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Sato 1984
Sato, H. (1984). Attenuation and envelope formation of three-component seismograms of small local earthquakes in randomly inhomogeneous lithosphere. Journal of Geophysical Research 89: doi: 10.1029/JB089iB02p01221. issn: 0148-0227.

A unified model is proposed for explaining the frequency dependence of Q-1 and the formation of velocity seismograms by a single scattering process. Adopting Birch's law and a linear correlation between P and S wave velocities, we statistically describe the inhomogeneous medium by one random fluctuation, which is spatially characterized by the exponential autocorrelation function. We calculate Q-1 for P and S waves on the basis of the Born approximation, supposing seismic waves attenuate due to scattering largely by rapidly fluctuating random structure. Resulting QS-1 explains the observed frequency dependent well, when the mean square fractional fluctuation and the correlation distance are chosen to be 0.01 and 2 km, respectively. Nonspherical radiation due to a point shear dislocation and frequency dependent nonisotropic scattering including conversion between P and S waves complicate the seismograms. Taking those complexities into account, we synthesize the ''envelopes'' of three-component velocity amplitudes of P and S coda waves by summing up energy singly scattered by distributed inhomogeneities. From numerical calculations, we found that the radial component of the P coda wave is excited even in the nodal direction of the P wave radiation mostly due to SP scattering occurring near the hypocenter. The P coda waves appearing on the transverse components are a complex mixture of PP, PS, and SP scattering. The S coda waves are excited mostly due to SS scattering in all directions, and appear in all three components; their polarizations are controlled by the radiation pattern even in the later part of S coda waves.

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Abstract

Journal
Journal of Geophysical Research
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American Geophysical Union
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