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Seismic Waves in Heterogeneous Earth, Scattering of

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Extreme Environmental Events

Article Outline

Glossary

Definition of the Subject

Introduction

Radiative Transfer Theory for a Scattering Medium

Wave Envelopes in Random Media and Statistical Characterization

Envelope Broadening of a High-Frequency Seismogram

Spatial Variation of Scattering Characteristics

Temporal Change in the Earth Medium Structure

Future Directions

Acknowledgments

Bibliography

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Abbreviations

Attenuation factor \({\boldsymbol{Q^{-1}}}\) :

A measure of attenuation characteristics of a medium caused by intrinsic absorption and scattering loss. The former means the transfer of vibration energy into heat and the latter means the transfer of vibration energy from the direct wave to coda waves caused by scattering due to medium heterogeneity.

Coda waves:

Wave trains that follow the arrival of the direct S‑wave phase are called S‑coda waves or simply coda waves. Coda waves are interpreted as a superposition of S waves scattered by distributed heterogeneities. Wave trains between direct P and S wave arrivals are called P‑coda waves.

Coda attenuation factor \({\boldsymbol{Q_\text{C}^{-1}}}\) :

This parameter characterizes the amplitude decay of S coda of a local earthquake with the lapse time increasing based on the S‑to‑S single scattering. The coda duration shortens for a larger coda attenuation factor.

Envelope broadening:

The source duration time of a microearthquake is short; however, the apparent duration time of the S‑wave seismogram increases with the travel distance increasing because of diffraction and scattering by medium heterogeneities. This phenomenon is called envelope broadening.

Radiative transfer theory:

A phenomenological theory that describes scattering process of wave energy in a scattering medium on the basis of causality, geometrical spreading and the energy conservation. It neglects the interference of waves but focuses on the intensity only. This theory admits various types of scattering patterns. It is often applied to model the energy propagation of high‐frequency seismic‐waves in heterogeneous Earth media.

Random media:

A mathematical model for media whose parameters are described by random functions of space coordinates. The stochastic properties of the ensemble of random media are characterized by their autocorrelation function or the power spectral density function.

Scattering coefficient \({\boldsymbol{g}}\) :

A measure of the scattering power in a unit solid angle at a certain direction by a unit volume of heterogeneous media for the incidence of unit energy flux density. The average of g over the solid angle gives the total scattering coefficient g 0, of which the reciprocal gives the mean free path. This quantity characterizes the coda excitation and the scattering loss in the heterogeneous media.

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Acknowledgments

The author thanks Michael Korn, Heiner Igel, and an anonymous reviewer. Their comments were helpful for improving the readability. The author is grateful to NIED, Japan for providing digital seismic data.

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  1. Department of Geophysics, Graduate School of Science, Tohoku University, Sendai-shi, Miyagi‐ken, Japan

    Haruo Sato

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Sato, H. (2011). Seismic Waves in Heterogeneous Earth, Scattering of. In: Meyers, R. (eds) Extreme Environmental Events. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7695-6_42

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