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Journal of Mining Sciences

2016 year, number 6

Intensification of Nonlinearity by Dispersed Events in Media with Structure and Generation of Various Dominant Frequencies in P- and S-Waves

B. P. SIBIRYAKOV1, E. B. SIBIRYAKOV2
1Trofimuk Institute of Oil and Gas Geology and Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 3, Novosibirsk, 630090 Russia
2Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
Keywords: оператор сплошности, микроструктура, солитоны, различие частот P- и S-волн, continuity operator, microstructure, soliton waves, different frequencies of P- and S-waves

Abstract

A model of a continuum with a structure described by infinite order equations of motion is proposed. In case that a wave is very long as compared with the size of the structure, equations are reduced to the fourth-order equations. A closed equation of motion, including nonlinear, dispersed and wave members, is derived. It is shown that solutions in the form of soliton waves exist only in media where wave velocity grows with pressure. In the media, where soliton waves do not exist, quasi-stationary solutions with multiple frequencies prevail. It is found that the nonlinear effect of multiple frequencies is unexpectedly high even for small deformation as dispersion violently intensifies nonlinear events. Moreover, in the domain of small deformation, there exist solutions for longitudinal and transversal waves with the same length and different frequencies. The solutions for the same length waves with different frequencies most often occur in seismology and seismic explorations.