The methodology to estimate the strong motion Fourier amplitude spectra in a short-period range (T ≦ 1 to 2 sec) on a bedrock level is discussed in this paper. The basic idea is that the synthetic strong motion Fourier spectrum F˜A(ω) calculated from smoothed rupture velocity model (Savage, 1972) is approximately similar to that of low-pass-filtered strong earthquake ground motion at a site in a period range T ≧ 1 to 2 sec: F˜A(ω)=B˜(ω)·A(ω). B˜(ω) is an observed Fourier spectrum on a bedrock level and A(ω) is a low-pass filter. As a low-pass filter, the following relation,


is assumed. In order to estimate the characteristic coefficients {n} and {a}, the Tokachi-Oki earthquake (1968), the Parkfield earthquake (1966), and the Matsushiro earthquake swarm (1966) were analyzed. The results obtained indicate that: (1) the coefficient {n} is nearly two for three earthquakes, and {a} is nearly one for the Tokachi-Oki earthquake, eight for the Parkfield earthquake, and four for the Matsushiro earthquake swarm, respectively; (2) the coefficient {a} is related with stress drop Δσ as (a = 0.07.Δσ). Using this relationship between {a} and Δσ, the coefficients {a} of past large earthquakes were estimated.

The Fourier amplitude spectra on a bedrock level are also estimated using an inverse filtering method ofA(T)=aT2aT2+1.

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