The problem of fitting of the zero-range model of the tectonic plate under a localized boundary stress

We suggest a method of fitting of the zero-range model of the tectonic plate under the boundary stress based on comparison of the theoretical formulae for the corresponding eigenfunctions/eigenvalues with the results of instrumental measurements of frequency and the shape and the shape of the relevant seismo-gravitational modes in the remoted zone. Comparison of the data of the instrumental measurements of the variation of frequency of seismo-gravitational oscillations with results of theoretical analysis of the fitted model permits to localize the stressed zone on the boundary of the tectonic plate and estimate the risk of a powerful earthquake at this zone. Key-words Thin plate, Zero-range potential, Operator extension 1 Dynamics of the system of tectonic plates and the motivation of the zero-range model. The lithosphere of Earth consists of 13 tectonic plates which jigsaw fit each other, contacting at some boundary zones. The plates are isolated from underlying solid structures within the Earth mantle by the liquid layer of astenosphere which is formed, due to high pressure and temperature, in the interval of depth between 100 200 km. Fig. 1 below 1 shows a complex Fig.1 is borrowed from the book of S. Aplonov, [3], and is included in our text on the permission of the Publishing House of the St. Petersburg University.