Development of a mathematical model of a layered heterogeneous medium as an integral part of the oceanographic data bank of the National Academy of Sciences of Ukraine
Abstract
The article develops and implements analytical and numerical methods for modeling layered geological structures with cavities of simple and complex shapes. The analysis of existing models of the real geological environment is carried out, information is provided on such models as: impedance and elastic models of bottom sediments, heterogeneous models of environments, statistical models of the bottom environment. There are developed analytical and numerical methods for mathematical modeling of the structure and spatial distribution of the acoustic properties of marine sediments, presented as a layered heterogeneous medium. Developed methods make it possible to create discrete, continuous or mixed structural-acoustic models of a heterogeneous seabed, taking into account stratification, fluid and gas-saturated bottom sediments, the presence of cavities and inclusions of various shapes and properties in them. Algorithms have been developed for obtaining a model acoustic response, which is a superposition of all acoustic signals reflected from geological boundaries, which have different reflection coefficients. Acoustic reflection is described by the so-called convolutional model. Mathematical modeling of the processes of determining the bottom topography by such means as an echo sounder, a multi-beam echo sounder and an interferometer has been carried out. With the help of the developed software package and using modern GIS-systems, digital elevation models and isobatic maps of individual surveyed water areas were created.
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