Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data

Abstract

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 A = 20", where triplications occur on the traveltime curve, drops to 0.15-0.8 s2 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 SIN = 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 (<300 km). The lower mantle is devoid of small-scale structure. It contains 0.1 per cent velocity variations at a characteristic scale of about lo00 km. This corresponds to a spectral band-width of 1~7 .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 350 km. The top of the lower mantle contains 0.3 per cent velocity variations on a scale of 500 km and also contains some srnall-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.

Effects of multiple phase transitions in a three‐dimensional spherical model of convection in Earth's mantle

“…The upper mantle (UM) is characterized by a high-amplitude "red" (i.e., longwavelength, peaking at oe•8) spectrum, although since it also contains narrow features, there is still significant amplitude at much higher degrees, as may be true in Earth [Gudmundsson et al, 1990;. The midmantle (MM), comprising the upper ~1000 km of the lower mantle, is characterized by a low-amplitude, broad spectrum, with a wide peak at oe--5-20, and the deep mantle (DM) is again characterized by a high-amplitude red spectrum (peak •6).…”

Whole Earth structure estimated from seismic arrival times

“…Furthermore, the spectrum of heterogeneity scale lengths, within the mantle, for example, has not been definitively established, and intermediate-and small-scale heterogeneity is probable [Gudmundsson et al, 1990] Each of the terms in the above expression may be related to variations in physical properties and processes within the Earth. Though the exact relationships are often nonlinear, we may linearize them under the assumption that deviations from our initial Earth model are small.…”

Detection of lower mantle scatterers northeast of the Marianna subduction zone using short‐period array data

“…Whole Earth tomographic studies yield considerably lower estimates of seismic heterogeneity within the lower mantle than in the upper mantle, -0.5% as compared to -5% [Dziewonski, 1984;Gudmundsson et al, 1990]. This relative homogeneity of the lower mantle may be real but may alternatively be due to the lack of resolution in current seismological techniques [Nolet, 1990;Machetel, 1990].…”