A number of recent papers (*Williams and Garnero*, 1996;
*Revenaugh and Meyer*, 1997; *Wen and Helmberger*, 1998a; 1998b)
have shown that the ratio of seismic velocity decrements
(where *v*_{s} is the shear velocity,
*v*_{p} is the compressional
velocity) is approximately equal to 3 in ultralow velocity zones near the
the core-mantle boundary (see *Young and Lay* (1987) for a review of
CMB issues).
Changes in both numerator and denominator are negative but the
ratio has been found to be on the order of 3, and
because this value is so high it is generally argued that these results
provide evidence of partial melt in these regions.
The rock physics analyses used in these papers
are generally based on classical effective medium theories
such as those reviewed by *Watt* *et al.* (1976). The main
problem with such analyses is that the results tend to be quite sensitive
to the assumed microstructure of the partial melt system
[see *Williams and Garnero* (1996)] and therefore may not be truly
representative of the system being studied. I will give a different
derivation here of the velocity decrement ratio that highlights the
key assumptions that must be made to arrive at this ratio.
This approach shows how general and insensitive to
microstructure the *ratio* really is for partial melt systems,
and shows furthermore how to analyze deviations from the assumptions
made. The methods presented may also be extended to permit estimates
of changes not only of the ratio but also of the two seismic
velocities themselves. A procedure for doing so is outlined at the
end of the paper.

10/25/1999