Numerical evidence of elliptical polarization in homogeneous fluid-saturated porous sandstone and the nexus to inhomogeneous plane waves

摘要

The polarization of body waves in a fluid-saturated homogeneous porous sandstone is quantified by computing the Green's function; the findings are confirmed with grid modeling. Both results agree that forces in an unbounded homogeneous isotropic porous medium generate harmonic perturbations whose particle motion varies along the wavefront from linear to elliptical; such behavior typically associated to homogeneous and inhomogeneous viscoelastic plane waves in layered media. Following this analogy, it is concluded that the attenuation angle y is the function of the direction of wave propagation, wave type, and direction of the applied force. With this information, the attenuation angle yl of the initial ray segment can be estimated, resolving in a different manner the issue of indeterminacy in the asymptotic ray solution. It is also concluded that the assumption of -yi = 0 for normally incident viscoelastic plane waves in layered media may be correct, but only for P waves generated by vertical forces; as propagation direction increases, so does the error, the rate depending on Q. The results also show that (1) a P wave resembles a S wave and vice versa for preferred directions and (2) the sense of particle motion is opposite for both waves, prograde and retrograde, respectively, and vice versa, depending on the direction of the applied force.