If the actual ratio *v*_{p}/*v*_{s} 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.

1.5

TABLE 1. Seismic *v*_{p}/*v*_{s} ratios and
predicted velocity decrement ratios
at the core-mantle boundary for some standard earth models,
and olivine at 2 GPa.

Earth Model | v_{p}/v_{s} |
PEMC-L01 |

1

10/25/1999