The geological environment is an open system, on which external and internal factors act. They lead it to an unstable state, which, as a rule, manifests itself locally in the form of zones, called dynamically active elements, which are indicators of potential catastrophic sources. These objects differ from the host geological environment by structural forms, which are often forming of a hierarchical type. The process of their activation can be observed using monitoring with wave fields, for mathematical support of which new modeling algorithms have been developed using the method of integral and integral-differential equations. A new approach to the interpretation of wave fields has been developed, to determine contours or surfaces of locally stressed hierarchical objects. An iterative process of solving the theoretical inverse problem for the case of determining configurations of 2D hierarchical inclusions of the k-th rank is developed. When interpreting monitoring results, it is necessary to use data from such monitoring systems that are tuned to study the hierarchical structure of the environment.
Part of the book: Computational and Experimental Studies of Acoustic Waves