We have inverted scatter in P- and S-wave travel-times to obtain a description of the spectrum of lateral heterogeneity as a function of depth through the mantle. The technique is robust in get- ting estimates of the product of a characteristic scale-length of heterogeneity and the square of the mean amplitude of the slowness (reciprocal of velocity) variations. With less confidence we can eval- uate the characteristic scale-length from the spectrum and hence
evaluate the mean amplitude of the slowness variations from the above product. By extrapolating the scatter to zero area we can also estimate the scale incoherent signal that is independent of structure and hence is a plausible lower-bound estimate of noise in the data- set.
1.6.a Intercepts
The estimates of the intercepts for the P- and S-wave studies are understandable from comparison with complexities on the travel-time curves. For the P-wave, studies these are high at re- gional epicentral distances, the distances at which we have large travel-time complexities from the presence of triplications due to the 400 and 660km discontinuities. Similarily, the intercepts are higher as we approach 100°, here PcP becomes asymptotic to P. Both P- and S-wave intercepts are lower over teleseismic distances away from these complexities.
The data from deeper source depths have lower inter- cepts; we suggest that this is partly due to a smaller degree of small- scale structure at depth. This is evidenced in the data as a sharper drop in variance as we approach the origin for the shallower curves.
There is some evidence of this even in our smallest-scale data, which is actually relatively large-scale (see the original data in figures 1.4 and 1.5). A more subtle effect of small-scale structure arises since component rays of a summary ray originate at different source depths even inside the same source depth bin. If there is hetero- geneity at the scale-length of the path difference, then this will in-
troduce scatter. Notice this scatter 1s independent of scale-length and hence will. contribute to the intercept. It is also reasonable to expect more scatter from shallower events, since their arrivals are fre- quently complex and emergent, while deeper events generally have simpler impulsive arrivals. This could be a function of the source and also the complexity of near source structure.
If we assume that the depth variation of the intercept is primarily a function of small-scale structure and finite binning, then it is reasonable to take the deep source bin intercept estimate as an estimate of the non-structural signal in the data. For teleseismic P- waves this is = 0.25s2 and = 5s2 for the S-waves. Estimates of the structural signal are around = 1 s2 for P-waves and = l 2s2 for the S- waves. We estimate the signal-to-noise ratio for P-waves as ✓ 1/✓ 0 .25
= 2; and ✓ 12/✓ 5= 1.5. for S-waves.
1.6.b Discussion of se1sm1c velocities
The most striking result of this study is the concentration of power in the upper mantle compared to the lower mantle and the similarity in the results for the shear and compressional wave structure. Given the fact that for teleseismic distances the lower mantle path length is appreciably larger than the upper mantle path length; the contribution of the lower-mantle on travel-time residuals will be larger than the low total power (the product of the half-width and the mean square amplitude of the slowness variations suggests [Zhou et al., 1988]). If the scale-lengths of the heterogeneity were the same in both regions, then the amplitude of slowness fluctuations
would equally be greater in the upper than lower mantle. There is a suggestion. in the results that the half-width in the lower mantle could be possibly 2 or 3 times larger. This is better resolved in the P- wave study than in the S-wave study. This decreases the relative amplitude of lower mantle slowness fluctuations compared to upper mantle slowness fluctuations, as based solely on total power. The re- sults suggest that the large scale-length slowness fluctuations in the mid-upper mantle are more than an order of magnitude larger than the large scale-length fluctuations m the mid-lower mantle.
A comparison of the P-wave results in the lower mantle are made with the statistics of previous P-wave lower mantle de- terministic studies in figure 1.29. It is seen that the lower mantle comparison is reasonably favorable. There are some variations in ab- solute magnitude with both deterministic studies showing higher heterogeneity than discovered m our statistical study. This additional signal could be the result of the aliasing of higher spectral power into the lower harmonics, spurious power due to inversion of noise into poorly resolved regions of the model, or leakage into lower mantle due to poor depth resolution in the deterministic inversions. Equally, it could be caused by insufficient power in the spectral model due to leakage of power out from low harmonic degrees into the higher harmonics. It is certain that all these effects are factors, but we have special reason to suspect the inversion of noise given the large noise level, (the results of Dziewonski [1984 #177] show large power in regions of the Earth where he has little or no coverage, and that the model of Clayton and Comer [1983 #122] has a large amount of high-frequency power (spectra are nearly white), hints that noise
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