1985 Volume 36 Issue 4 Pages 245-257
Recently, many seismologists have been analyzing the fine rupture process of earthquakes by the use of strong motion seismograms recorded near the source regions. Not only long-period waves, but also waves of periods less than several seconds are found to play an important role when analyze the detail of rupture processes. On the other hand, amplitudes and forms of seismic waves are strongly influenced by anelastic properties of the earth. In this paper, synthetic displacements are calculated on the surface of an anelastic layered half-space in order to estimate the effect of attenuation on the short-period waves near the source region.
If effective Q value is constant over the whole range of observed frequency (e.g. Q is constant in the frequency range of τ1-1<<ω<<τ2-1.), the effect of anelasticity is introduced by the use of the dispersive complex velocities as;
υ(ω) = υ1 [1+1/πQ ln (ω/2π) -i/2Q] (i)
where υ1 is a phase velocity at ω=2π. Moreover, we must introduce the velocity at ω=0 to evaluate the static deformation. Based on the relaxation mechanism of Liu et al. (1976), the velocity at zero frequency is approximately given as
υ0∼υ1 / [1+1/πQ ln (2π · τ1)] (ii)
In this paper, τ1 is assumed to be 2×104 sec, whose reciprocal approximately corresponds to the minimum angular frequency of the free oscillations of the earth.
Extending the approach by Yao and Harkrider (1983), dynamic displacements and strains on the free surface are given in terms of reflection-transmission matrix [Kennett and Kerry (1979)], and discrete wavenumber method [Bouchon (1981)] and by using the layered half-space structure with the complex velocities of the equations (i) and (ii). The Fourier spectrums of each displacement and strain component are given in this paper.
The conducted numerical calculation presented the ground displacements and velocities on the free surface sedimentary medium with low Q layer. We also calculated ground displacements and velocities without the effect of anelastic attenuation. A comparison of the synthetic waveforms shows the apparent effect of anelasticity. When the thickness of the sedimentary layer is more than 1km, the amplitudes of the later phases whose travel times are more than 10 seconds are attenuated remarkably. Though the synthetic waves may be within 10km of the epicenter, the amplitude calculated for the anelastic half-space is less than half of what is calculated for the elastic half-space.
In order to investigate the complicated rupture process of the earthquake, such as multiple events, a more realistic estimation of the amplitudes of the later phases must need the analysis of the near-field strong motion seismograms which are recorded on the sedimentary layer. Our method must be useful for such analysis.
