Mechanism of Elastic Waves Reflection in Geological Media

Affiliation(s)

Organization of Russian Academy of Sciences, Mining Institute Ural Branch RAS, Perm, Russia.

Organization of Russian Academy of Sciences, Mining Institute Ural Branch RAS, Perm, Russia.

ABSTRACT

Reflecting properties of layered geological media are substantiated in the framework of phonon-phonon mechanism of elastic wave propagation in porous media. In this scope the reflection coefficient is calculated using not impedances but impulses of phonons in adjoining porous media. Assuming for the first approximation that rocks do fulfill an average time equation we got an expression for the reflection coefficient via porosity factors of that geological medium. For calculation of reflection coefficient the wavelength is chosen as averaging line scale. These coefficients are calculated at every depth point for a set of frequencies in seismic range. Resulting curves have special depth points. Being cross-plotted in time-frequency space such points do form coherent units. These units we call effective boundaries, because they cause all reflections for the given media in the framework of considered model. Effective boundaries are not wide-band as for two half spaces but have a cutoff at some low frequency. Geological medium at a whole is characterized by the system of such effective boundaries that are capable to form a reflection waves field. To construct this field an algorithm is developed that solves the direct problem of seismic in the framework of effective boundaries theory. This algorithm is illustrated with vibroseis survey modeling for a specific geological section.

Reflecting properties of layered geological media are substantiated in the framework of phonon-phonon mechanism of elastic wave propagation in porous media. In this scope the reflection coefficient is calculated using not impedances but impulses of phonons in adjoining porous media. Assuming for the first approximation that rocks do fulfill an average time equation we got an expression for the reflection coefficient via porosity factors of that geological medium. For calculation of reflection coefficient the wavelength is chosen as averaging line scale. These coefficients are calculated at every depth point for a set of frequencies in seismic range. Resulting curves have special depth points. Being cross-plotted in time-frequency space such points do form coherent units. These units we call effective boundaries, because they cause all reflections for the given media in the framework of considered model. Effective boundaries are not wide-band as for two half spaces but have a cutoff at some low frequency. Geological medium at a whole is characterized by the system of such effective boundaries that are capable to form a reflection waves field. To construct this field an algorithm is developed that solves the direct problem of seismic in the framework of effective boundaries theory. This algorithm is illustrated with vibroseis survey modeling for a specific geological section.

Cite this paper

V. Sidorov and M. Tarantin, "Mechanism of Elastic Waves Reflection in Geological Media,"*International Journal of Geosciences*, Vol. 3 No. 1, 2012, pp. 175-178. doi: 10.4236/ijg.2012.31019.

V. Sidorov and M. Tarantin, "Mechanism of Elastic Waves Reflection in Geological Media,"

References

[1] V. K. Sidorov and M. V. Tarantin, “A Possible Mechanism for Elastic Wave Propagation in Porous Rocks,” Doklady Earth Sciences, Vol. 434, No. 1, 2010, pp. 1253- 1256. doi:10.1134/S1028334X10090242

[2] L. Knopoff, “Attenua-tion of Elastic Waves in the Earth,” In: W. P. Mason, Ed., Physical Acoustics: Principles and Methods, Academic Press, New York, 1965, pp. 287-324.

[3] M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid Saturated Porous Solid, 1. Lower Frequency Range,” Journal of the Acoustical Society of America, Vol. 28, No. 2, 1956, pp. 168-178. doi:10.1121/1.1908239

[4] M. A. Biot, “Theory of Propaga-tion of Elastic Waves in a Fluid Saturated Porous Solid, 2. Higher Frequency Range,” Journal of the Acoustical Society of America, Vol. 28, 1956, pp. 178-191.

[5] J. R. Dvorkin, R. Nolen-Hoeksema and A. Nur, “The Squirt-Flow Mechanism: Macroscopic Description,” Geophysics, Vol. 59, No. 3, 1994, pp. 428-438. doi:10.1190/1.1443605

[6] G. A. Gist, “Fluid Effects on Ve-locity and Attenuation in Sandstones,” Journal of the Acousti-cal Society of America, Vol. 96, No. 2, 1994, pp. 1158-1173. doi:10.1121/1.410389

[7] J. M. Carcione, C. Morency and J. E. Santos, “Computational Poroelasticity—A Review,” Geo-physics, Vol. 75, No. 5, 2010, pp. 75A229-75A243.

[8] V. K. Sidorov and M. V. Tarantin, “A Method for Estimation of a Dynamic Properties of Elastic Waves in Acoustic Logs,” Geo-physica, Vol. 3, 2011, pp. 7-12.

[9] L. M. Brekhovskih, “Waves in Layered Media,” 2nd Edition, Academic Press, New York, 1980.

[10] L. M. Brekhovskih and O. A. Godin, “Acoustics of Layered Media,” Nauka, Moscow, 1989 (in Rus-sian).

[11] G. N. Gogonenkov, “Synthetic Seismograms Cal-culation and Application,” Nedra, Moscow, 1972 (in Rus-sian).

[1] V. K. Sidorov and M. V. Tarantin, “A Possible Mechanism for Elastic Wave Propagation in Porous Rocks,” Doklady Earth Sciences, Vol. 434, No. 1, 2010, pp. 1253- 1256. doi:10.1134/S1028334X10090242

[2] L. Knopoff, “Attenua-tion of Elastic Waves in the Earth,” In: W. P. Mason, Ed., Physical Acoustics: Principles and Methods, Academic Press, New York, 1965, pp. 287-324.

[3] M. A. Biot, “Theory of Propagation of Elastic Waves in a Fluid Saturated Porous Solid, 1. Lower Frequency Range,” Journal of the Acoustical Society of America, Vol. 28, No. 2, 1956, pp. 168-178. doi:10.1121/1.1908239

[4] M. A. Biot, “Theory of Propaga-tion of Elastic Waves in a Fluid Saturated Porous Solid, 2. Higher Frequency Range,” Journal of the Acoustical Society of America, Vol. 28, 1956, pp. 178-191.

[5] J. R. Dvorkin, R. Nolen-Hoeksema and A. Nur, “The Squirt-Flow Mechanism: Macroscopic Description,” Geophysics, Vol. 59, No. 3, 1994, pp. 428-438. doi:10.1190/1.1443605

[6] G. A. Gist, “Fluid Effects on Ve-locity and Attenuation in Sandstones,” Journal of the Acousti-cal Society of America, Vol. 96, No. 2, 1994, pp. 1158-1173. doi:10.1121/1.410389

[7] J. M. Carcione, C. Morency and J. E. Santos, “Computational Poroelasticity—A Review,” Geo-physics, Vol. 75, No. 5, 2010, pp. 75A229-75A243.

[8] V. K. Sidorov and M. V. Tarantin, “A Method for Estimation of a Dynamic Properties of Elastic Waves in Acoustic Logs,” Geo-physica, Vol. 3, 2011, pp. 7-12.

[9] L. M. Brekhovskih, “Waves in Layered Media,” 2nd Edition, Academic Press, New York, 1980.

[10] L. M. Brekhovskih and O. A. Godin, “Acoustics of Layered Media,” Nauka, Moscow, 1989 (in Rus-sian).

[11] G. N. Gogonenkov, “Synthetic Seismograms Cal-culation and Application,” Nedra, Moscow, 1972 (in Rus-sian).