Trigger mechanisms are proposed for gas hydrate decomposition, methane emissions, and glacier collapse in polar regions. These mechanisms are due to tectonic deformation waves in the lithosphere–asthenosphere system, caused by large earthquakes in subduction zones, located near the polar regions: the Aleutian arc, closest to the Arctic, and the Antarctica–Chilean and Tonga–Kermadec–Macquarie subduction zones. Disturbances of the lithosphere are transmitted over long distances (of the order of 2000–3000 km and more) at a speed of about 100 km/year. Additional stresses associated with them come to the Arctic and Antarctica several decades after the occurrence of seismic events. On the Arctic shelf, additional stresses destroy the microstructure of metastable gas hydrates located in frozen rocks at shallow depths, releasing the methane trapped in them and leading to filtration and emissions. In West Antarctica, these wave stresses lead to decreases in the adhesions of the covered glaciers with underlying bedrock, sharp accelerations of their sliding into the sea, and fault occurrences, reducing pressure on the underlying rocks containing gas hydrates, which leads to their decomposition and methane emissions.

The analytical solution to the problem of thermal convection in the upper mantle adjoined to the subduction zone is constructed. The results of seismotomographic mantle shooting are used in the formulation of problem. The corresponding nonlinear problem of mathematical physics can be integrated analytically and reduced to a significantly simpler system of nonlinear algebraic equations. The main aim of the present study is to justify mathematically a new regional model of evolution of the Arctic and North East Asia lithosphere [1–5]. In particular, the possibility of existence of the single -cell flow structure strongly stretched in the horizontal direction in the upper mantle is needed to test.

This paper defines a generalized mathematical model of filtration in a double porosity medium, taking into account recent ideas on liquid and gas flow in rocks with an anomalously low...

The problem of the development of thermomechanical waves in the system consisting of two horizontal layers with rheology of a linearly elastic medium for the upper layer (lithosphere) and a viscous fluid for the lower layer (asthenosphere) is considered with regard to phase transition on their common boundary. The exact solution to the problem is found and its properties as functions of the parameters are studied. It is shown that for the characteristic physical parameters of the lithosphere and asthenosphere there exist solutions in the form of moderately damped strain tectonic waves and a geophysical interpretation of the results obtained is given.

We present a generalization of the mathematical model of gas discharge from frozen rocks containing gas-saturated ice and gas hydrates in a metastable state (due to the self-preservation effect) caused by the drop in external stress associated with various geodynamic factors. These factors can be attributed, for example, to a decrease in hydrostatic pressure on a gas-bearing formation due to glacier melting, causing an isostatic rise, or to the formation of linear depressions in the bottom topography on the shelf due to iceberg ploughing. A change in external pressure can also be associated with seismic and tectonic deformation waves propagating in the lithosphere as a result of ongoing strong earthquakes. Starting from the existing hydrate destruction model, operating at the scale of individual granules, we consider a low-permeable hydrate and ice-saturated horizontal reservoir. Generalization is associated with the introduction of a finite threshold for the external pressure drop, which causes the destruction of the gas hydrate and gas-saturated microcavities of supramolecular size. This makes it possible to take into account the effect of anomalously high pressures occurring in the released gas as a result of partial hydrate dissociation. Numerical and approximate analytical solutions to the problem were found in the self-similar formulation. A parametric study of the solution was carried out, and regularities of the hydrate decomposition process were revealed.

The generalized equations of solution motion are given both in porous media and in cavities taking into account the osmotic effect. In certain cases, commonly small relevant corrections play a key role since they are mainly causing the solution motion. Based on the generalized equations, a number of problems have been solved that are of practical value. Owing to the limited volume of this paper, only a simplified example is given.