Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range
1956/03/01 by M. A. Biot · 8,090 citations
Earth and Planetary Sciences · Engineering · #Attenuation #Classical mechanics #Composite material #Compressibility #Dispersion (optics) #Drilling and Well Engineering #Flow (mathematics) #Fluid Dynamics and Vibration Analysis #Hagen–Poiseuille equation #Materials science #Mechanics #Optics #Phase (matter) #Phase velocity #Physics #Porosity #Porous medium #Range (aeronautics) #Seismic Imaging and Inversion Techniques #Viscous liquid #Wave propagation
paper · open access · doi:10.1121/1.1908239
published in The Journal of the Acoustical Society of America 28(2), 168-178 (Acoustical Society of America)
openalex publication_date 1956/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
A theory is developed for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid. The emphasis of the present treatment is on materials where fluid and solid are of comparable densities as for instance in the case of water-saturated rock. The paper denoted here as Part I is restricted to the lower frequency range where the assumption of Poiseuille flow is valid. The extension to the higher frequencies will be treated in Part II. It is found that the material may be described by four nondimensional parameters and a characteristic frequency. There are two dilatational waves and one rotational wave. The physical interpretation of the result is clarified by treating first the case where the fluid is frictionless. The case of a material containing viscous fluid is then developed and discussed numerically. Phase velocity dispersion curves and attenuation coefficients for the three types of waves are plotted as a function of the frequency for various combinations of the characteristic parameters.
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