Analysis of global traveltime data has been formulated in terms of the stochastic properties of the Earth's heterogeneity pattern and random errors in the data. the formalism relates the coherency of traveltime residuals within bundles of rays (summary rays) of varying size to the spherical harmonic power spectrum of the slowness field of the medium. It has been applied to mantle P-wave data from the ISC catalogue. the measure of coherency is the variance within summary rays. It is estimated within bins in source depth, epicentral distance and the scale size of the area defining a summary ray. the variance at infinitesimal scale length represents the incoherent component of the data (random errors). the variation of the variance with scale length contains information about the autocorrelation function or power spectrum of slowness perturbations within the Earth. the variation with epicentral distance reflects the depth variation of the spectrum. the formalism accounts for the uneven distribution (clustering) of stations and events.
We find that estimates of random errors correlate well with complexities on the traveltime curve of P-waves. the variance peaks at 1.0–2.0 s2 at δ20°, where triplications occur on the traveltime curve, drops to 0.15–0.8s2 at teleseismic distances, and rises to 0.4–1.3 s2 approaching the core shadow, where the traveltime curves of P-waves and PcP-waves merge. These estimates should be considered upper bounds for the random error variance of the data. the signal to random noise ratio in the teleseismic ISC P-wave data is about S/N= 2.
Inversion of the scale-dependent structural signal in the data yields models that concentrate heterogeneity strongly in the upper mantle. the product of correlation length and power drops by about two orders of magnitude from the surface of the Earth to the lower mantle. About half of this quantity in the upper mantle is due to small-scale features (<300km). the lower mantle is devoid of small-scale structure. It contains 0.1 per cent velocity variations at a characteristic scale of about 1000km. This corresponds to a spectral band-width of l= 7. the D″ layer at the bottom 100–200 km of the mantle shows up as a distinct layer in our results. It has 0.3 per cent velocity variations at a characteristic scale of 350km. the top of the lower mantle contains 0.3 per cent velocity variations on a scale of 500km and also contains some small-scale power.
These results are compatible with previous deterministic lower mantle studies, although some details differ. the strength of heterogeneity in the upper mantle may obscure attempts to model the Earth's deep interior.