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The T-matrix approach can be used to calculate the effective properties of rocks. In this study, we demonstrate that the Tmatrix method (generalized optical potential approximation) is capable of calculating the effective viscoelastic properties of fractured rocks, while taking into account the spatial distribution of fractures, as well as, the effect of low-velocity and dispersive Krauklis waves, arising in thin fractures. We show that the developed theory can be used with any homogenisation scheme for rock physics applications. In this study, we introduce viscoelastic components which have complex moduli of the Krauklis wave — "Krauklis substance". As a result, the effective properties of a fractured rock become complex. We analyse the stiffness tensor dispersion and seismic attenuation, as well as, anisotropic behavior of seismic waves, caused by thin fractures filled with visloelastic substance. We demonstrate the results for two models of fractured carbonate rock, having a set of fluid filled aligned fractures.