Scattering of P, SV Waves by Random Distribution of Aligned Open Cracks.

Simulations of P-SV wave scattering due to cracks by the 2-D finite difference method

“…In the present case, with such dense distributions, the randomness would be largely degraded, which results in large approximation errors. Note that a more rigorous treatment of mean waves revealed that the terms of order 2 , neglected in the FAT of Kawahara (1992), can be described in terms of such nonrandomness (Keller, 1964). Only in the case of P wave incidence on the horizontal cracks, may one also perceive the first motion of the predicted mean wave prior to the onset of the initial wavelet without cracks (at around t = 7.3), which is not observed for the synthetic case ( Fig.…”

“…We determined experimentally the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It was shown that the results are well described by the FAT of Kawahara (1992), if the crack density is sufficiently low, say, 0.01. The FAT apparently remains to be always valid with up to at least 0.1 for SV wave incidence, whereas the validity limit seems to be lower for P wave incidence; it may be, say, 0.05 for normal incidence and even lower for grazing incidence.…”

“…Using the method, we investigate here the validity of the FAT of Kawahara (1992), which predicts the scattering attenuation and velocity dispersion of P-SV waves in 2-D media with identical parallel cracks. Here, the prediction is stochastic in the sense that the theory is based on the mean wave formalism; i.e., it treats the ensemble average of real wavefields.…”

“…Kawahara and Yamashita (1992) solved it for P-SV as well as SH wave scattering due to cracks filled with an incompressible viscous fluid, and obtained the attenuation and phase velocity of the mean waves to the first order in the crack density. Kawahara (1992) then analyzed the case for P-SV wave scattering due to empty (traction-free) cracks. In Paper I, we validated in a numerical-experimental manner the FAT of Kawahara and Yamashita on SH wave scattering in the case of cracks filled with an inviscid fluid (or equivalently, shear stress-free cracks); the same experimental procedures are again adopted here, which are summarized below.…”

“…Although considerable efforts have been made to propose alternative approximations that are claimed to be valid for more densely distributed scatterers, the original Foldy approximation theory (hereafter, FAT) has maintained its popularity probably because of its mathematical simplicity (Kawahara, 2011) and the lack of consensus on which approximation is best as an alternative to the FAT (Kawahara et al, 2009). The FAT was applied to cracked media first by Kikuchi (1981a, b) and then by many authors in seismology and acoustics (Yamashita, 1990;Kawahara and Yamashita, 1992;Kawahara, 1992;Zhang and Gross, 1997;Caleap and Aristégui, 2010). However, its actual validity limit with respect to crack density remains unclear.…”