The elastic moduli of a solid permeated with an isotropic distribution of flat cracks have been calculated from the energy of a single crack by use of a self-consistent approximation. The results are applicable for a dense network of cracks and give physically reasonable results up to the point that the shear modulus vanishes. Results for both circular and elliptical cracks are essentially the same if the crack density is characterized by 2N〈A2/P〉/π, where N is the number of cracks per unit volume, A is the area of crack, and P is the perimeter of cracks; for circular cracks of radius a this becomes N〈a3〉. This crack density parameter can be related quantitatively to crack traces observed in thin section. Results for completely dry or saturated cracks, for mixtures of dry and saturated cracks, and for cracks saturated with a compressible fluid are presented. For all cases, both seismic wave velocities decrease with increasing crack density. The velocity ratio VP/VS decreases for dry cracks and increases for saturated cracks. For the analysis of data a plot of VP/VS versus VS uniquely specifies the crack density. Comparison of the theory with wave velocities measured in laboratory rock samples demonstrates its validity for large crack densities. Interpretation of velocity changes before the San Fernando earthquake indicates that the region contained a substantial density of cracks at all times, that the anomalous decrease in VP/VS was due to the vaporization of pore fluid in nearly all of the previously saturated cracks without the introduction of new dry cracks, and that during the period of the recovery of the velocities to previous values the number of cracks in the region away from the epicentral zone decreased as they were resaturated, whereas the crack density increased following resaturation in the epicentral zone. Such use of the theoretical results may be useful in further investigations of preseismic phenomena.
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