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7 - Acoustic Properties of Rocks

Published online by Cambridge University Press:  19 November 2021

Nikolai Bagdassarov
Nikolai Bagdassarov
Affiliation:
Goethe-Universität Frankfurt Am Main
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Summary

Acoustic properties of rocks relate alternating stresses of varying frequency and elastic strains. In solids there are longitudinal and transversal waves, whose propagation is described by the wave equation. Longitudinal velocity Vp correlates with density and mean atomic weight of rocks. For rocks with a similar mean atomic weight there is a linear dependence of acoustic impedance Z vs. Vp. As a function of porosity, Vp may be estimated from modified Hashin-Shtrikman bounds. For sands and cemented sandstones the models of Dvorkin and Nur are applicable. Propagation velocities of elastic waves in rocks decrease with increasing temperature and increase with increasing pressure. To describe viscoelastic behavior of rocks, the concept of complex elastic moduli is used. Inner friction in rocks depends on temperature, pressure, porosity and pore saturation. Absorption coefficient and quality factor of rocks are frequency dependent. Rocks possess elastic intrinsic and extrinsic anisotropies. Anisotropy of elastic waves in minerals may be represented using pole diagrams. Focus Box 7.1: Models of sandstones after Dvorkin & Nur. Focus Box 7.2: Christoffel matrix and elastic wave velocities.

Keywords

Elastic wave velocitieswaves in anisotropic mediumphase and group velocitieseffect of porosity and fluid saturationviscoelastic models of rocksinternal friction and damping of elastic waves.
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Chapter
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Fundamentals of Rock Physics , pp. 245 - 291
Publisher: Cambridge University Press
Print publication year: 2021

