Effect of mesoscopic-flow loss on seismic reflections in media with penny-shaped inclusions

We obtain the amplitude and energy reflection coefficients of seismic waves in porous media with penny-shaped inclusions, based on the generalized Biot-Rayleigh model that takes into account the attenuation due to mesoscopic local fluid flow (LFF). We consider two cases, including a contact between two porous media having either different fluids (gas-water contact) or crack density and aspect ratio, as well as a water half-space overlying a porous medium, and study the frequency-dependent reflection-transmission (scattering) coefficients for open- and sealed-pore boundary conditions. Our examples show that the LFF mechanism mainly reduces the reflection coefficients (amplitude and energy) at the gas-water contact and at a water-porous medium interface for frequencies less than 10 kHz, due to the fact that the velocity in the lower medium decreases. For the latter case, if the fluid is gas, the LFF effect becomes only important at frequencies between 0.0001 and 10 Hz for the open-pore case. This is due to the fact that the acoustic impedance contrast between water and gas is high. At frequencies less than 0.0001 Hz, the interface is equivalent to a water-elastic medium one, and hence the results are the same as those of the sealed-pore case. Moreover, the crack density and aspect ratio affect the mesoscopic attenuation and relaxation frequency, and therefore the reflection coefficients.