Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves

A. L. Krylov; N. G. Mazur; V. N. Nikolayevskii; G. A. El'

doi:10.1016/0021-8928(93)90083-X

Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves

A. L. Krylov^*, N. G. Mazur, V. N. Nikolayevskii, G. A. El'

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

The equations of the propagation of weak non-linear waves are obtained by a detailed analysis of the gradient-consistent micropolar model of a granular continuous medium. The high-frequency mode of oscillation is associated with ultrasonic waves, and the low-frequency mode is associated with the usual seismic waves in rocks. The evolution equations that include the case of long-wave-short-wave resonance are obtained by an asymptotic consideration. This resonance corresponds to the case of the generation of ultrasound (noise) by travelling seismic waves.

Original language	English
Pages (from-to)	1057-1066
Number of pages	10
Journal	Journal of Applied Mathematics and Mechanics
Volume	57
Issue number	6
DOIs	https://doi.org/10.1016/0021-8928(93)90083-X
Publication status	Published - 1993
Externally published	Yes

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title = "Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves",

abstract = "The equations of the propagation of weak non-linear waves are obtained by a detailed analysis of the gradient-consistent micropolar model of a granular continuous medium. The high-frequency mode of oscillation is associated with ultrasonic waves, and the low-frequency mode is associated with the usual seismic waves in rocks. The evolution equations that include the case of long-wave-short-wave resonance are obtained by an asymptotic consideration. This resonance corresponds to the case of the generation of ultrasound (noise) by travelling seismic waves.",

author = "Krylov, \{A. L.\} and Mazur, \{N. G.\} and Nikolayevskii, \{V. N.\} and El', \{G. A.\}",

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AU - Krylov, A. L.

AU - Mazur, N. G.

AU - Nikolayevskii, V. N.

AU - El', G. A.

PY - 1993

Y1 - 1993

N2 - The equations of the propagation of weak non-linear waves are obtained by a detailed analysis of the gradient-consistent micropolar model of a granular continuous medium. The high-frequency mode of oscillation is associated with ultrasonic waves, and the low-frequency mode is associated with the usual seismic waves in rocks. The evolution equations that include the case of long-wave-short-wave resonance are obtained by an asymptotic consideration. This resonance corresponds to the case of the generation of ultrasound (noise) by travelling seismic waves.

AB - The equations of the propagation of weak non-linear waves are obtained by a detailed analysis of the gradient-consistent micropolar model of a granular continuous medium. The high-frequency mode of oscillation is associated with ultrasonic waves, and the low-frequency mode is associated with the usual seismic waves in rocks. The evolution equations that include the case of long-wave-short-wave resonance are obtained by an asymptotic consideration. This resonance corresponds to the case of the generation of ultrasound (noise) by travelling seismic waves.

UR - https://www.scopus.com/pages/publications/0342862828

U2 - 10.1016/0021-8928(93)90083-X

DO - 10.1016/0021-8928(93)90083-X

M3 - Article

AN - SCOPUS:0342862828

SN - 0021-8928

VL - 57

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EP - 1066

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

IS - 6

ER -

Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves

Abstract

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