Tectonic plate under a localized boundary stress: fitting of a zero-range solvable model

We suggest a method of fitting of a zero-range model of a tectonic plate under a boundary stress on the basis of comparison of the theoretical formulae for the corresponding eigenfunctions/eigenvalues with the results extraction under monitoring, in the remote zone, of non-random (regular) oscillations of the Earth with periods 0.2-6 hours, on the background seismic process, in case of low seismic activity. Observations of changes of the characteristics of the oscillations (frequency, amplitude and polarization) in course of time, together with the theoretical analysis of the fitted model, would enable us to localize the stressed zone on the boundary of the plate and estimate the risk of a powerful earthquake at the zone. Key-words Tectonic plate, Zero-range interaction, Operator extension PACS numbers 91.45.D, 02.30.Jr, 02.30.Tb 1 Dynamics of the system of tectonic plates and the motivation of the zero-range model. The lithosphere of Earth consists of 14 tectonic plates which jigsaw fit each other. The plates are isolated from underlying solid structures within the Earth mantle by the low-viscosity layer of the asthenosphere which is formed, due to various conditions, including high pressure and temperature, in the interval of depth 100 -200 km. The plates move on the surface of Earth, due to convective flows and variations of the angular speed of Earth, gliding on the low-viscosity layer of asthenosphere and interacting with each other at some active boundary zones, see below. Fig. 1 below 1 shows a complex form 1 Fig.1 is borrowed from the book of S. Aplonov, [3], and is included in our text with permission of the Publishing House of the St. Petersburg University. 1 ar X iv :0 80 1. 27 99 v1 [ m at hph ] 1 8 Ja n 20 08