The problem on excitation and propagation of slow eigen mode in thin fluid-filled fracture under action of external seismic wave is considered in the report. Based on averaging procedure the non-uniform pseudo-differential wave equation for slow eigen mode in fluid-filled fracture is derived in space-time representation for the long wave approximation by fracture opening. The derived wave equation takes into account strong dispersion of slow eigen mode and contribution of incident external seismic field. The space-time description of slow eigen mode in fracture allows to state and solve the boundary problem on the slow mode excitation by fracture tips and to estimate the contribution of this effect at the tube wave generation in a well. Numerical calculation show that the magnitude of this effect can achieve several percents of the principal tube wave amplitudes and hence it can be used for fracture size characterization.


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