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

Applications of Fuzzy Mathematics 317Table 3. Data Used for Determination of Source Mechanismof the 1920 Haiyuan (M = 8.5) EarthquakeNo. Place A; A (km) 2/L Sign /-L1 Haiyuan 105.3 GF.5 70.9 + 0.92 Xij i 136.8 108.5 78.0-0.73 Guyuan 122.4 143.5 80.9 - 0.34 Jingning 150.9 152.25 81.4-0.95 Tongwei 168.9 168 82 + 0.9G Qinan 160.7 215.25 84-0.97 Tinnshui 163.3 245 85 0.98 Gangu 170.1 224 84 + 0.99 Jingchuan 124.4 269.5 53 - 0.710 Lingwu 39.4 197.75 83.4 + 0.911 Liangdnrig 157.7 33 F 53 - 0.712 Zhenyuan 118.1 236.25 84.4 - -13 Weixian 161.4 343 53 - 0.714 Lintnn 212.6 264.25 53 f 0.915 Huaxinn llG.7 503 53-0.916 Zhaoyi 111.4 518 53-0.917 Hongdong 91.5 GO 9 53-0.918 Guide 258.1 316.75 53 f 0.919 Xi angfen 95.7 59 2 53 - 0.9.o(2) The ratio between the nuiriber of points having corisisteiit stress siaris and thetotal number of points having stress signs. For each possible fault plane solutionthe ratiol?L,si = l-(E!Lk)/N,, 2=1,2, ...!?Ik=lmay be taken as a factor for fuzzy inultifactorial evaluation, where p,k is the membershipfunction of the k-th iiicoiisisteiit point, Icr; is the total number of points,and m; is the number of inconsistent points for the i-tli fault plane solution.(3) Qiiayterly clistri1,ution of compressioiial aiid rarefactional points. For each faultplane solution we may count the percent of points distributed in the j-tli quarterk.. z3 .- rij/Ni, i = 1, 2,. .. ,n; j = I, 2, 3, 4;where rij denotes the iiuinber of points in the 3’-th quarter for the i-th fault planesolut ion.Taking k:? = 0.25/k;j, when kij > 0.25; or kij = k;j/0.25, when kij < 0.25, theaverage value ki = Cki,./4 may be considered as a factor for fuzzy multifactorialevaluation.Then, we may obtain a fuzzy evaluation matrix Q as:(1-01) (1--2) ... (1 -on)) Q = ( s1 $2 ... snEl L2 ... En. (6)