In this article a new macroscopic theory for acoustic wave propagation through fluid-saturated porous media will be derived in which losses of the interface type are incorporated. It is argued that in order to explain the occurrence of a slow compressional wave (which is typical for fluid-saturated porous media), a discontinuity in the tangential components of traction and particle velocity at the microscopic fluid/solid interface is essential. The method of spatial volume-averaging will be applied in order to translate the microscopic field equations pertaining to the constituents of the porous medium to the macroscopic level (i.e., several times the wavelength). This method clearly demonstrates the interaction between the fluid and the solid phase at the microscopic fluid/solid interface by means of surface integrals which arise as a consequence of the averaging procedure. These surface integrals are assumed to be linearly related to the volume-averaged state quantities of the phases involved. In this way the interface-type losses are also incorporated. These losses are assumed to be of the inertial type and are triggered by the possible strong fluctuations in the spatial gradients of the microscopic fluid/solid interface (tortuosity). The resulting macroscopic theory, which is assumed to be valid at relatively high frequencies (the frequency range where we observe a slow P wave), mathematically has the same appearance as the most general Biot theory but with a different physical interpretation.
A new lossless poroelastic wave propagation theory is verified by means of ultrasonic transmission measurements on artificial rock samples in a water-filled tank. The experiments involved are similar to those performed by Plona ͓Appl. Phys. Lett. 36, 259-261 ͑1980͔͒. In this physically and mathematically mutual consistent new theory the coupling terms between the fluid and solid phase of the porous medium are completely determined by the measured wave speeds and the mass densities and constitutive parameters of both constituting phases. Verification of the amplitudes of the received bulk waves in both the time domain and frequency domain provide information on the validity of the combined effect of propagation characteristics and new macroscopic fluid/ fluid-saturated-rock boundary conditions resulting from this theory. The comparison technique between theory and experiments is based on the Fraunhofer diffraction theory, and is first tested in a perfectly elastic medium transmission configuration. Subsequently, this comparison technique is used for the poroelastic medium. It is shown that this technique is very accurate and reliable. The experimental results for the compressional wave and the shear wave in the perfectly elastic medium are in excellent agreement with the theoretical predictions. For the fluid-saturated porous samples, good agreement is found only for the fast compressional wave. For both the shear wave and the slow compressional, it is obvious that there is some kind of loss mechanism involved, which cannot be explained by the current theory. Despite the fact that the bulk losses in the porous medium can be explained qualitatively by the full frequency range Biot theory, it is conjectured that even a quantitative fit is feasible if Johnson's loss model ͓D. L. Johnson et al., J. Fluid Mech. 176, 379-402 ͑1987͔͒ is applied in the lossy counterpart of the current theory
We develop a simple and efficient method for correcting the borehole flexural‐wave slowness dispersion effects. We demonstrate its validity on synthetic and field data. The theory underlying the method is derived from first principles and shows the general result that semblance‐derived wave slowness is a spectral‐amplitude weighted average of the wave‐slowness dispersion curve. The theory also explains that a dispersion correction on the borehole flexural wave slowness is not necessary if the source frequency content is sufficiently low.
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