Estimation of Horizontal Amplification Factor and Incident Spectrum at Seismic Bedrock during Strong Shaking Based on Diffuse Field Concept

Nonlinear response of subsurface structures during strong shakings has a large impact on results of strong motion predictions, but proper nonlinear parameters of soils should be selected and arranged to prediction models based on limited given information when we reproduce the nonlinear behavior theoretically. We propose a method to estimate an incident wave at the seismological bedrock and a horizontal amplification factor during strong shaking by a linear spectral analysis without nonlinear parameters, assuming the diffuse field concept for earthquake and the linearity of vertical amplification hold during a single strong earthquake. We first verified the proposed method by using weak earthquake motions. Second we investigated the applicability of the proposed method to strong motions recorded at several sites in Japan, and compared the estimated results by the proposed method with those estimated by the equivalent linear analysis which uses nonlinear parameters. In some cases, the diffuse field concept did not hold when we used strong motions started from the S-wave arrival time. However, when we used strong motions started from a later half of S-wave, horizontal-to-vertical spectral ratios and surface-to-borehole spectral ratios showed similar nonlinearity, especially in the high frequency range to those of strong motions started from the S-wave arrival, and the diffuse field concept is considered to be held in the later S-wave part. The seismic bedrock spectra estimated by the proposed method showed good agreements to those estimated by the equivalent linear analysis. We reproduced the strong motions observed on the ground surface by the equivalent linear analysis with the incident waves at the seismological bedrock which were made from the estimated spectral amplitudes by the proposed method and the spectral phases of the observed motions on the surface.