Seismic wave properties in time-dependent porosity homogeneous media

Abstract

S U M M A R YIt is quantified the properties of seismic waves in fully saturated homogeneous porous media within the framework of Sahay's modified and reformulated poroelastic theory. The computational results comprise amplitude attenuation, velocity dispersion and seismic waveforms. They show that the behaviour of all four waves modelled as a function of offset, frequency, porosity, fluid viscosity and source bandwidth depicts realistic dissipation within the sonicultrasonic band. Therefore, it appears that there is no need to include material heterogeneity to model attenuation. By inference it is concluded that the fluid viscosity effects may be enhanced by dynamic porosity.

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

“…The band‐limited time domain synthetics are produced by the application of a vertical force in the plane ( x 1 , x 2 , 0). Considering water as saturate, the corresponding quality factors of the fast P and SV wave are Q p = 24 and Q s = 15, respectively [ Quiroga‐Goode et al , 2007]. The source temporal function corresponds to a 7 kHz dominant frequency Ricker wavelet.…”

“…The recording geometry was chosen slightly different to emphasize the wavefront geometrical divergence. It can be noticed that ellipticities of the wave polarization are much more pronounced in this case since attenuation has increased significantly due to the larger porosity/permeability [ Quiroga‐Goode et al , 2007]. The sense of particle motion is indicated schematically with arrows in the hodograms of receiver number four.…”

“…While being in general similar to the theory of Biot [1962] in that both predict wave‐induced fluid flow, dynamic porosity is missing in Biot's derivation of elastic energy potential; loss of momentum within the fluid is also obviated; the ultimate result is that dispersion and attenuation are underestimated. Based on developments of Sahay [1996, 2001] and the theory of de la Cruz and Spanos [1985], it has been demonstrated that the waveforms display realistic levels of dissipation [ Quiroga‐Goode et al , 2007].…”

A FEM for three‐field u–p–η poroelasticity with nonreciprocal interactions

“…in terms of macroscopic compressibilities of the medium, which can be obtained through laboratory experiments. These are valid, however, only for low‐frequency wave propagation, and need to be experimentally determined for different problem configurations and materials 6 . For certain compliance parameters, the porosity equation can be substituted into the previous momentum and continuity equations so that one can return to the Biot format of governing equations.…”

“…Following that, the Biot theory (BT) of consolidation 3,4 provided stress–strain relationships for the solid matrix and an expression for the variation in water pressure content while using known material constants and proposing new ones to account for the solid–fluid coupling mechanisms. Although BT has a wide range of applications, it still contains an unrealistic representation of the velocity dispersion and wave attenuation 5,6 . Furthermore, its restriction to low‐frequency regimes lead to the necessity of developing more complex theories, for example, to describe squirt flow 7,8 …”