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References

Literature

Abramson, E. H., Brown, J. M., Slutsky, L. J. & Zaug, J. (1997). The elastic constants of San Carlos olivine to 17 GPa. Journal of Geophysical Research 102(B6), 12253–12263. doi:10.1029/97JB00682.CrossRefGoogle Scholar
Amalokwu, K., Best, A. I. & Chapman, M. (2016). Effects of aligned fractures on the response of velocity and attenuation ratios to water saturation variation: A laboratory study using synthetic sandstones. Geophysical Prospecting 64(4), 942–957.CrossRefGoogle Scholar
Avseth, P., Dvorkin, J., Mavko, G. & Rykkje, J. (2000). Rock physics diagnostic of North Sea sands – Link between microstructure and seismic properties. Geophysical Research Letters 27, 2761–2764.CrossRefGoogle Scholar
Avseth, P., Mukerji, T., Mavko, G. & Dvorkin, J. (2010). Rock-physics diagnostics of depositional texture, diagenetic alterations, and reservoir heterogeneity in high-porosity siliciclastic sediments and rocks – A review of selected models and suggested work flows. Geophysics 75(5), 75A31–75A47.CrossRefGoogle Scholar
Barton, P. J. (1986). The relationship between seismic velocity and density in the continental crust – a useful constraint? Geophysical Journal of the Royal Astronomical Society 87, 195–208.CrossRefGoogle Scholar
Berryman, J. G. (1979). Long-wave elastic anisotropy in transversely isotropic media. Geophysics 44(5), 896–917.CrossRefGoogle Scholar
Biot, M. A. (1941). General theory of three-dimensional consolidation. Journal of Applied Physics 12, 155–164.CrossRefGoogle Scholar
Biot, M. A. (1956). Theory of propagation of elastic waves in a fluid-saturated porous solid – I. Low-frequency range. Journal of the Acoustical Society of America 28, 168–178.CrossRefGoogle Scholar
Birch, F. (1961a). Composition of the earth’s mantle. Geophysical Journal of the Royal Astronomical Society 4, 295–311. https://doi.org/10.1111/j.1365-246X.1961.tb06821.x.CrossRefGoogle Scholar
Birch, F. (1961b). Velocity of compressional waves in rocks to 10 kilobars, Part 2. Journal of Geophysical Research 66, 2199–2224.Google Scholar
Boness, D. A. & Ware, L. (2015). Birch’s law for high-pressure metals and ionic solids: Sound velocity data comparison between shock wave experiments and recent diamond anvil cell experiments. Shock Compression of Condensed Matter – 2015, AIP Conference Proceedings 1793, 050016-1–050016-5. doi:10.1063/1.4971550.Google Scholar
Browaeys, J. T. & Chevrot, S. (2004). Decomposition of the elastic tensor and geological applications. Geophysical Journal International 159, 667–678.CrossRefGoogle Scholar
Castagna, J. P., Batzle, M. L. & Eastwood, R. L. (1985). Relationships between compressional-wave and shear-wave velocities in elastic silicate rocks. Geophysics 50(4), 571–581.CrossRefGoogle Scholar
Castagna, J. P., Batzle, M. L. & Kan, T. K. (1993). Rock physics – The link between rock properties and AVO response. In: Castagna, J. P. & Backus, M. (Eds.) Offset-Dependent Reflectivity – Theory and Practice of AVO Analysis. Investigations in Geophysics Series No. 8. Society of Exploration Geophysicists, Tulsa, OK, 135–171.CrossRefGoogle Scholar
Christensen, N. I. & Lundquist, S. M. (1982). Pyroxene orientation within the upper mantle. GSA Bulletin 93(4): 279–288. doi:10.1130/0016-7606(1982)93<279:POWTUM>2.0.CO;2.2.0.CO;2>CrossRefGoogle Scholar
Digby, P. J. (1981). The effective elastic moduli of porous granular rocks. Journal of Applied Mechanics 48, 803–808.Google Scholar
Dutta, T. (2009). Integrating sequence stratigraphy and rock-physics to interpret seismic amplitudes and predict reservoir quality, PhD thesis, Stanford University, CA.Google Scholar
Dvorkin, J., Mavko, G. & Nur, A. (1991). The effect of cementation on the elastic properties of granular material. Mechanics of Materials 12, 207–217.CrossRefGoogle Scholar
Dvorkin, J., Nur, A. & Yin, H. (1994). Effective properties of cemented granular material. Mechanics of Materials 18, 351–366.CrossRefGoogle Scholar
Dvorkin, J. & Nur, A. (1996). Elasticity of high-porosity sandstones: Theory for two North Sea data sets. Geophysics 61, 1363–1370. doi:10.1190/1.1444059.CrossRefGoogle Scholar
Dvorkin, J., Mavko, G. & Nur, A. (1999). Overpressure detection from compressional and shear-wave data, Geophysical Research Letters 26, 3417–3420.CrossRefGoogle Scholar
