Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

Abstract

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.

Seismic reflection and transmission coefficients of a single layer sandwiched between two dissimilar poroelastic solids

“…K c ¼ rK cap ; where K cap is the equivalent bulk modulus (Garg and Nayfeh 1986) for macroscopic capillary pressure between wetting and non-wetting fluids. Following Kumar and Saini (2012), the displacement potentials u i ; ði ¼ 1; 2; 3; 4Þ; represent the propagation of P 1 ; P 2 ; P 3 ; SV waves with velocities V 1 ; V 2 ; V 3 ; V 4 ; respectively. The velocities ðV 1 ; V 2 ; V 3 Þ of longitudinal waves are derived from the three roots of a cubic equation in V 2 ; given by…”

Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores

“…The Biot (1956) model illustrated the rock consolidation under elastic wave and was one of the representative models. Since then, substantial efforts have been exerted (e.g., Dvorkin and Nur 1993;Grant 1994;Cai et al 2006;Gan et al 2007;Kumar and Saini 2012;Reine et al 2012;Wang et al 2012) to develop a detailed theoretical model or correlation expression around wave velocity, attenuation, rock type, fluid content, and anisotropy. Although the general Darcy law is shown in the motion equation, the way which Darcy equation is incorporated in the models above is substantially different from that in seismic production technology.…”

Reflection and Refraction of Waves at the Boundary of a Non-Viscous Porous Solid Saturated with Single Fluid and a Porous Solid Saturated with Two Immiscible Fluids

“…Phenomenon of reflection and refraction of waves from the boundaries of poroelastic materials has been discussed by many researchers, for example, Deresiewicz (1960Deresiewicz ( , 1964a, Deresiewicz and Rice (1962), Dutta and Ode (1983), Sharma and Gogna (1991), Sharma and Saini (1992), Sharma (2008), Lin et al (2005), Tomar and Arora (2006), Arora and Tomar (2007), Yeh et al (2010), Markov (2009), Sharma andKumar (2011), Kumar and Saini (2012), Sharma and Saini (2012), Kumar and Sharma (2013), Kumar and Kumari (2014). Present problem considers to study the reflection and refraction phenomenon at a plane interface between a non-viscous porous solid saturated with single fluid and a porous solid saturated by two immiscible fluids.…”