DISCUSSION

We can compare the results obtained with results obtained for the same rocks using differential effective medium theory to fit data. The two characteristics that will interest us here are: (1) comparisons between the values chosen in our examples for the anisotropic $\beta'$s and the best fitting crack aspect ratios found in Berryman (2004a), and (2) comparisons between the magnitudes of changes in the overall shear moduli from their drained to undrained values.

The preferred crack aspect ratios found for Sierra White granite, Schuler-Cotton Valley sandstone, and Spirit River sandstone in Berryman (2004a) were respectively, 0.005, 0.015, and 0.0125. Here we found that ($\beta'_1$,$\beta'_3$) for the same samples were, respectively, (0.05,0.90), (0.20,0.60), and (0.25,0.50). Clearly, these values are at least weakly correlated with those of the aspect ratios for the same samples, but no stronger conclusions can be reached at the present time concerning these values.

Similarly, the comparisons of the changes in shear modulus magnitude from drained to undrained also show a weak correlation. The increases in shear moduli observed in the measured laboratory data for Sierra White granite, Schuler-Cotton Valley sandstone, and Spirit River sandstone are, respectively, about 10%, 10%, and 20%. As seen in the TABLE, the magnitude of the changes predicted here is essentially about 10% in all three of these cases. Thus, agreement is good both qualitatively and semi-quantitatively in all cases. We conclude that the theory presented here is correctly predicting the magnitudes of these shear modulus enhancements due to pore-fluid effects.