Eberhart-Phillips, D., Han, D. H. & Zoback, M. D. (1989). Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone. Geophysics 51, 82–89.CrossRefGoogle Scholar
Gardner, G. H. F., Gardner, L. W. & Gregory, A. R. (1974). Formation velocity and density – the diagnostic basics for stratigraphic traps. Geophysics 39, 770–780.Google Scholar
Gassmann, F. (1951). Über die Elastizitȧt poröser Medien. Veirtelsjahresschrift der Naturforschenden Gesellschaft in Zürich 96, 1–23.Google Scholar
Gomez, C. (2009). Reservoir characterization combining elastic velocities and electrical resistivity measurements, PhD thesis, Stanford University, CA.Google Scholar
Grana, D. (2016). Pressure–velocity relations in reservoir rocks: Modified MacBeth’s equation. Journal of Applied Geophysics 132, 234–241.Google Scholar
Greenberg, M. L. & Castagna, J. P. (1992). Shear-wave velocity estimation in porous rocks: Theoretical formulation, preliminary verification and applications. Geophysical Prospecting 40, 195–209.CrossRefGoogle Scholar
Han, D. H. (1986). Effects of porosity and clay content on acoustic properties of sandstones and unconsolidated sediments, PhD thesis, Stanford University, CA.Google Scholar
Han, D. H., Nur, A. & Morgan, D. (1986). Effects of porosity and clay content on wave velocities in sandstones. Geophysics 51, 2093–2107.Google Scholar
Hill, R. (1963). Elastic properties of reinforced solids: Some theoretical principles. Journal of the Mechanics and Physics of Solids 11, 357–372.Google Scholar
Hughes, D. S. & Cross, J. H. (1951). Elastic wave velocities in rocks at high pressures and temperatures. Geophysics 16, 577–593.Google Scholar
Idelfonce, B., Lardeaux, J.-M. & Caro, J.-M. (1990). The behavior of shape preferred orientations in metamorphic rocks: Amphiboles and jadeites from the Monte Mucrone area (Sesia-Lanzo zone, Italian Western Alps). Journal of Structural Geology 12(8), 1005–1011.Google Scholar
Jaeken, J. W. & Cottenier, S. (2016). Solving the Christoffel equation: Phase and group velocities. Computer Physics Communications 207, 445–451.CrossRefGoogle Scholar
Johnson, K. L., Kendall, K. & Roberts, A. D. (1971). Surface energy and the contact of elastic solids. Proceedings of the Royal Society, London A 324, 301–313.Google Scholar
Kassab, M. A. & Weller, A. (2015). Study on P-wave and S-wave velocity in dry and wet sandstones of Tushka region, Egypt. Egyptian Journal of Petroleum 24, 1–11.Google Scholar
Kern, H., Mengel, K., Strauss, K. W., et al. (2009). Elastic wave velocities, chemistry and modal mineralogy of crustal rocks sampled by the Outokumpu scientific drill hole: Evidence from lab measurements and modeling. Physics of the Earth and Planetary Interiors 175, 151–166.CrossRefGoogle Scholar
Kuster, G. T. & Toksöz, M. N. (1974). Velocity and attenuation of seismic waves in two phase media. Geophysics 39, 587–618.CrossRefGoogle Scholar
Landau, L. D. & Lifschitz, E. M. (1999). Theory of Elasticity. Theoretical Physics, Vol. 7, 3rd edition. Butterworth-Heinemann, Oxford, §§ 8 and 9.Google Scholar
Lin, W. & Wang, C.-y. (1980). P-wave velocities in rocks at high pressure and temperature and the constitution of the central California crust. Geophysical Journal of the Royal Astronomical Society 61, 379–400.Google Scholar
Lindseth, R. O. (1979). Synthetic sonic logs – a process for stratigraphic interpretation. Geophysics 44, 3–26.Google Scholar
Ludwig, J. W., Nafe, J. E. & Drake, C. L. (1970). Seismic refraction. In: Maxwell, A. E. (Ed.) The Sea 4, 53–84. Wiley, New York.Google Scholar
MacBeth, C. (2004). A classification for the pressure-sensitivity properties of a sandstone rock frame. Geophysics 69, 497–510.CrossRefGoogle Scholar
Maurel, A., Lund, F. & Montagnat, M. (2015). Propagation of elastic waves through textured polycrystals: Application to ice. Proceedings of the Royal Society A 471(20140988), 1–28. http://dx.doi.org/10.1098/rspa.2014.0988.Google ScholarPubMed
Mavko, G., Mukerji, T. & Dvorkin, J. (1998). The Rock Physics Handbook. Cambridge University Press, Cambridge.Google Scholar
Mihály, L. & Martin, M. C. (2008). Solid State Physics: Problems and Solutions. Wiley-VCH, New York, p. 261.Google Scholar
Miller, S. L. M. (1992). Well log analysis of Vp and Vs in carbonates. CREWES Research Report 4, 12.1–12.11.Google Scholar
Mindlin, R. D. (1949). Compliance of elastic bodies in contact. Transactions of the ASME 71, A–259.Google Scholar
