Frequency-Dependent Seismic Reflectivity of Randomly Fractured Fluid-Saturated Media

Fractures exist on a wide range of scales from microns to hundreds of meters. Throughout this scale range, fractures have a significant influence on fluid flow and physical properties of rocks. The average elastic properties of a randomly fractured fluid-filled rock were discussed for different fracture distribution laws in association with the extremely slow and dispersive guided wave propagation within individual fractures. Krauklis wave was used as an asymptotic solution of the fluid interface wave (FIW) equations. Different fracture distribution laws (exponential, power, fractal and gamma laws) within the rock in the seismic range of frequencies ($10-100Hz$) initiated high-velocity dispersion and attenuation of the P-wave. Calculations showed that increase of one order of fracture density enhances velocity dispersion and attenuation by 20%, in particular, at low seismic frequencies. Different cases of acoustic impedance distributions versus depth for assessing reflection properties from fractured and non-fractured layers have been considered. Results demonstrated the remarkable difference between the P-wave reflection coefficient from the fractured layer and the P-wave reflection coefficient from the non-fractured layer: about 30-40% decrease in amplitude for the fractured high-impedance layer, about 30-50% increase of amplitude for the fractured low-impedance layer and about 20% decrease for the intermediate case. The biggest difference in the behavior of reflection coefficient versus incident angle is observed at seismic low-frequencies (Hz). The thickness related tuning effect has the different impact on the seismic signal in the fractured and homogeneous layers for all acoustic impedance cases. The approach and results of calculations allow an interpretation of abnormal velocity dispersion, high attenuation, and special behavior of reflection coefficients vs. frequency and angle of incidence as the indicators of fractures. The analysis of the seismic monitoring data from the Royal Center Field, Indiana, indicates the frequency-dependent difference of attenuation and velocity of the P-wave in water saturated and gas saturated formation. It is in agreement with numerical modeling results involving Krauklis wave theory. The difference is bigger at low frequencies. The numerical modeling explains a low-frequency seismic anomaly, detected in fractured zones within source rock in the East-Surgut Basin, Western Siberia. The study of the laboratory measurements on the fractured 3-D printed samples indicates the possibility of a P-wave velocity prediction in the fluid-filled fractured sample based on the velocity of non-fractured porous saturated background.