B. M. Naimark and A. T. Ismail-zadeh


Gravity is a driving force in processes developing in the interior and at the surface of the Earth. Phase transitions in the mantle, chemical differentiation, thermal expansion, and other factors result in accumulation of stress upsetting the balance of masses, which leads to gravitational instability. The theory of gravitational instability is well developed for the case of viscous fluid and explains many tectonic processes. However, the rheology of the mantle is more complex. Maxwellian rheology is often more adequate in description of tectonic processes. The analysis of gravitational instability developing in a Maxwell mantle is not complete. We study a system of two Maxwell layers with an inverse density contract. To obtain the solutions we reduce the problem of gravitational instability to the eigenvalue problem for a set of ordinary differential equations with no-slip or perfect slip boundary conditions. The eigenvalues are zeros of an analytic functions derived for the problem. We suggest an algorithm for computation of the zeros based on the maximum principle for holomorphic functions and the principle of the argument for meromorphic functions. Using the suggested algorithm we establish the instability of the system of two Maxwell layers, compute rates of growth of maximum instability modes, and derive spatial wavelengths. The results are applicable to diapiric process under ridges and to the problem of salt tectonics.

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Computational Seismology, Vol. 1.