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

Applications of Fuzzy Mathematics 315Supposing that the rock fissure arid ground fissure have equal weight for evaluatingthe earthquake intensity, i.e., taking W = (0.5, 0.5), we may obtain the vectorfor fuzzy iiiultifactorial evaluation asP = W o Q = (0.5, 0.4).According to the principle of clioosiiig the closest approach, tlie intensity ili theHaiyuan region may be estimated as XI1 degree (see Figure 2).3. Fuzzy Determination of Source Mechanism of Historical Earthquakes3.1. Fuzzy Descraptaon of Hzstorical Phenomena on Earthquake EffectsIn the absence of enough seismograms, the source mechanism of a historicalearthquake may be determined on the basis of macroscopic phenomena related tothe earthquake effects. Among them, the geoniorphological and geological effectscaused by a historical earthquake often become very important. For example, localupheaval, spouting of water and sand, etc. may be considered as the compressionaleffects of an earthquake, but ground fissure, collapse, etc. must be related to itsrarefactional effects.Generally, we may consider any set of macroscopic phenomena to be a fuzzyset characterized by some membership function. A direct method for a fuzzy descriptionof earthquake effects is based upon the nienibersliip functions of differentphenomena. Therefore, its effectiveness depeiids on the technique of constructingthe membership functions.Here, for a fuzzy description of the compressional and rarefactional effects of anearthquake, we simply construct the corresponding membership functions as:pruref. = pficcure v pcollnpae v pother ruref. effectuswhere the sign v denotes the disjunction, i.e., p1 v p2 = rnax(p1, p2). Then, thecharacter of the mechanical effects of the earthquake at an observational point callbe estimated by the total membership function:p = /Icurripr. v proref:The pup~Lcuvui, p,poutlrLgl pjzeaure, pL,uiiaL,ye, etc. must be defined elnpirically ontlie basis of abundant macroscopic phenomena. Here we define:puI,~Leavul = 0.7 when the local upheaval appears, or = 0 otherwise;pILBF)O,lfi,LII = 0.9 when the spouting of water and sand occur, or = 0 otherwise;puttLcr c,,rrLl,r. effectc = 0.5 if some other compressional effects are discovered, or= 0 otherwise;pjzJBure = 0.3 when a ground fissure with width d < 5 cm appears, or= 0.5 when d M 5 cni, or= 0.7 when d > 5 cm, or= 0 when 110 remarkable fissure is observed;pcollapse = 0.9 wlieii the ground collapses, or = 0 otherwise;pot+r r(rre~. = 0.5 if Some other rarefactional effects are discovered, or= 0 otherwise.