Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid

1992 ◽  
Vol 138 (2) ◽  
pp. 249-266 ◽  
Author(s):  
M. D. Sharma ◽  
M. L. Gogna
Keyword(s):  
Viscous Liquid ◽  
Elastic Solid ◽  
Porous Solid ◽  
Harmonic Waves ◽  
Reflection And Refraction ◽  
Plane Harmonic Waves

Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid-saturated porous solid

1982 ◽  
Vol 72 (5) ◽  
pp. 1509-1533
Author(s):  
Sushama Hajra ◽  
Arabinda Mukhopadhyay
Keyword(s):  
Seismic Waves ◽  
Elastic Solid ◽  
Porous Solid ◽  
P Wave ◽  
Porous Solids ◽  
Reflection And Refraction ◽  
Theoretical Investigations ◽  
Energy Ratios ◽  
P And Sv Waves ◽  
Refracted Waves

abstract A systematic theory of the propagation of seismic waves in liquid-saturated porous solids was first developed by Biot in 1956. Since then, some theoretical investigations have been carried out on the propagation of body and surface waves in such media. Further studies in this area may be useful in giving greater insight into the propagation of seismic waves in underground layers of porous solids saturated with oil or groundwater. In this connection, the transmission of normally incident seismic waves across the boundary of a liquid-saturated porous solid has been considered earlier. Keeping in view the fact that oblique incidence is more likely than normal incidence for such seismic waves, the authors have investigated the reflection and refraction of P and SV waves, which become obliquely incident at the boundary of a liquid-saturated porous solid, after propagating through an elastic solid. It is found that, corresponding to both P and SV waves obliquely incident at the boundary, there will be two refracted dilatational waves traveling with different velocities, which may be called the Pf and Ps waves, and one refracted SV wave, in the liquid-saturated porous solid, together with reflected P and SV waves in the elastic solid. The amplitude and energy ratios for the different reflected and refracted waves have been calculated theoretically. Numerical values of the amplitude and energy ratios have been computed for different angles of incidence for P and SV waves which propagate through granite, and then become incident at the boundary between the granite and oil-saturated sandstone, using results of laboratory experiments on the elastic behavior of oil-saturated sandstone. It is found that the amplitudes of the reflected and refracted waves depend significantly on the angle of incidence. It is also found that the amplitude of the second refracted P wave is usually much smaller than that of the other reflected and refracted P and SV waves, so that this slower refracted P wave will be difficult to detect. Similar amplitudes and energy ratios are also calculated for P and SV waves incident at the boundary between granite and dry sandstone. Comparison between the cases of dry sandstone and oil-saturated sandstone shows that the presence of oil usually has a significant effect on the amplitudes of the reflected and refracted P and SV waves. It is noted that such theoretical investigations may be useful in utilizing the amplitudes and other characteristics of reflected and refracted seismic waves in the detection and study of underground layers of porous solids saturated with oil or groundwater.

The scattering cross-section of an obstacle in an elastic solid for plane harmonic waves

1965 ◽  
Vol 61 (4) ◽  
pp. 969-981 ◽  
Author(s):  
P. J. Barratt ◽  
W. D. Collins
Keyword(s):  
Cross Section ◽  
Scattering Amplitude ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Scattering Cross Section ◽  
Harmonic Waves ◽  
Far Field ◽  
Scattering Cross ◽  
Plane Harmonic Waves

AbstractIt is shown that, when a plane harmonic P or S wave is incident upon a two-or three-dimensional obstacle in an infinite elastic solid, the scattering cross-section of the obstacle can be calculated from an appropriate far-field scattering amplitude.

Comments on “Lamb's problem for fluid-saturated porous media”

1992 ◽  
Vol 82 (5) ◽  
pp. 2263-2273
Author(s):  
M. D. Sharma
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Elastic Solid ◽  
Porous Solid ◽  
Surface Boundary ◽  
Vertical Force ◽  
Saturated Porous Media ◽  
Concentrated Load ◽  
Lamb’S Problem

Abstract Philippacopoulos (1988) discusses axisymmetric wave propagation in a fluid-saturated porous solid half-space. The disturbance is considered to be produced by the concentrated load P0exp(iωt) acting vertically at the surface. Boundary conditions chosen imply that a vertical force acting on the surface of fluid-saturated porous solid exerts no pressure on the interstitial liquid. These boundary conditions do not seem appropriate. In the present study, the boundary conditions have been changed in order to satisfy the concept of porosity. These are also in accordance with those discussed by Deresiewicz and Skalak (1963) for the special case of interface between liquid and liquid-saturated porous media. Analytic expressions have been derived for the displacements at the surface. The limiting case of a dry elastic solid is also deduced. Effects of intergranular energy losses due to solid phase and of dissipation due to flow of pore fluid are exhibited on the displacements at the surface. Contrary to Philippacopoulos (1988), the displacements in saturated poroelastic solids are found to be larger than those in a dry elastic solid with same Lamb's moduli.

On uniqueness in dynamic poroelasticity

1963 ◽  
Vol 53 (4) ◽  
pp. 783-788 ◽  
Author(s):  
H. Deresiewicz ◽  
R. Skalak
Keyword(s):  
Porous Media ◽  
Liquid Medium ◽  
Uniqueness Theorem ◽  
Dissimilar Materials ◽  
Elastic Solid ◽  
Porous Solid ◽  
Uniqueness Of Solution ◽  
Biot’S Theory ◽  
Field Equations ◽  
Special Cases

Abstract Conditions are derived sufficient for uniqueness of solution of the field equations of Biot's theory of liquid-filled porous media, particular attention being paid to continuity requirements at an interface between two such dissimilar materials. It is found that at an interface two distinct sets of conditions will satisfy the demands of the mathematical uniqueness theorem, one of them being discarded on physical grounds. The permissible set is then discussed in relation to a number of possible models of the structure of a pair of elements in contact. The special cases of an impermeable elastic solid or a liquid medium in contact with a saturated porous solid are also examined.

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