Gudmundsson, O. and Davies, J. H. and Clayton, R. W. (1990) Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data. Geophysical Journal International, 102 (1). pp. 2543. ISSN 0956540X. http://resolver.caltech.edu/CaltechAUTHORS:20121017163209315

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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 Pwave 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 Pwaves. The variance peaks at 1.0–2.0 s^2 at Δ ≈ 20°, where triplications occur on the traveltime curve, drops to 0.15–0.8s^2 at teleseismic distances, and rises to 0.4–1.3 s^2 approaching the core shadow, where the traveltime curves of Pwaves and PcPwaves 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 Pwave data is about S/N ≈ 2. Inversion of the scaledependent 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 smallscale features (<300km). The lower mantle is devoid of smallscale structure. It contains 0.1 per cent velocity variations at a characteristic scale of about 1000km. This corresponds to a spectral bandwidth 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 smallscale 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.
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Additional Information:  © 1990 John Wiley and Sons. Accepted 1989 December 18; Received 1989 December 12; in original form 1989 March 16. We appreciate helpful comments by Don L. Anderson, Dave Stevenson and Hiroo Kanamori. This manuscript was greatly improved by the critical review of Bryndis Bimir and Hiroo Kanamori. This work was supported by NSF awards EAR8317623 and EAR8351371. The Phillips Petroleum Company provided fellowship support for O.G. This study was only possible because of the tremendous service performed by the ISC. Contribution 4748, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California.  
Group:  Seismological Laboratory  
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Subject Keywords:  heterogeneity; mantle; power spectrum; random error; traveltime; variance  
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Record Number:  CaltechAUTHORS:20121017163209315  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20121017163209315  
Official Citation:  Gudmundsson, O., Davies, J. H. and Clayton, R. W. (1990), Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data. Geophysical Journal International, 102: 25–43. doi: 10.1111/j.1365246X.1990.tb00528.x  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  34958  
Collection:  CaltechAUTHORS  
Deposited By:  Aucoeur Ngo  
Deposited On:  18 Oct 2012 15:57  
Last Modified:  23 Aug 2016 00:15 
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