Seismic attenuation due to patchy saturation

In porous rocks saturated in patches by two immiscible fluids, seismic compression causes the fluid with the larger bulk modulus to respond with a larger change in fluid pressure than the fluid with the smaller bulk modulus which results in fluid movement and seismic attenuation. For virtual rock samples having fluid distributions obtained using the invasion percolation model, attenuation is determined using finite difference numerical experiments based on the laws of poroelasticity. Analytical models are also proposed to explain the numerical results. When oil invades water, the equilibration is controlled by the geometry of the invading oil which has a narrow range of small diffusion lengths resulting in a single relaxation frequency at high frequencies and not much seismic band attenuation. When water invades oil, the defending oil controls the equilibration, and a power law emerges for how attenuation varies with frequency due to the fractal nature of how saturation is varying with scale in the defending oil. For air invading water, the geometry of the defending water controls the equilibration, and a large amount of attenuation is observed over a wide range of frequencies including the seismic band due to the wide range in water patch sizes. However, when water invades air, the narrow fingers of invading water control the equilibration, and there is a single relaxation frequency at high frequencies that does not result in much seismic band attenuation.