Open AccessAttenuation due to second‐order scattering in material containing cracks.
Author(s) -
Hudson J. A.
Publication year - 1990
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1990.tb04480.x
Subject(s) - scattering , attenuation , wavelength , smoothing , computational physics , optics , physics , materials science , mathematics , statistics
SUMMARY The method of smoothing has lead to the calculation of overall or effective elastic parameters for wave propagation in material containing cracks, valid to second order in the number density of the cracks. Wavespeeds are obtained for wavelengths long compared with crack dimensions by working to the lowest order in frequency. To find the attenuation due to scattering of energy out of the mean wave, calculations to higher order in frequency are necessary and, up to now, attenuation has been obtained by summing over the scattering cross‐sections of the cracks, thus neglecting any crack‐crack interactions. Here we evaluate scattering attenuation to higher order in the series obtained from the smoothing approximation in order to allow for multiple scattering. It turns out that, for crack radii and crack spacing small compared with a wavelength, the term of lowest order taken from the double scattering component exactly cancels out the sum over scattering cross‐sections, leaving only higher order terms to account for attenuation due to scattering. In other words, the effective material parameters contain no attenuation component arising from scattering.