Attenuation and dispersion of antiplane shear waves due to scattering by many two-dimensional cavities

Abstract

Propagation and scattering of antiplane shear waves within media with two-dimensional cavities are numerically simulated, and the attenuation and phase velocities are experimentally determined. The results are compared with the predictions by the Foldy theory and its three corrected versions. If the cavity concentrations are small such as 0.02, the differences among the theoretical predictions are insignificant, and every theory is consistent with the experimental results. For higher concentrations such as 0.1, the differences become significant, but there are no objective grounds to say that any of the corrected versions of the Foldy theory works better than the original. If the error tolerance is as high as 10%, the simple Foldy formula may remain useful for concentrations up to about 0.1.

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

“…The examples are cracks filled with a viscous fluid (Murai et al, 1995), randomly oriented cracks (Yoshida et al, 2003), and cracks of unequal lengths (Paper I). On the basis of the same approach as the present study, Kawahara et al (2009) also proved that the FAT is nearly valid for SH wave scattering due to 2-D round cavities-possibly identified with high-aspect-ratio cracks-with a volume concentration up to 0.1. All these results suggests that the validity of the FAT would be universal as long as the scatterers are sparsely distributed, irrespective of the geometry and physical properties (boundary conditions) of the cracks, the wave modes, and, possibly, the spatial dimensions.…”

“…This approximation is based on the assumption of many scatterers distributed randomly and sparsely (Ishimaru, 1978), and it is expected to give results accurate to the first order in the distribution density (Keller, 1964). 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).…”

Voids and Rock Friction at Subseismic Slip Velocity

“…This difference might be related to the temporal variation of the thickness of the layer, which we could not monitor accurately at this moment. It should also be noted that the void does not have to be empty inside but can be filled with liquid material (Kikuchi 1981;Yamashita 1990;Benites et al 1992;Kelner et al 1999;Kawahara et al 2010). In this case, the theoretical prediction of the absolute values of Q -1 could be different but the general tendency with respect to ak does not change.…”

“…It should be noted that Q -1 could be affected by the changes in the thickness of the gouge layer during the experiment even when the cavity density does not change (Kikuchi 1981;Yamashita 1990;Kawahara et al 2010). If the cavity distribution is uniform, Q -1 is proportional to the thickness of the gouge layer.…”

“…To interpret the above results, we referred to a theoretical investigation of scattering waves caused by cavities (Yamashita 1990;Benites et al 1992;Kelner et al 1999;Kawahara et al 2010). In the scattering theory, ak defines the type of scattering, where a is the characteristic size of scatterers and k is wavenumber (= 2p/k, where k is wavelength) (e.g., Aki 1973).…”