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SH Wavelet Propagation Through the Random Distribution of Aligned Line Cracks Based on the Radiative Transfer Theory

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Abstract

This paper studies the propagation of SH wavelet intensity through the random distribution of aligned line cracks in a two-dimensional (2-D) homogeneous medium as the simplest mathematical model of the heterogeneous Earth medium. The scattering process of a single line crack is described by Mathieu functions. The random distribution of cracks is well represented by the scattering coefficient, that is, the scattering power per unit area. Two methods are proposed for the derivation of the space–time distribution of the intensity Green function for the unit isotropic radiation from a point source: one is the single scattering approximation and the other is the Monte Carlo simulation. The former and the latter are deterministic and stochastic methods, respectively. In the case that the wavenumber is larger than the reciprocal of the crack length, synthesized time traces show that direct wavelets near the ray direction parallel to the line cracks decrease according to the geometrical decay with increasing travel distance as if there exists a transparent channel along the crack line direction; however, those near the direction normal to the line cracks decrease more rapidly because of strong scattering attenuation. At large lapse times, multiple scattering produces a swelling around the source location, which is prolonged to the crack line direction. Those characteristics well reflect the anisotropy of the line crack scattering. The Monte Carlo simulation presented here could be a fundamental base for the study of more realistic crack scattering problems.

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Acknowledgements

The author is grateful to two anonymous reviewers. Their comments and suggestions were helpful for improving the manuscript.

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  1. Geophysics, Science, Tohoku University, Aoba-ku, Sendai, Miyagi, 980-8578, Japan

    Haruo Sato

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Sato, H. SH Wavelet Propagation Through the Random Distribution of Aligned Line Cracks Based on the Radiative Transfer Theory. Pure Appl. Geophys. 178, 1047–1061 (2021). https://doi.org/10.1007/s00024-021-02680-8

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