**Geophysical Journal International**

# Spectra of mantle shear wave velocity structure

## SUMMARY

We applied the stochastic method of Gudmundsson, Davies & Clayton (1990) (which was applied to ISC *P*-wave data) to teleseismic ISC *S*-wave data to obtain an independent estimate of mantle structure. We inverted the variance of *S*-wave traveltime residuals of bundles of rays to obtain a description of the spectrum of lateral heterogeneity as a function of depth through the mantle. The technique yields robust estimates of the traveltime scattering power (the product of a characteristic scalelength of heterogeneity and the mean square of slowness perturbations). We can estimate the characteristic scalelength (half-width), from the autocovariance; which can be reconstructed from the spectra. Hence by division, we can estimate the root mean square slowness. By extrapolating the variance of bundles of rays to bundles of zero cross-sectional area we can also estimate the scale-incoherent signal (which is a plausible estimate of the noise in the data), which is removed from the data.

We find that most of the structure generating shear wave traveltime residuals is located in the uppermost mantle. About half of the structure is short scale (harmonic degree *l* > 50). The large-scale structure (*l* > 50) has a half-width of about 500 km in the upper half of the mantle. This *S*-wave half-width is consistent with the *P*-wave half-widths determined by Gudmundsson *et al.* (1990). The *S*-wave half-width in the lower half of the mantle is poorly constrained. It varies from 500 to 3000 km, which spans the better constrained value of 1200 km found by Gudmundsson *et al.* (1990) for *P*-waves. The incoherent scatter suggests that the signal-to-noise ratio of the *S*-wave data set is around 1.5.

Assuming that the compressional and shear wave velocity variations are correlated then the signal weighted value of the ratio *d* In (*V _{s}*)/

*d*In (

*V*) is ∼ 2, as also found in normal mode studies. This is much larger than the value of ∼ 0.8–1.4 suggested by laboratory experiments undertaken at atmospheric pressure. There is no evidence of periodicity in the traveltime autocovariance; this suggests little or no periodicity in the underlying convection. The short half-width through most of the mantle suggests high Rayleigh number convection, with its attendant small-scale structures. The power decreases by an order of magnitude or more in going from the upper mantle to the lower mantle, the same as found by Gudmundsson

_{p}*et al.*(1990) for

*P*-waves. This large difference suggests either a change in convective regime and/or a difference in the temperature sensitivity of elastic constants in both layers. The increased short-scale structure at the top of the mantle suggests that a large part of the seismic signature at this boundary is compositional, since one would expect a red spectrum for a thermal boundary layer. The derived spectra between

*l*∼ 10 and

*l*∼ 50 are similar in shape to spectra from the mantle convection simulations of Glatzmaier (1988) with a Rayleigh number of 10

^{6}-10

^{7}, which would suggest layered convection, if the comparison is valid.