To the study of the resonance behavior of volcanic structures

Abstract

It is known that the geophysical medium in the vicinity of volcanoes is characterized by the presence of significant structural heterogeneities, which differ in their internal structure from the surrounding geological environment. This gives reason to attribute the volcanic structure with heterogeneities to the geological structures of the resonance type, which determine the mechanisms of preparation and development of the catastrophic event, both earthquakes and activation and eruption of the volcano.

It is known that the geophysical environment in the vicinity of volcanoes is characterized by the presence of significant structural heterogeneities, which differ in their internal structure from the surrounding geological environment. This gives reason to attribute the volcanic structure with heterogeneities to the geological structures of the resonance type, which determine the mechanisms of preparation and development of the catastrophic events such as earthquakes, and the activation and eruption of the volcano.

During the study of the volcanic structure resonance behavior modeled by a block structure, it is necessary to analyze the pseudo-differential equations that arise in the implementation process of the block element method and the differential factorization method. By extracting from them the corresponding integral or integro-differential equations, we are able to write out the conditions that describe the so-called "natural viruses", which can be considered as a generalization of the static conditions. Mathematical descriptions of the "viruses" allow us to find the conditions when the localization of selected parameters occurs, possible under certain conditions in reality.

In the paper we study the resonance properties of particular models of volcanic structures. We obtain an expression for the ``virus'' of a volcanic structure modeled by a stamp on an elastic foundation in the form of a layer, as well as establish the existence of system parameters which lead to the occurrence of unlimited resonance.

To study processes in the environment of trap provinces, we present a model of a tectonic plate, represented by a layer of finite thickness with the distributed load applied to the upper surface simulating anthropogenic effect and distributed load applied to lower surface simulating the effect of the environment of mantle plumes. In the model under consideration, we use the integral Fourier transform, which allows us to reduce the dimension of the problem and construct functional relations for obtaining the Fourier images of the main characteristics of the system, which are further determined by applying the inverse Fourier transform using the apparatus of residue theory. The obtained expressions provide an opportunity for studying the laws of the emerging fields of displacements and stresses in the environment of the trap province.