地震動強さの距離減衰式 (経験式) に関する最近の研究動向

Abstract

Recent studies on the attenuation relations of earthquake ground motion, which have been derived mainly by multiple regression analyses of observed data, are surveyed. Since the studies on the attenuation relations are involved with not only derivation of attenuation characteristics but also evaluation of source and site effects, they have wide variety of theme. In this report, these studies are reviewed by dividing them into four aspects of the study: parameters used in regression models, observed data, regression models and methods of statistical analyses.Main topics of recent studies are as follows. (a) Ordinary regression models that assume linear relationship with respect to magnitude will fail to represent the response spectra in wider magnitude range, since magnitude dependency of the ω-2 source spectra is not linear around corner frequencies. (b) Distance coefficients of attenuation relations obtained from the regression analyses can be converted to the Q values, which agree well to those derived by different approaches. (c) The phenomena of amplitude saturation in the near source region, which is prominent in high-frequency components of strong ground motion, can be expressed by substituting the hypocentral distance with the minimum distance to the fault plus the source region size. Another approach is to sum up the contributions from small elements located on a large fault plane. (d) Significantly smaller distance coefficients for large numbers of earthquake than for an individual earthquake will be derived by the ordinary one-step regression analysis, because usually strong correlation between magnitude and distance exists in such a large database. The two-step stratified regression analysis using dummy variables is a very effective method to correct these unreasonable results. Thus care should be taken for the choice of the regression procedures and models, especially in case that the observed data have a bias.Since attenuation relations are derived based on observed records, the ground motion predicted by these relations will be a good approximation of the actual value as long as the model parameters for prediction fall within the range of the data for regression. In near future, the attenuation relations applicable to wider frequency, magnitude, and distance ranges are anticipated to be developed with the help of increasing strong motion data and appropriate physical modeling.