SEISMIC ATTENUATION FOR RESERVOIR CHARACTERIZATION

In fully-saturated rock and at ultrasonic frequencies, the microscopic squirt flow induced between the stiff and soft parts of the pore space by an elastic wave is responsible for velocity-frequency dispersion and attenuation. In the seismic frequency range, it is the macroscopic cross-flow between the stiffer and softer parts of the rock. We use the latter hypothesis to introduce simple approximate equations for velocity-frequency dispersion and attenuation in a fully water saturated reservoir. The equations are based on the assumption that in heterogeneous rock and at a very low frequency, the effective elastic modulus of the fully-saturated rock can be estimated by applying a fluid substitution procedure to the averaged (upscaled) dry frame whose effective porosity is the mean porosity and the effective elastic modulus is the Backus-average (geometric mean) of the individual dry-frame elastic moduli of parts of the rock. At a higher frequency, the effective elastic modulus of the saturated rock is the Backus-average of the individual fully-saturated-rock elastic moduli of parts of the rock. The difference between the effective elastic modulus calculated separately by these two methods determines the velocity-frequency dispersion. The corresponding attenuation is calculated from this dispersion by using (e.g.) the standard linear solid attenuation model