open access

https://hdl.handle.net/2115/17232

Scattering attenuation, dispersion and reflection of SH waves in two-dimensional elastic media with densely distributed cracks

英語

synthetic seismograms

2007-01

Blackwell Publishing

Geophysical Journal International

168(1)

211-223

http://www.blackwell-synergy.com

We compute the synthetic seismograms of multiply scattered SH waves in 2-D elastic media with densely distributed parallel cracks. We assume randomly distributed cracks in a rectangular-bounded region, which simulate a cracked zone. The crack surfaces are assumed to be stress-free. When the incident wavelength is longer than the crack size, the delay in the arrival of the primary wave is observed at stations beyond the cracked zone and the amplitude of the primary wave is amplified in the cracked zone in the synthetic seismograms. This is because the cracked zone behaves as a low velocity and soft material to the incident long-wavelength wave due to the crack distribution. When the half-wavelength of the incident wave is shorter than the crack length, the scattered waves are clearly observed in the synthetic seismograms and the amplitude of the primary wave is largely attenuated beyond the cracked zone. The calculated attenuation coefficient Q-1 of the primary wave is directly proportional to the crack density in the range of νa2 ≤ 0.1, where ν and a are the number density and half the length of cracks, respectively. This is consistent with that obtained by a stochastic analysis based on Foldy's approximation. A periodic distribution of cracks in a zone is considered as an utterly different model in order to investigate the effect of spatial distributions on the attenuation and dispersion of seismic waves. When cracks are distributed densely, the values of Q-1 for the periodic crack distribution appear to differ from those for the random distribution of cracks in the low wavenumber range. This suggests that the effect of multiple interactions among densely distributed cracks depends on not only the density but also the spatial distribution of cracks at low wavenumbers. The calculated phase velocity of the primary wave is consistent with that from the stochastic analysis in the range of νa2 ≤0.1 and does not depend on the spatial distribution of cracks. This suggests that the multiple crack interactions have a smaller effect to the phase velocity. Therefore, the crack density can be estimated from the values of the phase velocity for the cases of densely distributed cracks even if the effect of the multiple crack interactions is not considered. We can clearly observe the reflected waves in the synthetic seismograms. The elastic constant of a single anisotropic layer equivalent to the cracked zone is derived from the crack density at the long-wavelength limit. The reflection coefficients calculated from the synthetic seismograms are consistent with those of the anisotropic layer calculated from its elastic constants and thickness in low wavenumber range. This means that a fracture zone distributed parallel cracks is considered as an anisotropic layer for long incident wavelengths. Therefore, the elastic constants, crack density and the thickness of the fracture zone can be estimated from the frequency dependence of the reflection coefficients for long incident wavelengths. On the contrary the wavenumber dependence of the reflection coefficients cannot be explained theoretically in the high wavenumber range.

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