Scattering and attenuation of elastic waves in random media

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

“…Adopting a pair-correlation function properly describing the cavity distributions would be necessary to recover the agreement with the experiments. This inference may be supported by a theoretical result of Varadan et al 11 In order to make comparison with a laboratory-experimental result, they derived dispersion curves for lead spheres of a finite size embedded in an epoxy matrix, using the quasicrystalline approximation and a realistic pair-correlation function. Their results were given for two cases with C = 0.05 and 0.15, and the dispersion curve for the latter case shows oscillation much more noticeably than the former.…”

“…Here C is employed instead of n as a measure of the distribution density, following the convention in laboratory experiments. 11,12,[16][17][18][19][20][21][22][23] It may be worth mentioning, however, that the use of C may not be effective if the aspect ratios of scatterers are much deviated from unity. An example is distribution of highly oblate cavities ͑or cracks͒, for which C would remain negligibly small even for considerably large n; there "crack density" nr 3 ͑r is the major axis͒ is conventionally used instead.…”

“…Treating scatterers with finite sizes will be possible by using a proper pair-correlation function, but then the solution K would be obtained only numerically. [9][10][11][12] The 2D version of Foldy's formula ͑with Lax's correction͒ ͑2͒ can be found in, e.g., Linton and Martin. 28 It is written in the form…”

“…Other researchers applied more appropriate pair-correlation functions for scatterers with finite sizes. [9][10][11][12] Still other researchers proposed corrected versions of Foldy's theory not based on the quasicrystalline approximation. Examples are the works based on a diagram method 13,14 and the combinations of the Waterman-Truell formula and a self-consistent method.…”

Multiple scattering of elastic waves from a continuous and heterogeneous region

“…Gao et al (1983a,b) extended the single-scattering theory of Aki (1969) for coda waves to the multiple case for 2-D and 3-D media consisting of a random distribution of numerous but statistically uniform and isotropic scatterers. Using the T matrix formulation of multiple scattering, Varadan, Ma & Varadan (1989) studied the problem of scattering and attenuation of elastic waves in random media. Their model elastic medium consists of randomly distributed inclusions with a non-dilute concentration, and the waves incident on such a heterogeneous medium undergo single and double scattering due to the presence of the inclusions.…”