Seismic wave propagation through material containing partially saturated cracks

Expressions for the wave speeds and attenuation of elastic waves through material containing aligned cracks are available in an approximation valid up to second order in the number density of cracks and for wavelengths that are long compared with the size of the cracks. Conditions within the crack may vary from dry (stress-free) to fluid or solid-filled. The situation where cracks are partially filled with liquid (and part with gas) is very different from either extreme of dry or liquid-filled cracks since the liquid is forced to flow laterally within a crack, at the expense of the more compressible gas, by tensions or compressions imposed normal to the plane of the crack. Expressions are derived here which enable the range of internal crack-conditions to be extended to the case of partial saturation in the formulae for the propagation characteristics of waves of long wavelength through material containing such cracks. Key words: Seismology, composites, anisotropy