Attenuation models derived from recorded ground motions are still important elements of probabilistic seismic hazard studies. Engineers use empirical attenuation models to derive the displacement demand for a site of interest from an earthquake at a given location. Many attenuation models have been published for different parts of the world and for different types of earthquakes. Most models have a simple function of constant or magnitude-dependent geometric spreading, and seldom consider well-known seismological effects such as Moho reflection for shallow crustal earthquakes, multiple travel paths and constructive interference for subduction earthquakes, and special characteristics of volcano zones. The reason for not accounting for such effects may be the desire for simplicity in the attenuation functional forms for engineering applications and a lack of records from which to reliably identify these effects quantitatively. In this article, a large set of strong-motion records obtained from dense recording networks in Japan is used to derive geometric attenuation functional form and a possible manner to model the effect of volcanic zones. A liberal approach is taken to introduce a relatively large number of parameters that can account for known seismological effects while retaining a fairly simple attenuation functional form, based on analyses of residuals from simple models similar to those published previously. Preliminary results are reported here, together with the proposed geometric attenuation function forms and plausible explanation of the physical process that leads to the proposed geometric attenuation functions. The proposed model shows a large increase in the maximum likelihood from the random effects methodology, the elimination of bias in the distribution of residuals with respect to source distance, and much improved fitting for well-recorded earthquakes.

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