This analysis has shown that a seismic velocity decrement ratio of
about 3 is expected in partial melt systems at the core mantle
boundary based on an elementary
use of Gassmann's equations (*Gassmann*, 1951)
and some simple assumptions about small
changes in density and bulk modulus near the CMB.

Corrections to these results can also be computed using the formulas
presented. If the density changes significantly, then (dlnvp) and
(dlnvs) must be modified using (vp) and (vs).
Rao's rule (*Rao*, 1941)
can then be used to obtain estimates
of *K*_{f}, and these results substituted into (c1). Effective
medium theory (*Watt et al.*, 1976; *Berryman*, 1995)
is required in these more precise calculations to determine
*K*_{dr} for use in (BiotWillis) and again in (c1),
and similarly to determine *c _{2}* for the shear modulus.

Figure 1

10/25/1999