CONCLUSIONS

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 c₂ for the shear modulus.

 

various
Figure 1 Plot of the dependence of the theoretically predicted seismic velocity decrement ratio on the v_p/v_s ratio. Specific points shown correspond to values of v_p/v_s for the lower mantle just above the core-mantle boundary for various models: PEMC-L01 (Doornbos and Mondt, 1979), PREM (Dziewonski and Anderson, 1981) and IASP91 (Kennett and Engdahl, 1991). For comparison, the result for olivine at 2 GPa with $v_p/v_s \simeq 1.72$, which would be typical of upper mantle conditions, is also shown.