Modeling and Interpretation Wave Fields in Hierarchical Heterogeneous Medium

Abstract

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.

"New Monitoring Geophysical Systems by Oil Deposits Extraction"

“…A concept was suggested in the paper Hachay et al [12] for solution of the direct problem for the 2-D case of longitudinal wave propagation through a local elastic heterogeneity with a hierarchical structure, located in the J-th layer of an N-layered medium. = , which coincides with the corresponding expression in the paper Hachay et al [12]. Let us extend this to the case, on the L th hierarchical level, of the occurrence of a porous fluid-saturated inclusion.…”

“…is the source function of the seismic field, the boundary value problem for which was formulated in the paper Hachay et al[12], is the wave number for the longitudinal wave; in the above expression, the index ji denotes the property of the medium inside the heterogeneity, ja is outside the heterogeneity, λ is the Lamé constant, σ-density of medium, ω -circular frequency, u gradϕ =  -vector of displacements, 0 ϕpotential of normal seismic field in layered medium in the absence of heterogeneity: is the potential of a normal seismic field in a layered medium in the absence of an heterogeneity of the previous rank l, if l = 2 ... L,…”

"Modeling and Using the Phase Diagram Method for Analyzing Active Acoustic Monitoring Data from Oil Wells"

“…The idea outlined in [7] for solving a direct problem for a two-dimensional case of propagation of a longitudinal wave through a local elastic heterogeneity with a hierarchical structure located in the J-th layer of the N-layer medium will be extended to the case when porous appears on the L-th hierarchical level fluid saturated inclusion.…”

“…If, on going to the next hierarchical level, the axis of twodimensionality does not change, but only the geometries of sections of nested structures change, then, similarly to [7], an iterative process of modeling a seismic field can be written (the case of a longitudinal wave only). The iteration process refers to the modeling of the displacement vector during the transition from the previous hierarchical level to the next level.…”