Abstract
The influence of the elastic and hydrodynamic properties of a rock on the time attenuation coefficient of an acoustic wave, which is reflected from the borehole wall, is considered using the methods of the mechanics of saturated porous media. The calculations were performed for a system consisting of an acoustic logging tool of a finite with a finite diameter, a fluid-filled borehole, and a porous permeable rock. The performed simulation showed that in rocks with a low hydrodynamic permeability, the acoustic-reverberation time is determined by the acoustic impedance of the borehole wall (product of the rock density and the longitudinal-wave velocity in it). In the case of rocks with a permeability of about several hundred millidarcy, the time signal’s attenuation coefficient substantially depends on the rock’s permeability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Berryman, J.G., Long wavelength propagation in composite elastic media, J. of the Acoust. Soc. Am., 1980, vol. 68, pp. 1809–1831.
Biot, M.A., Theory of propagation of elastic waves in a fluid-saturated porous solid, J. Acoust. Soc. Am., 1956, vol. 28, no. 2, pp. 168–191.
Biot, M.A. and Willis, D.G., The elastic coefficient of the theory of consolidation, J. Appl. Mech., 1957, vol. 24, pp. 594–601.
Bourbie, T., Coussy, O., and Zinzner, B., Acoustics of Porous Media, Houston: Gulf Publishing Co., 1987.
Deresiewicz, H. and Scalak, R., On uniqueness in dynamic poroelasticity, Bull. Seism. Soc. Amer., 1963, vol. 53, no. 4, pp. 783–788.
Frenkel’, Ya.I., To the theory of seismic and seismoelectric phenomena in a wet soil, Izv. Akad. Nauk SSSR, Ser. Geogr. Geophys., 1944, vol. 8, no. 4, pp. 133–149.
Gurevich, B. and Schoenberg, M., Interface conditions for Biot’s equations of poroelasticity, J. Acoust. Soc. Amer., 1999, vol. 105, no. 5, pp. 2585–2589.
Ivakin, B.N., Karus, E.V., and Kuznetsov, O.L., Akusticheskii metod issledovaniya skvazhin (Acoustic Method for Studying Boreholes), Moscow: Nedra, 1978.
Kanasevich, E.R., Analiz vremennykh ryadov v geofizike (Analysis of Time Series in Geophysics), Nedra, 1988, vol. 450.
Kazatchenko, E., Markov, M., and Mousatov, A., Joint modeling of acoustic velocities and electrical conductivity from unified microstructure of rocks, J. Geophys. Res., 2004, vol. 109, B01202, doi: 10.1029/2003JB002443
Kosachevskii, L.Ya., On reflection of acoustic waves from layered two-component media, Prikl. Mat. Mekh., 1961, vol. 25, no. 6, pp. 1076–1082.
Krutin, V.N., Kuznetsov, O.L., and Strekozin, V.V., Evaluation of the acoustic reverberation time for a borehole, in Izuchenie gornykh porod akusticheskim metodom (Investigation of Rocks Using an Acoustic Method), Moscow: VNI-IYaGG, 1978, pp. 33–43.
Krutin, V.N., Markov, M.G., and Yumatov, A.Yu., Evaluation of the acoustic reverberation time for a borehole in a saturated porous medium, Izv. Akad. Nauk SSSR, Ser. Fizika Zemli, 1986, no. 2, pp. 85–89.
Krutin, V.N., Markov, M.G., and Yumatov, A.Yu., Velocity and attenuation of a Lamb-Stoneley wave in a borehole located in a saturated porous medium, Izv. Akad. Nauk SSSR, Ser. Fizika Zemli, 1987, no. 9, pp.33–38.
Markov, M.G., Propagation of longitudinal elastic waves in a fluid-saturated porous medium with spherical inclusions, Acoust. Phys., 2005, vol. 51,Suppl. Geoacoustics, pp. 132–139.
Markova, I.A. and Sadovnychiy, S.N., Geometrical spreading factor of head waves in cased and open boreholes, Izv., Phys. Solid Earth, 2011, vol. 47, no. 9, pp. 827–834.
Nikolaevskii, V.N., Basniev, K.S., Gorbunov, A.T., and Zotov, G.F., Mekhanika nasyshchennykh poristykh sred (Mechanics of Saturated Porous Media), Moscow: Nedra, 1970.
Oppenheim, A.V., Schafer, R.W., and Buck, J.R., Discrete-Time Signal Processing, 2nd ed., Upper Saddle River, NJ: Prentice-Hall, 1999.
Plona, T., Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies, Appl. Phys. Lett., 1980, vol. 36, pp. 251–259.
Tang, X. and Cheng, C.H., Quantitative Borehole Acoustic Methods, Amsterdam: Elsevier, 2004.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.M. Markov, M.G. Markov, G. Ronquillo Jarillo, S.N. Sadovnychiy, 2014, published in Fizika Zemli, 2014, No. 2, pp. 299–305.
Rights and permissions
About this article
Cite this article
Markov, A.M., Markov, M.G., Ronquillo Jarillo, G. et al. Acoustic reverberation in a logging tool-borehole-saturated porous medium system. Izv., Phys. Solid Earth 50, 289–295 (2014). https://doi.org/10.1134/S1069351314020050
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1069351314020050