Shundel O. Development of a mathematical model of a layered heterogeneous medium as an integral part of the oceanographic data bank.

Analytical and numerical methods for modelling layered geological structures with cavities of simple and complex form have been developed and implemented in the thesis work. Existing models of the real geological environment have been analyzed, and information on such models as impedance and resilient models of sediments, heterogeneous models of media, statistical models of bottom media, models of Bio and their modification has been presented. Analytical-numerous methods have been developed for mathematical modelling of the structure and spatial distribution of acoustic properties of marine sediments, represented as layered heterogeneous medium. The methods developed make it possible to create discrete, continuous or mixed structural-acoustic models of the heterogeneous seabed, taking into account the stratification, fluid and gas-saturated bottom sediments, the presence therein of cavities and the inclusion of various forms and properties. Algorithms have been developed for obtaining model acoustic response, which is the superposition of all acoustic signals reflected from geological boundaries, which have different reflectance coefficients. Acoustic reflection is described by the so-called convergent model. Mathematical modeling of bottom relief processes by means such as echo sounder, multi-beam echosounder and interferometer has been performed. With the aid of the developed software system, digital elevation models and isobathic maps of individual surveyed areas are created according to algorithms, which are described in this thesis work and using modern GIS systems. Key words: spatial spectrum, bottom sediments, Fourier transformations, echo sounders, geoacoustic parameters of sediments, partition boundary, GIS technologies.