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

320 De-yi Feng, “ding-zhou Lin, and Kun-yuan ZhuangFor pz, p3, and p4, the upward semi-normal distribution niny be taken as: p(z) =0, or p(z) = 1 - exp[-k(z - a)’]. On the basis of empirical data, we have obtainedthe following preliniiiinry results:p2 = 0 for 0 5 z 5 0.3, or p2 = 1 - exp[-69.S1(z - 0.S)2] for 0.3 < z.p3 = 1 - exp[-0.011~’].p4 = 0 for 0 5 z 5 50, or p4 = 1 - exp[-O.OOl(z - for 50 < z.For ps, the downward semi-normal distribution is taken as p(z) = exp[-kz’].When 5 = 30°, we took p = 0.5, so that k = 2.5. Then we have pug = exp[-2.5~~1.The parameter z in the expressions of p2, p3, p4, and p5 is in units of kilometers,meters, kilometers, and radians, respectively.(2) Landslide. We can take tlie downward semi-normal distribution as p(z) =exp[-kz’], where z is the slope angle measured in radians, k is an empirical coefficientdepending on earthiness and saturation. For non-saturated loessial mild clay,k = 3.61.4.2. Example of ApplicationAn example was taken from tlie Seismological Bureau of Shanxi (1982). At theold Yulin grike of Kangding 011 the Xiansliuihe fault zone, where the slope angle is28”, the accuniulation of many collapsed bodies was discovered.Based on tlie thkd criterion, from p3 = exp[-2.5z2], we obtain p3 = 0.547 > 0.5.As mentioned above, this phenomenon may be recognized as a possible relic ofpale oe art 11 quake.5. DiscussionsIt should be emphasized that this paper is mainly for describing methods of fuzzyresearch. It is only a first step that we have done. Obviously, the methods suggestedby the authors need to be further exaniined, tested and developed in the future.REFERENCESDubois, D. and H. Prade (1980). Fuzzy Sets and Systems: Theory and Application, AcademicPress.Feng, D. Y. and X. H. Liu (Editors) (1985). Fuzzy Mathematics in Earthquake Research,Seismological Press of China.Feng, D. Y., M. Z. Lin, and others (1983~). Application of fuzzy integrated evaluationarid close press to the studies of seismic source, Di Zhen (Earthquake), No. 4.Feng, D. Y., S. B. LOU, and others (1983b). The Methods of Fuzzy Mathematics and TheirApplicatzons, Seismological Press of China.Feng, D. Y., S. B. Lou, and others (1934). Quantitative evaluation of earthquake intensitybased on the fuzzy standards of seismic scale, Proceedings of Eighth World Conferenceon Earthquake Engineering, Vol. 11, 819-828, San Francisco.Gu, G. X. (Editor) (1983). Catalogue of Earthquakes in China, Scientific Press.Seismological Bureau of Sansi (1982), Papers of Prehistoric Earthquakes and QuaternaryGeology, Scientific Technical Press of Sansi.Seismological Institute of Lanzhou and Seismological Bureau of Ningxia (1980). The 1920Haiyuan Great Earthquake, Seismological Press of China.