Mathematical Analysis of Continuum Mechanics and Industrial Applications by Hiromichi Itou Masato Kimura Vladimír Chalupecký Kohji Ohtsuka Daisuke Tagami & Akira Takada

Author:Hiromichi Itou, Masato Kimura, Vladimír Chalupecký, Kohji Ohtsuka, Daisuke Tagami & Akira Takada
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

It is impossible to deterministically estimate the small-scale velocity fluctuations that affect short-period seismograms because we do not have a sufficient distribution of earthquakes and stations. Therefore, we assume random velocity fluctuations. We consider an ensemble of random heterogeneous media and discuss the statistical properties of wave propagation. In seismology, several statistical methods that calculate the mean square (MS) envelopes in random media have been used to estimate the random heterogeneities in the Earth [28]. The Markov approximation is a statistical method to calculate MS envelopes in random heterogeneous media and a multiple forward-scattering approximation. Because we are neglecting the back- and wide-angle scatterings, we cannot model the latter coda part of the envelope; however, we can construct the envelope near its peak amplitude. In this study, we review the development of the Markov approximation and its applications in seismology. For simplicity, we restrict the derivation of the Markov approximation to the case of two-dimensional (2D) random heterogeneous media.

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