Linearized reflection coefficient and reflectivity modeling in fractured and attenuative reservoirs

Huaizhen Chen, Kristopher Innanen


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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