Abstract
On the base of assumption that the rotational movements of the chain of the crust blocks and the corresponding rotational waves characterizing the redistribution of tectonic stresses are described by the sine-Gordon equation with dissipation, the dispersion properties of this equation are analyzed. It is shown that the dispersion is manifested in the low-frequency range at high values of the dissipation factor. The presence of anomalous dispersion has been revealed for all values of the dissipation factor. Influence of this factor on dispersion is investigated. Some features of propagation of a stationary shock wave in a geomedium are studied. It has been found that the shock wave front width is directly proportional to the nonlinear wave velocity and to the dissipation factor of the medium, but it is inversely proportional to the nonlinearity coefficient.
Highlights
The classical theory of elasticity is based on idea that solid is a continuum of material points possessing only translational degrees of freedom
It is assumed that the rotational movement of crust blocks and the corresponding rotational waves characterizing redistribution of tectonic stresses are described by the sine-Gordon equation [16, 21]
The friction is considered as a dissipation factor, which, on account of frictional forces between blocks of a geomedium, prevents their rotational interaction [16]
Summary
The classical theory of elasticity is based on idea that solid is a continuum of material points possessing only translational degrees of freedom. Recent data of geological and geophysical research argue that the Earth’s crust consists of non-point particles-blocks that are able to rotate. PAVLOV to solving geodynamic problems (see, for example, [16, 19]) This approach is based on the following assumptions: an elementary part of the rotating solid body – the Earth’s crust block – is, first of all, a rigid non-deformable volume; secondly, its motion occurs under the action of its own moment; thirdly, such a motion leads to change of the stress state of the crust surrounding the block [16]. In accordance with this approach, we shall consider motion of two interacting crust blocks in a geomedium rotating with angular velocity Ω
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