An extensive existence of strong small-scale heterogeneity in the earth is suggested by the great variability of direct waves and remarkable stability of scattered waves, both in the case of teleseismic P coda and in the case of local earthquake S coda.

Quantitative studies of small-scoale heterogeneities have been made by the following three methods. A lower bound of heterogeneity in the lithosphere has been estimated by the deterministic or stochastic modeling of travel-time and amplitude fluctuation of teleseismic P waves across a large aperture seismic array. An upper bound of heterogeneity has been estimated by modeling the attenuation of S waves as a scattering loss due to heterogeneity. These two approaches suggest the existence of heterogeneity with rms velocity fluctuations from 3 to 10 per cent. The third method is based on the estimation of heterogeneity from the amplitude of coda waves. We found a significant discrepancy between the result obtained by the third method and those from the first two, and attribute the discrepancy to the assumption of a single-scattering model adopted in the coda generation theory. The need for including multiple scattering as well as for considering vector elastic waves rather than scalar waves is emphasized.

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