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 Kf, and these results substituted into (c1). Effective medium theory (Watt et al., 1976; Berryman, 1995) is required in these more precise calculations to determine Kdr for use in (BiotWillis) and again in (c1), and similarly to determine c2 for the shear modulus.