Historical Seismograms - Evidence from the AD 2000 Izu Islands ...

318 De-yi Feng, Ming-zhou Lin, and Kun-yuan ZhuangTaking a suitable weight vector W = (W1, W2, W3) for three factors, we mayobtain the fuzzy miiltifactorial evaluation on the basis of the formula:P = W .Q = (Pi, P2, ..., P,) (7)where tlie syiribol "0" denotes product of CV and Q.According to tlie principle of clioosiiig the closest approach, we may obtain theoptimal source mechanism of an historical earthquake.The formulas (4) and (7) represent two possible ways of fuzzy niultifactorialevaluat ion.3.8. ExampleAs an example, we have studied the source mechanism of the 1920 Haiyuan(M = 8.5) earthquake. The original macroscopic phenomena were taken from theSeisniological Institute of Lanzhou and the Seismological Bureau of Ningxia Region(1980). Based on these phenomena, we obtained tlie data for compressional andrarefactional points (Table 3). By use of the mentioned method, we derived fourmodels of source mechanism (Figure 3). The optimal model of source mechanismis Model 1 in Figure 3. The nodal plane trends N 17" W dipping SW at an angleof 80°, the another nodal plane strikes N 86' E, dipping NW at 39", the principalcompressional stress axis has an orientation of N 72" W with dip angle of 41", andthe principle dilatational stress axis is oriented N 45' E with dip angle of 35".4. Fuzzy Description of Macroscopic Criteria for Recognizing PaleoseismicEvents4.1. MethodSo far, tlie data relevant to recognition criteria of paleoseisniic events have beenaccuniulating, but all these criteria are often described by very fuzzy languages. Wenow attempt to describe these criteria by use of membership functions with landfalland landslide as examples.(1) Landfall. We take the following five fuzzy subsets as the recognition criteria fora paleoearthquake:NU1: In tlie case of intact rocks such as granite, and massive limestone withoutmickle iriterlayer, break plienomena and tlie trace of river erosion suggestthat great collapse occurred.NU2: The size of the collapsed body is great, the valley bottom of the collapsedN sphere is very deep, and its depth often equals to 300-500 m.U,: The collapsed body is displaced very far, its distance could be farther thantwelve kilometers.NU4: On the end levee of the collapsed body high-dip-angle steep gradient ap-N peared, it is higher than the background by 50-100 m.Us: The collapse occurred at a slope whose angle is smaller than 30 degrees.Then, we may consider the paleoeartliquake as a fuzzy set:N Nu = u1 u z2 u c3 u 34 u 35,