Figure 3 shows three examples of the results obtained with plots
in the (*S*, )-plane and in the
(, )-plane (using as a proxy for *S*)
for two limestones and one andesite
from laboratory data of Cadoret (1993) and Cadoret *et al.* (1995; 1998).
In Figure 3, the true saturation data are used in the Figures on the
left
and the proxy for saturation () is used on the right.
We therefore call the right hand diagrams ``saturation-proxy'' plots.
Using the interpretations arising for our analysis
of Gassmann-Domenico partial-saturation theory, we see that
Figures 3(a) and (b) indicate homogeneous mixing of liquid and
gas, while Figures 3(e) and (f) indicate extremely patchy mixing,
and Figures 3(c) and (d) show an intermediate state of mixing
for the drainage data, but more homogeneous mixing (as expected) for the
depressurization data. The Espeil limestone was observed to be
the most dispersive of all those rocks considered in the data sets
of Cadoret (1993) and Carodet *et al.* (1995; 1998).
So this case is a very stringent
test of the method. In fact, if we were to plot the corresponding
data for Espeil limestone
at 500 kHz, we would not find such simple and easily
interpreted behavior on these plots. Our explanation for this
difference between the 500 kHz and 1 kHz results for Espeil limestone
is that the dispersion introduces effects not accounted for by
the simple Gassmann-Domenico theory, and that there is then no
reason to think that our method should work for
such high frequencies as 500 kHz.
We have found other examples where it does work for frequencies
higher than one
might expect the method to be valid.
The point is that, if we
restrict the range of frequencies considered to 1 kHz or less,
the method appears to work quite well on most (and perhaps all) samples.
[But, at higher frequencies, the solid and fluid can move out of phase and
other relations developed by Biot (1956a,b; 1962) and others
(O'Connell and Budiansky, 1977;
Mavko and Nur, 1978; Berryman, 1981; McCann and McCann, 1985; Johnson
*et al.*, 1987; Norris, 1993; Best and McCann, 1995)
apply.]

4/28/2000