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2009, 9

S. Muraviev

On application of Biot theory to spectral analysis of borehole sonic logging signals

language: Russian

received 07.07.2009, published 10.09.2009

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The paper describes some aspects of the application of Biot theory to sonic signals spectrum analysis. It contains some theoretical remarks about behavior of real rocks and fluids. There are also formulas for estimation rock physical properties by sonic signal spectrum characteristics. To find out these estimates, numerical methods are suggested. The approach can also be useful for a wide range of sonic measurements in the field of porous media acoustics.

Key words: Biot theory, porous media, sonic measurements, spectrum, sonic logging

15 pages, 6 figures

Сitation: S. Muraviev. On application of Biot theory to spectral analysis of borehole sonic logging signals. Electronic Journal “Technical Acoustics”,, 2009, 9.


1. Френкель Я. И. К теории сейсмических и сейсмоэлектрических явлений во влажной почве. Изв. АН СССР. Сер. геогр. и геофиз., т. VIII, №4, 133-149, 1944.
2. Цвиккер К., Костен К. Звукопоглощающие материалы. М., изд-во иностр. лит., 1952.
3. Gassman F. Elastic waves through a packing of spheres. Geophysics, 16 and 18, 1951.
4. Biot M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid. Low-frequency range. Journal of the Acoustical Society of America, 28(2), 168-178, 1956.
5. Biot M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid. Higher-frequency range. Journal of the Acoustical Society of America, 28(2), 179-191, 1956.
6. Biot M. A. Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 33, 1482-1498, 1962.
7. Plona T. Observation of a Second Bulk Compressional Wave in a Porous Medium at Ultrasonic Frequencies. Applied Physics Letters, 36, 259-251.
8. Косачевский Л. Я. О распространении звуковых волн в двухкомпонентных средах. ПММ, т. XXIII, № 6, 1115-1123, 1959.
9. Иванов В. Н., Карус Е. В., Кузнецов О. Л. Акустический метод исследования скважин. М., «Недра», 1978.
10. Mavko G., Mukerji T., Dvorkin J. The rock physics handbook. Cambridge Univ. Press, 1998.
11. Hashin Z., Shreikman S. Note on a variational approach to the theory of composite elastic materials. J. Franklin Inst., 271, 336-341, 1961.
12. J. G. Berryman. Confirmation of Biot's theory, Appl. Phys. Lett., 37, 382-384, 1980.
13. K. L. Williams, D. R. Jackson, E. I Thorsos. Comparision of sound speed and attenuation measured in a sandy sediment to predictions based on the Biot theory of porous media. IEEE J. Oceanic Eng., vol. 27, 413-428, July 2002.
14. R. Stoll. Acoustic waves in ocean sediments. Geophysics, vol. 42, no 4, 715-725, 1977.
15. Tsiklauri D. Phenomenological model of propagation of the elastic waves in a fluid-saturated porous solid with non-zero boundary slip velocity. J. Acoust. Soc. Am., 112, 843-849, 2002
16. Tsiklauri D., Beresnev I. Properties of Elastic Waves in a Non-Newtonian Fluid Saturated Porous Medium. Transport in Porous Media, 53, 39-50, 2003.
17. del Rio J. A., de Haro M. L. and Whitaker S. Enhancement in the dynamic response of a viscoelastic fluid flowing in a tube. Phys. Rev., E58, 6323-6327.
18. Boyle F. A., Chotiros N. P. Experimental detection of a slow acoustic wave in sediment at shallow grazing angels. J. Acoust. Soc. Am., v. 91, 2615-2619, 1992.
19. Nagy P. B., Adler L., Bonner P. B. Slow wave propagation in air-filled porous materials and natural rocks. Appl. Phys. Lett., v. 56, №25, 2504-2506, 1990.
20. Johnson D. L., Hemmic D. L., Kojima H. Probing porous media with first and second sound. J. Appl. Phys., v. 76, 104-125, 1994.
21. Уайт Дж. Э. Возбуждение и распространение сейсмических волн. М., «Недра», 1986.
22. Николаевский В. Н. Механика пористых и трещиноватых сред, М.,1984.
23. Булатова Ж. М., Волкова Е. А., Дубров Е. Ф. Акустический каротаж. Л. «Недра», 1970.
24. Detournay E., Cheng A. Fundamentals of Poroelasticity, Comprehensive Rock Engineering. Pergamon Press, 113-171, 1993.
25. Химмельблау Д. Прикладное нелинейное программирование. М., «Мир», 1975.
26. Chabot L. Single-Well Imaging Using Full-Waveform Sonic Data. PhD Thesis. University of Calgary, 75-80, 2003.


Sergey A. Muraviev - post graduate student at information and measurements department in the Russian Gubkin State University. The main scientific interests are borehole acoustic logging and software development.

e-mail: muraviev.sergey(at)