Open AccessCrack distributions which account for a given seismic anisotropy
Author(s) -
Hudson J. A.
Publication year - 1991
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.1991.tb05698.x
Subject(s) - isotropy , anisotropy , geology , matrix (chemical analysis) , distribution function , seismic anisotropy , transverse isotropy , orientation (vector space) , scale (ratio) , harmonics , materials science , mechanics , geometry , mineralogy , physics , mathematics , optics , composite material , thermodynamics , quantum mechanics , voltage
SUMMARY The effect of microfractures or small‐scale inclusions within Earth structures may be measured seismically. Wavespeeds, as a function of wave‐normal direction, lead to effective or mean elastic parameters and the difference between these and the values for unfractured material is related to parameters for the size, distribution and internal conditions of the cracks or inclusions. Thus it appears that measurement of the seismic wavespeeds for a sequence of different propagation directions can lead to information about fractures or inclusions within the rock, even though the scale‐size of this microstructure may be very small compared with a wavelength. However, the crack parameters are continuous functions of orientation and the elastic parameters for the material provide values for only 21 independent quantities. This is enough to describe the crack distribution in terms of spherical surface harmonics up to fourth order only. The relationship between the effective elastic parameters and the crack distribution is accurate to second order in the number density which limits the applications to materials where the contribution of microfractures is less than 10 per cent. The relationships referred to above show that inherent material anisotropy is equivalent to a distribution of (hypothetical) cracks embedded in an isotropic material. It then follows that the effect of microfractures in an anisotropic solid may be calculated by imposing both systems of cracks (real and hypothetical) on an isotropic matrix, for which solutions are known.