Murphy, W. F. (1982). Effects of microstructure and pore fluids on the acoustic properties of granular sedimentary materials, PhD dissertation, Stanford University.Google Scholar
Murphy, W. F., Winkler, K. W. & Kleinberg, R. L. (1984). Frame modulus reduction in sedimentary rocks: The effect of adsorption on grain contacts. Geophysical Research Letters 1(9), 805–808.CrossRefGoogle Scholar
Nur, A., Marion, D. & Yin, H. (1991). Wave velocities in sediments. In: Hovem, J. M., Richardson, M. D. & Stoll, R. D. (Eds.) Shear Waves in Marine Sediments. Springer, Dordrecht. https://link.springer.com/chapter/10.1007%2F978-94-011-3568-9_15.Google Scholar
Panayiotopoulos, K. (1989). Packing of sands – A review. Soil and Tillage Research 13(2), 101–121.Google Scholar
Peskin, C. S. (2010). Wave Momentum. Courant Institute of Mathematical Sciences, New York University. www.math.nyu.edu/faculty/peskin/papers/wave_momentum.pdf.Google Scholar
Pimienta, L., Schubnel, A., Violay, M., et al. (2018). Anomalous Vp/Vs ratios at seismic frequencies might evidence highly damaged rocks in subduction zones. Geophysical Research Letters 45, 12210–12217. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2018GL080132.Google Scholar
Popov, V. L. (2010). Contact Mechanics and Friction: Physical Principles and Applications. Springer-Verlag, Berlin-Heidelberg, p. 362.CrossRefGoogle Scholar
Prasad, M. & Manghnani, M. H. (1997). Effects of pore and differential pressure on compressional wave velocity and quality factor in Berea and Michigan sandstones. Geophysics 62, 1163–1176.Google Scholar
Quijada, M. F. & Stewart, R. R. (2007). Density estimations using density-velocity relations and seismic inversion. CREWES Research Report – Volume 19, pp. 1–20.Google Scholar
Rowland, D. R. & Pask, C. (1999). The missing wave momentum mystery. American Journal of Physics 67, 378–388. doi:10.1119/1.19272.CrossRefGoogle Scholar
Schön, S. J. (2011). Handbook of Petroleum Exploration and Production. Elsevier, Oxford, Amsterdam. Vol. 8: Chapter 6 – Elastic properties, pp. 149–243.Google Scholar
Schumann, K., Stipp, M., Behrmann, J. H., Klaeschen, D. & Schulte-Kortnack, D. (2014). P and S wave velocity measurements of water-rich sediments from the Nankai Trough, Japan. Journal of Geophysical Research: Solid Earth 119, 787–805. doi:10.1002/2013JB010290.Google Scholar
Singh, K., Jaisval, A. C., Singh, C. S. & Shrivastva, B. K. (2010). A correlation between elastic properties of coal and seismic wave velocities vis-à-vis cleat density and its orientation. International Journal of Earth Sciences and Engineering 3(4), 454–458.Google Scholar
Smeraglia, L., Trippetta, F., Carminati, E. & Mollo, S. (2014). Tectonic control on the petrophysical properties of foredeep sandstone in the Central Apennines, Italy. Journal of Geophysical Research: Solid Earth 119, 9077–9094. doi:10.1002/2014JB011221.Google Scholar
Tatham, R. H. (1982). VP/VS, and lithology. Geophysics 47(3), 336–344.CrossRefGoogle Scholar
Thomsen, L. (1986). Weak elastic anisotropy. Geophysics 51, 1954–1966.CrossRefGoogle Scholar
Toksöz, M. N., Cheng, C. H. & Timur, A. (1976). Velocities of seismic waves in porous rocks. Geophysics 41(4), 621–645.CrossRefGoogle Scholar
Truell, R., Elbaum, C. & Chick, B. B. (1969). Ultrasonic Methods in Solid State Physics. Academic Press, New York, p. 478.Google Scholar
Tsvankin, I. (1997). Anisotropic parameters and p-wave velocity for orthorhombic media. Geophysics 62(4), 1292–1309.Google Scholar
Vogelaar, B., Smeulders, D. & Harris, J. (2010). Exact expression for the effective acoustics of patchy-saturated rocks. Geophysics 75(4), N87–N96. doi:10.1190/1.3463430.Google Scholar
Weidner, D. J., Wang, H. & Ito, J. (1978). Elasticity of orthoenstatite. Physics of the Earth and Planetary Interiors 17, 7–13.CrossRefGoogle Scholar
White, J. E. (1975). Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40, 224–232.Google Scholar
Zhang, X., Tsang, L. H., Wang, Y. & Zhao, B. (2009). Petrologic composition model of the upper crust in Bohai Bay basin, China, based on Lamé impedances. Applied Geophysics 6(4), 327–336. doi:10.1007/s11770-009-0039-5.Google Scholar
Zong, J., Stewart, R. R., Dyaur, N. & Myers, M. T. (2017). Elastic properties of rock salt: Lab measurements and Gulf of Mexico well log analysis. Geophysics 82(5), 1–80. doi:10.1190/geo2016-0527.1.CrossRefGoogle Scholar

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