Existence of perturbed equilibrium states in some two-layer systems with density inversionстатья
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Дата последнего поиска статьи во внешних источниках: 11 января 2019 г.
Аннотация:In the system formed by a heavy elastic layer (lithosphere) and a half-space
filled by an ideal incompressible fluid (asthenosphere), the possibility of the existence of
equilibrium states with curved boundaries near an equilibrium of a system with rectilinear
boundaries is investigated. Using an analysis of the characteristic equation, we obtain a relationship
between the wave number of the desired static perturbation and the dimensionless
parameters of the problem, namely, the dimensionless shear modulus, Poisson’s ratio, and the
decompression. The assumption that the deformations are small imposes conditions on the
ranges of modification of the quantities. For example, for a moderately compressible elastic
material, the equilibrium which is called tectonic waves in geophysical applications is possible
only in the long-wavelength range in the presence of the inversion of density and very
strong decompression. The stability problem with respect to small dynamical perturbations
of an (obtained) equilibrium with curved boundaries is stated. A wave dispersion relation
connecting the complex frequency of oscillations with the wave number of perturbations and
with the above dimensionless parameters of the system is derived.