Based on the complex linear slip theory, we derive complex stiffness parameters in terms of fracture weaknesses and induced attenuation factor under the assumption of the host rock being elastic and isotropic. Incorporating with the attenuative crack model, we relate the induced attenuation factor to fracture properties (fracture density and aspect ratio)andﬂuidparameters(ﬂuidbulkmodulusandviscosity),andstudyhowfracturedensity and water saturation affect the variation of the induced factor in seismic frequency range (1-100 Hz). Using perturbations in the complex stiffness parameters, we derive a complex linearized reﬂection coefﬁcient involving the induced attenuation factor and fracture weaknesses. The accuracy of the derived reﬂection coefﬁcient is conﬁrmed by comparing the result calculated using the extended reﬂectivity method and that computed using the derived equation. We ﬁnally use the derived linearized reﬂection coefﬁcient to obtain the seismic reﬂection response for the case of fractured reservoirs with different values of fracture density and water saturation. We conclude that the attenuation factor is applicable to distinguishing between oil-bearing and water-bearing reservoirs, and seismic response difference induced by fracture density and water saturation increases with the incidence angle.
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