Abstract：
Mesoscopic fluid flow is the major cause of wave attenuation and velocity dispersion at seismic frequencies in porous rocks. The Johnson model provides solutions for the frequency-dependent quality factor and phase velocity in partially saturated porous media with pore patches of arbitrary shapes. We use the Johnson model to derive approximations for the quality factor Q at the high and low frequency limit, and obtain the approximate equation for Qmin based on geophysical and geometric parameters. A more accurate equation for Qmin is obtained after correcting for the linear errors between the exact and approximate Q values. The complexity of the pore patch shape affects the maximum attenuation of Qmin and the transition frequency ftr; furthermore, the effect on ftr is stronger than that on Qmin. Numerical solutions to Biot’s equation are computationally intensive; thus, we build an equivalent viscoelastic model on the basis of the Zener model, which well approximates the wave attenuation and dispersion in porous rocks in the seismic band.
LING Yun,HAN Li-Guo,ZHANG Yi-Ming. Viscoelastic characteristics of low-frequency seismic wave attenuation in porous media[J]. APPLIED GEOPHYSICS, 2014, 11(4): 355-363.
[1]
Batzle, M., Han, D., and Hofmann, R., 2006, Fluid mobility and frequency-dependent seismic velocity-Direct measurements: Geophysics, 71(1), N1-N9.
[2]
Biot, M. A., 1956, Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range The Journal of the Acoustical Society of America, 28(2), 168-178.
[3]
Biot, M. A., 1956, Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher-frequency range: Acoustical Society of America Journal, 28, 179-191.
[4]
Carcione, J. M., 2007, Wave fields in real media: theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media: Elsevier.
[5]
Carcione, J. M., and Picotti, S., 2006, P-wave seismic attenuation by slow-wave diffusion: Effects of inhomogeneous rock properties: Geophysics, 71(3), O1-O8.
[6]
Dutta, N. C., and Odé, H., 1979, Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model)-Part I: Biot theory: Geophysics, 44(11), 1777-1788.
[7]
Hill, R., 1964, Theory of mechanical properties of fibre-strengthened materials: I. Elastic behavior: Journal of the Mechanics and Physics of Solids, 12(4), 199-212.
[8]
Johnson, D. L., 2001, Theory of frequency dependent acoustics in patchy-saturated porous media: The Journal of the Acoustical Society of America, 110, 682-694.
[9]
Müller, T. M., Gurevich, B., and Lebedev, M., 2010, Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks-A review: Geophysics, 75(5), 75A147-175A164.
[10]
Picotti, S., Carcione, J. M., Germán R. J., and Santos, J. E., 2007, P-wave seismic attenuation by slow-wave diffusion: Numerical experiments in partially saturated rocks: Geophysics, 72(4), N11-N21.
[11]
Picotti, S., Carcione, J. M., Rubino, J. G., Santos, J. E., and Cavallini, F., 2010, A viscoelastic representation of wave attenuation in porous media: Computers and Geosciences, 36(1), 44-53.
[12]
Pride, S. R., and Berryman, J. G., 2003, Linear dynamics of double-porosity dual-permeability materials. I. Governing equations and acoustic attenuation: Physical Review E, 68(3), 036603.
[13]
Pride, S. R., Berryman, J. G., and Harris, J. M., 2004, Seismic attenuation due to wave-induced flow: Journal of Geophysical Research, 109(B1), B01201.
[14]
Quintal, B., Schmalholz, S. M., and Podladchikov, Y. Y., 2008, Low-frequency reflections from a thin layer with high attenuation caused by interlayer flow: Geophysics, 74(1), N15-N23.
[15]
Wang, S. X., Zhao, J. G., Li, Z. H., Harris, J. M., and Quan, Y. L., 2012, Differential Acoustic Resonance Spectroscopy for the acoustic measurement of small and irregular samples in the low frequency range: Journal of Geophysical Research: Solid Earth, 117(B6), B06203.
[16]
White, J. E., 1975, Computed seismic speeds and attenuation in rocks with partial gas saturation: Geophysics, 40(2), 224-232.
[17]
White, J. E., Mikhaylova, N. G., and Lyakhovitskiy, F. M., 1976, Low-frequency seismic waves in fluid saturated layered rocks: Physics of the Solid Earth, 11, 654-659.
[18]
Wood, A. B., 1955, A Textbook of sound: The physics of vibrations: G. Bell and Sons Ltd., London.
[19]
Zhao, J. G., Tang, G. Y., Deng, J. X., Tong, X. L., and Wang, S. X., 2013, Determination of rock acoustic properties at low frequency: A differential acoustical resonance spectroscopy device and its estimation technique: Geophysical Research Letters, 40(12), 2975-2982.
2014, Vol. 11 
|
