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**ms_quadratic
**

Figure 9
Comparison between the points that solve the dispersion
relation in the complex *k*_{z}^{2}-plane, and a simple quadratic fit
in water saturation *S*, for
the Massillon sandstone measured by Murphy. The fit is nearly perfect
for this case.

**swg_quadratic
**

Figure 10
Comparison between the points that solve the dispersion
relation in the complex *k*_{z}^{2}-plane, and a simple quadratic fit
in water saturation *S*, for
the Sierra White granite measured by Murphy. The fit is also good
for this case, but not as good as it was for Massillon sandstone.

Since the curves obtained in FIGS.6 and 8 are very well-behaved, it
seemed like a good idea to check for simple dependencies on the
saturation parameter *S*. Both curves look like they might be
quadratic in *S*. This hypothesis is tested in FIGS.9 and 10.
We find that the quadratic dependence is essentially exact to
graphical accuracy for Massillon sandstone, and it is close but not
exact for the Sierra White granite. We have not yet tried to analyze
this behavior and will therefore not attempt an explanation of it at
this time.

** Next:** SUMMARY
** Up:** SOLVING THE DISPERSION RELATION
** Previous:** Sierra White granite
Stanford Exploration Project

11/11/2002