Figure 5

Figure 6

For Massillon, we have the Gassmann-like situation in which the shear
wave speed for the drained case is smaller than that for the fully
saturated case and therefore *Re*(*k*_{s}^{*}) < *Re*(*k*_{s}). FIG.5 shows
how the imaginary parts of the dispersion function change in this case
as the real part of *k*_{z}^{2} varies from *Re*((*k*_{s}^{*})^{2}) to *Re*(*k*_{s}^{2})
(*i.e.*, from air saturated to water saturated). FIG.5 shows
four of these curves (*S* = 0.2 to 0.8). FIG.6 was generated by
completing the procedure for 19 equally spaced points in saturation *S*.
FIG.6 shows furthermore that the curve obtained actually fits the
data for Massillon better than Gassmann does (the straight line
between the end points). This is a bit of a surprise as virtually everyone
(including the present authors) have often considered these data to be
the best known proof of the accuracy of Gassmann's equations for
partial saturation problems.

11/11/2002