Now we have derived all the results needed to interpret Eq. (28) and show how it is related to (27). First, we note some of the main terms missing from (28) are those due to approximations made to and the denominators of (27), which have been approximated as instead of .Then, from (56), it is easy to see that the final term in (28) vanishes to lowest order, and that the remainder is given exactly by the shear modulus fluctuation terms in brackets in (53) -- in complete agreement with the final terms of (27). Then, from (60), it follows that the leading contribution to the factor is
In the case of very strong fluctuations in the layer shear moduli, then (53) and (60) both show that pore fluids effects are magnified due to the fluctuations in layer shear moduli and, therefore, contribute more to the anisotropy correction factors and for undrained porous media. So these effects will be more easily observed in seismic, sonic, or ultrasonic data under these circumstances. When these effects are present, the vertically polarized quasi-shear mode will show the highest magnitude effect, the horizontally polarized shear mode will show no effect, and the quasi-compressional mode will show an effect of intermediate magnitude. It is known that these effects, when present, are always strongest at , and are diminished when the angle of propagation is either or relative to the layering direction. We will test these analytical predictions with numerical examples in the next section.
To summarize our main result here: The most significant contributions
of the liquid dependence to shear waves comes into the wave
dispersion formulas through coefficient a (or equivalently ).
Equations (53) and (54) show that