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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 integraldifferential 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.

Abstract. Geological medium is an open system which is influenced by outer and inner factors that can lead it to a unstable state. That non stability is as a rule occurred locally and these zones are named as dynamically active elements, which are indicators of potential catastrophic sources. These objects differ from the embedded geological medium by their structural forms, which often are of hierarchical type. The process of their activisation can be searched, using wave fields monitoring. For that purpose it is needed to develop new algorithms of modeling wave field's propagation through the local objects with hierarchical structure. Also it is needed to develop new theory of interpretation the wave field distribution for defining the contours of these local hierarchical objects. It had been constructed algorithms for 2D modeling of sound diffraction and linear polarized transversal seismic wave on an intrusion of hierarchic structure, located in the layer number J of N-layered elastic medium. We used the method of integral and integral-differential equations for a space frequency presentation of wave field's distribution. It is developed an algorithm for constructing the equation of theoretical inverse problem for 2-D electromagnetic field of E and H polarization and linear polarized longitudinal elastic wave by excitation of the N-layered conductive or elastic medium with hierarchic conductive or elastic inclusion located in the m-th layer. From the theory it is obviously that for such complicated medium each wave field contains its own information about the inner structure of the hierarchical inclusion. Therefore it is needed to interpret the monitoring data for each wave field apart, and not to mix the data base. These results will be the base for constructing new systems of monitoring observations of dynamical geological systems. Especially it is needed to prevent rock shocks in deep mines by their exploitation.

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