Green’s Function Database and Detailed Ground Motion Prediction for Central Japan Based on the Reciprocity Theorem

Abstract eng:
Detailed prediction of ground motion is important in the design of high-rise, base-isolated, and other key buildings. In general, the predominant period of ground motion is considered to be constant at each site. However, some recent studies have reported that the predominant period of observed ground motion can vary according to the source direction at sites on sedimentary basins. Therefore, detailed ground motion prediction with waveforms should be advanced for sites containing the types of buildings described above. The waveform of long-period ground motion is often predicted using the finite difference method, since the complicated soil structure of a sedimentary basin can be considered with this method. However, ground motion calculations using the finite difference method require large amounts of computational resources and time. If many possible earthquakes are assumed around an important site, it is very expensive to predict the long-period ground motion. In this study, we propose an efficient method for predicting long-period ground motions due to many possible earthquakes for a specific site. In this method, the Green’s functions of the ground motions are calculated using the finite difference method based on the reciprocity theorem. According to this theorem, the displacement at the site due to a double couple force at the source equals the strain at the source due to a single force at the site. By using the reciprocity of Green’s functions, the computational cost of obtaining a complete set of Green’s functions can be dramatically reduced. Once the Green’s functions representing the displacement at the site due to every element fault have been compiled in a database, the ground motions at the site due to earthquakes with arbitrary mechanisms can be easily predicted by superposing Green’s functions. We apply above scheme to predict ground motions at several important sites in central Japan. As a result, the ground motions at the sites due to several cases of future earthquakes can be calculated efficiently. In addition, our scheme is useful for discussing the behavior of ground motion and the impact on the buildings in relation to seismic mechanisms.

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