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Synthesis of Seismic Wave Envelopes Based on the Markov Approximation

  • Kentaro EmotoEmail author
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 26)

Abstract

In this study, we use stochastic methods to analyze complex short-period seismograms reflecting small-scale heterogeneities in the Earth. We consider an ensemble of random velocity-fluctuated media and the statistical characteristics of wave propagation. The Markov approximation is a stochastic method and a multiple forward-scattering approximation. In the Markov approximation, we neglect wide-angle and conversion scatterings and directly calculate the statistical average wave envelopes. Even though we cannot model the latter part of the envelope because we neglect wide-angle scattering, we can adequately describe the initial part of the envelope, i.e., from the onset to near the peak arrival time. We can estimate the statistical properties of the small-scale heterogeneities in the Earth by analyzing the envelope broadening effect. The Markov approximation was developed in optics and was introduced to seismology in the late 1980s. Here, on the basis of the Markov approximation, we summarize the development of envelope modeling and describe a method to calculate envelopes on a layered random heterogeneous media.

Keywords

Scattered Wave Random Medium Angular Spectrum Velocity Discontinuity Markov Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We are very grateful to the staff of the National Research Institute for Earth Science and Disaster Resilience enable Hi-net to continue functioning. The author would like to thank an anonymous reviewer for his valuable comments to improve this manuscript.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2017

Authors and Affiliations

  1. 1.Graduate School of ScienceTohoku UniversitySendaiJapan

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