LONG-PERIOD SURFACE VELOCITIES AND ACCELERATIONS DUE TO A DISLOCATION SOURCE MODEL IN A MEDIUM WITH SUPERFICIAL MULTI-LAYERS PART I

Abstract

Recent proliferation of large high-rise buildings makes it important to investigate long-period seismic particle velocities and accelerations besides displacements generated by the present rather simple dislocation source model.
In this paper, expressions are derived for obtaining a displacement spectrum on the surface of a layered structure, when seismic waves due to a dimensional fault are incident at the lowest interface of the layer, The assumptions in the derivation are: (1) displacements at the base of the layer are taken as twice those due to the source, (2) only the base displacements in the distance range from r=r₀-0.3λ to r=r₀+0.3λ contribute to the surface displacements at r=r₀, λ being the wave length considered, and the spectrum for this wave-length does not vary very much in this distance range, and (3) the layer effect is taken into account by numerically evaluating an integral with respect to the angle of incidence from 0 to π/2 instead of the rigorous limits from 0 to π/2+i∞ (complex angle of incidence). The numerical inverse Fourier transform is carried out by using the Filon formula to obtain displacements in the time domain. Particle velocities and accelerations can be found in a similar manner.
Surface displacements, velocities and accelerations in Tokyo due to a hypothetical Kanto earthquake proposed by KANAMORI (1974) are calculated assuming the surface structures beneath Tokyo metropolis obtained by SHIMA et al. (1975). The maximum displacement (u_m), velocity (u_m) and acceleration (ü_m), when the final dislocation is assumed to be 2m, are 44cm, 15 kine and 15gal, respectively. When evaluating these quantities, a Hamming frequency window is applied to the frequency range from 0Hz to 1Hz, to avoid the truncation effect of the spectrum. The apparent predominant period of acceleration is about 4sec or longer.
If the epicenter of the hypothetical earthquake is located at a position about 50km northwest of the original (Kanamori's) position, u_m, u_m and ü_m in Tokyo are obtained to be 73cm, 18 kine and 19gal, respectively.