A numerical study on reflection coefficients of fractured media

Abstract

Effective-medium theories can be used to predict reflection coefficients of an interface between an unfractured layer overlying a fractured half-space. In 2D and 3D computer simulations, we analyze wavefields that are emitted by an explosion line or point source and reflected from a fractured area in a digital rock model. The reflection coefficients from the simulations are compared to several predictions given by static effective-medium theories. The agreement between our numerical results and the theoretical reflection coefficients is best for differential effective-medium schemes in 2D as well as in 3D. This result agrees with previously published numerical static and numerical transmission-time experiments. By varying the wavelength to crack-length ratio, we consider the application range of different effective-medium theories. We observe good agreement with theoretical predictions even for a ratio equal to 9. An angle-dependent analysis of the reflected amplitude of our numerical results is also compared to results given by effective-medium theory in combination with exact reflection-coefficient formulas. As expected, the fluctuations of the reflection coefficients decrease for wider angles. In our 3D digital rock models, we vary the crack density and the infill of the crack (i.e., water [cold and hot] and oil [cold and hot]).