribution pattern of data points, and the deviation of data values.

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[in Japanese]

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