THE APPLICATION OF FUZZY MATHEMATICS IN MULTI-APPROACH EARTHQUAKE PREDICTION

In this paper, the direct and indirect methods for fuzzy recognition developed in fuzzy mathematics are applied to the study of multi-approach earthquake prediction.The direct method for fuzzy recognition consists of assessment of earthquake risk and making prediction by use of membership functions of different precursors directly. Its effectiveness depends on the technique of constructing these membership functions. Based on the various data of radon content of underground water, apparent earth resistivity, seismic velocities and other precursors, the concrete methods and formulae for constructing the corresponding membership functions have been suggested by employing mainly the rate of precursor change and coefficient of correlation and by other means. In applying these menbership functions, the abnormal features of a precursor can be recognized more clearly and the times of beginning, finishing or transitions of an anomaly more easily.The indirect method for fuzzy recognition, used in this paper, is the method of fuzzy clustering analysis, which depends on the selection of similarity coefficient or distance. Here we use a method of clustering analysis based on the fuzzy equivalent relation. This method includes the following steps: obtaining first a fuzzy compatible relation according to the degrees of similarities between samples; then transforming this compatible relation into a fuzzy equivalent relation by use of combinational operation; finally selecting a suitable value for parameter A, and classifying the original samples.Taking some statistical indices of seismicity in a given region, or taking the data of a number of precursors observed (crustal deformation, radon content of underground water, apparent resistivity etc.) at one station or of one precursor at a series of stations, then multi-approach earthquake prediction may be made by using the method of fuzzy clustering analysis as mentioned. For illustration of this method some preliminary results obtained for large and moderate earthquakes occurred in the western part of China were shown. It can be seen from these results that the prediction by using fuzzy clustering analysis is generally in better conformity with the actual cases of earthquake occurrence.It is considered therefore that the prospect for using the methods of fuzzy mathematics in multi-approach earthquake prediction is optimistic.