Bulk elastic wave propagation in partially saturated porous solids

Abstract

The linear equations of motion that describe the behavior of small disturbances in a porous solid containing both liquid and gas are solved for bulk wave propagation. The equations have been simplified by neglecting effects due to changes in capillary pressure. With this simplifying assumption, the equations reduce to two coupled (vector) equations of the form found in Biot’s equations (for full saturation) but with more complicated coefficients. As in fully saturated solids, two shear waves with the same speed but different polarizations exist as do two compressional waves with distinct speeds. Attenuation effects can be enhanced in the partially saturated solid, depending on the distribution of gas in the pore space. Two models of the liquid/gas spatial distribution are considered: a segregated-fluids model and a mixed-fluids model. The two models predict comparable attentuation when the gas saturation is low, but the segregated-fluids model predicts a more rapid roll-off of attenuation as the gas saturation increases.

Final Report U.S. Department of Energy Joint Inversion of Geophysical Data for Site Characterization and Restoration Monitoring

“…Although these relations provide the correct expressions for velocities in terms of the mechanical properties (bulk modulus, shear modulus), densities, and relative amounts of component minerals and fluids in a rock or soil, it has not been possible to invert these relations easily to determine porosity and saturation when the velocities are known. Also, the distribution of saturation, whether it is homogeneous or patchy (e.g., Berryman et al, 1988;Endres and Knight, 1989), is another important parameter that we would like to know. We determined that by expressing velocities in terms of ratios of densities and the LamŽ elastic parameters (see Sheriff, 1994 for definition), the part of the elastic behavior that is influenced by the presence of fluid can be separated from the part that theoretically should be independent of fluid effects.…”

Elastic wave theory for propagation of Rayleigh waves at surface of unsaturated semi-infinite media

“…44 the Rayleigh phase velocity and attenuation are calculated for Massillon sandstone, which the P-waves and S-wave were investigated in literature (Berryman et al 1988 Similarly, Figs. 5 to 7 present the attenuation of the three Rayleigh waves R1, R2, and R3, respectively.…”

Asymptotic and exact fundamental solutions in hereditary media with singular memory kernels

“…In Biot's poroelasticity [5], G0o(t, x) = pi pfI pfl N(r, x) (2.8) where I denotes the 3x3 unit matrix and the viscodynamic operator N(r, x), explicitly known for some idealized pore geometries, has a singularity ~ r-1'2 [5,36,4,53,7,2,56]. The singularity of the viscodynamic operator is important for frequencies w > wb 1 0r,Hz, where wb denotes Biot's frequency.…”

“…The following recurrence relations can be used to calculate the basis functions: §£ -<3 is> and N A') = a/Q+i(t, A') 4-^2 X)- (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) l/=l Equation (3.14) is a generalization of a recurrence relation from [6]. It can be proved by applying integration by parts to Eq.…”