Porosity of fluid-saturated porous media from measured seismic wave velocities

Abstract

This paper presents a novel procedure for determining porosity in fluid-saturated porous media from measured shear and dilatational wave velocities. The method is developed using the theory of linear poroelasticity in the low-frequency limit, which is equivalent to considering the fluid-saturated porous medium as a closed (un-drained) system with the pore fluid moving in phase with the soil skeleton. The new procedure for the in-situ measurement of porosity has been applied at two sites in Italy using cross-hole seismic data. The results obtained are in excellent agreement with independent laboratory data gathered from undisturbed soil specimens.

Joint inversion of Rayleigh-wave dispersion and P-wave refraction data for laterally varying layered models

“…Also, the knowledge of physical links between model parameters to which the different data sets are sensitive can improve the reliability of final results. In the presented cases, we have introduced a link between P-and S-wave velocities based on Poisson's ratio assumptions, but in the future, other physical laws based, for instance, on the porosity (Foti et al, 2002), could be introduced and tested. The main drawbacks of the proposed method are the need of defining a reference model with the same parameterization for V P and V S and the computational cost related to the building of the sensitivity matrix for each perturbed model parameter.…”

Stable inversion of measured VP and VS to estimate porosity in fluid-saturated soils

“…Using the analytical expressions of V S and V P derived from Biot's theory in the low-frequency approximation, assuming that the (small-strain) shear modulus of the (evacuated) soil skeleton G SK is equal to the shear modulus G of the saturated, porous medium, Foti et al (2002) derived the following relation…”

“…A relatively recent, apparently promising approach for determining porosity is that proposed by Foti et al (2002), which is based on exploiting the results of linear poroelasticity in the low-frequency limit (Biot, 1956a(Biot, , 1956b. A specific aspect of the method proposed by Foti et al (2002) is that its application only requires measurement of the speeds of propagation of transversal and longitudinal waves V S and V P in the medium, which are quantities that can be easily measured using conventional seismic prospecting methods such as cross-hole and down-hole tests.…”

“…A specific aspect of the method proposed by Foti et al (2002) is that its application only requires measurement of the speeds of propagation of transversal and longitudinal waves V S and V P in the medium, which are quantities that can be easily measured using conventional seismic prospecting methods such as cross-hole and down-hole tests. The other required parameters are the Poisson ratio of the (evacuated) soil skeleton í SK and four physical constants which assume standard numerical values.…”

“…Usually the parameter í SK is unknown a priori; however, Foti et al (2002) and Foti & Lancellotta (2004) have shown through numerical examples and experimental data that the computed values of porosity are a little sensitive to this parameter. Although these studies confirm the validity of the method, this has not yet been applied to all categories of soils and thus there is a possibility that for certain combinations of V S and V P , porosity may exhibit a strong dependence on í SK :…”