If the actual ratio vp/vs differs significantly from (vpovervs), then we can repeat the calculation using the parametrization
v_pv_s = 21-, where is a small number on the order of or less. The general result then becomes
d v_sd v_p 3v_p^24v_s^2 = 3(1-), showing, for example, that solid material or 1.7 implies a decrement ratio or 2.2, respectively. A plot of these results is shown in Figure 1, where various models (Doornbos and Mondt, 1979; Dziewonski and Anderson, 1981; Kennett and Engdahl, 1991) of the velocities at the core-mantle boundary are used to provide specific examples of the predictions obtained using this approach. For comparison, the value anticipated for olivine at 2 GPa in the upper mantle is also plotted to show that the results obtained are very close to those of Mavko (1980), who used much more detailed model calculations to arrive at the result. (Mavko (1980) found, using various assumed microstructures and a self-consistent effective medium approach, that the expected change was about 10% in shear velocity and about 5% in compressional velocity, giving a decrement ratio of about 2 - which compares favorably with the result 2.2 obtained here for olivine.) Table 1 lists the special values used for the plot.
To see how these results compare with the observations, consider the plots of Revenaugh and Meyer (1997) showing that, for the most credible models of lower mantle deviations from IASP91, the seismic velocity decrement can lie in the range from 2 to 5, with the most likely value being approximately equal to 3.