Low‐frequency incoherent scattering from Biot’s theory

1994 ◽  
Vol 95 (5) ◽  
pp. 2334-2339
Author(s):  
Anthony Purcell
Keyword(s):  
Low Frequency ◽  
Incoherent Scattering ◽  
Biot’S Theory ◽  
Biot's Theory

ADDENDUM TO “STUDIES OF ELASTIC WAVE ATTENUATION IN POROUS MEDIA” BY M. R. J. WYLLIE, G. H. F. GARDNER, AND A. R. GREGORY (GEOPHYSICS, OCTOBER, 1962, PP. 569–589)

Geophysics ◽  
1963 ◽  
Vol 28 (6) ◽  
pp. 1074-1074 ◽  
Author(s):  
M. R. J. Wyllie ◽  
G. H. F. Gardner ◽  
A. R. Gregory
Keyword(s):  
High Frequency ◽  
Critical Angle ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Shear Velocity ◽  
Confining Pressure ◽  
Biot’S Theory ◽  
Biot's Theory ◽  
Angle Method ◽  
Frequency Pulse

In the paper published last year we noted that the shear velocity through liquid‐saturated rocks often appeared to exceed the shear velocity through the same rocks when dry. Our results were based on measurements made by the critical‐angle method on rocks subjected to heavy confining pressure. We felt constrained to observe that, if shear velocities through liquid‐saturated rocks were higher than through their dry counterparts, the applicability of Biot’s theory to any but low‐frequency resonating systems was open to question. Because Biot’s theory will be of maximum use only if it can be applied to systems in which velocities are measured by high‐frequency pulse techniques, our warning diminished the practical value of our other results.

Biot’s theory and granular media

Poromechanics ◽  
2020 ◽  
pp. 191-196
Author(s):  
Nicholas P. Chotiros
Keyword(s):  
Granular Media ◽  
Biot’S Theory ◽  
Biot's Theory

scholarly journals Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Spherical Shell ◽  
Wave Number ◽  
Biot’S Theory ◽  
Impervious Surfaces ◽  
Axially Symmetric ◽  
Spherical Shells ◽  
Biot's Theory

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.

Wave propagation in cancellous bone in terms of Biot's theory

2008 ◽  
Vol 123 (5) ◽  
pp. 3513-3513
Author(s):  
Michal Pakula ◽  
Frederic Padilla ◽  
Mariusz Kaczmarek ◽  
Pascal Laugier
Keyword(s):  
Wave Propagation ◽  
Cancellous Bone ◽  
Biot’S Theory ◽  
Biot's Theory

Modification of Biot’s theory of porous materials

1997 ◽  
Vol 101 (5) ◽  
pp. 3145-3145
Author(s):  
H. Tavossi ◽  
B. R. Tittmann
Keyword(s):  
Porous Materials ◽  
Biot’S Theory ◽  
Biot's Theory

A theory of compressional wave attenuation in noncohesive sediments

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1311-1317 ◽  
Author(s):  
C. McCann ◽  
D. M. McCann
Keyword(s):  
Wave Attenuation ◽  
Compressional Wave ◽  
Solid Particles ◽  
Biot’S Theory ◽  
Attenuation Coefficients ◽  
Low Frequencies ◽  
Biot's Theory ◽  
Compressional Waves ◽  
High Frequencies ◽  
Water Saturated

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.

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