Coupled Waveform Analysis in Dynamic Characterization of Lossy Solids
Publication: Journal of Engineering Mechanics
Volume 128, Issue 4
Abstract
By means of the viscoelastic wave propagation model for a homogeneous semi-infinite solid, a rational analytical and computational framework is developed for nonintrusive, wave-based characterization of lossy media. The problem of estimating the equivalent uniform material properties from surface observations is formulated in the Bayesian setting for two canonical testing configurations, one involving a vertically and the other a horizontally polarized wave field. By enhancing the treatment of the inverse problem through a fully coupled viscoelastic analysis of the observed waveforms, the method provides consistent estimates of the in situ material stiffness, damping, and density which are not available from conventional seismic interpretations. For a rigorous treatment of the gradient search technique employed by the inverse solution, the necessary derivatives of the predictive model are evaluated analytically. A set of results with noise-contaminated synthetic measurements is included to highlight several key features of the back analysis.
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References
Aki, K., and Richards, P. G. (1980). Quantitative seismology: Theory and methods, Freeman, New York, Vol. 1.
Bjorck, A. (1996). Numerical methods for least squares problems, SIAM Publications, Philadelphia.
Breckenridge, F. R., and Greenspan, M.(1981). “Surface-wave displacement: absolute measurement using a capacitative transducer.” J. Acoust. Soc. Am., 69, 1177–1185.
Causse, E., Mittet, R., and Ursin, B.(1999). “Preconditioning of full-waveform inversion in viscoacoustic media.” Geophysics, 64(1), 130–145.
Chaderjian, B. J.(1994). “A uniqueness theorem for a lossy inverse problem in reflection seismology.” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 54, 1224–1249.
Copson, E. T. (1948). An introduction to the theory of functions of a complex variable, Oxford Univ. Press, London.
Couvreur, J. F., Thimus, J. F., Vervoort, A., and King, M. S. (1998). “Damage process of sedimentary rocks: advanced processing of ultrasonic waves.” Advances in rock mechanics, Y. Lin, ed., World Scientific, Singapore, 59–66.
Eason, G., Noble, B., and Sneddon, I. N.(1955). “On certain integrals of Lipschitz-Hankel type involving products of Bessel functions.” Philos. Trans. R. Soc. London, Ser. A, 247, 529–551.
Ewing, W. M., Jardetzky, W. S., and Press, F. (1957). Elastic waves in layered media, McGraw-Hill, New York.
Findley, W. N., Lai, J. S., and Onaran, K. (1989). Creep and relaxation of nonlinear viscoelastic materials, Dover, New York.
Ganji, V., Gucunski, N., and Nazarian, S.(1998). “Automated inversion procedure for spectral analysis of surface waves.” J. Geotech. Geoenviron. Eng., 124(8), 757–770.
Luenberger, D. G. (1973). Introduction to linear and nonlinear programming, Addison-Wesley, Reading, Mass.
Martinez, R. D., and McMechan, G. A.(1991). “Tau-p seismic data for viscoelastic media, part 2: Linearized inversion.” Geophys. Prospect., 39(2), 157–181.
Menke, W. (1989). Geophysical data analysis: Discrete inverse theory, Academic, San Diego.
Mridha, M., Odman, S., and Oberg, P. A.(1992). “Mechanical pulse wave propagation in gel, normal, and oedematous tissues.” J. Biomech., 25, 1213–1218.
Naik, T. R., and Malhotra, V. M. (1991). “The ultrasonic pulse velocity method.” Handbook on nondestructive testing of concrete, V. M. Malhotra and N. J. Carino, eds., CRC, Boca Raton, Fla., 169–188.
Pak, R. Y. S.(1987). “Asymmetric wave propagation in an elastic half-space by a method of potentials.” J. Appl. Mech., 54, 121–126.
Royston, T. J., Mansy, H. A., and Sandler, R. H.(1999). “Excitation and propagation of surface waves on a viscoelastic half-space with application to medical diagnosis.” J. Acoust. Soc. Am., 106(6), 3678–3686.
Sharma, P. V. (1997). Environmental and engineering geophysics, Cambridge Univ. Press, Cambridge, U.K.
Stokoe, K. H., II, and Nazarian, S. (1983). “Effectiveness of ground improvement from spectral analysis of surface waves.” Proc., 8th European Conf. on Soil Mechanics and Foundation Engineering, Balkema, Rotterdam, 31–38.
Stubbs, N., Torpunuri, V. S., Lytton, R. L., and Magnuson, A. H.(1994). “A methodology to identify material properties in pavements modeled as layered viscoelastic halfspaces (theory).” ASTM Spec. Tech. Publ., 1198, 53–67.
Tarantola, A. (1987). Inverse problem theory, Elsevier, Amsterdam.
Tikhonov, A. N., and Arsenin, V. Y. (1977). Solution of ill-posed problems, Winston-Wiley, New York.
Toksoz, M. N., Johnston, D. H., and Timur, A.(1979). “Attenuation of seismic waves in dry and saturated rocks: I. laboratory measurements.” Geophysics, 44(4), 681–690.
Uzan, J.(1994). “Advanced backcalculation techniques.” ASTM Spec. Tech. Publ., 1198, 3–37.
Winkler, W., and Nur, A.(1979). “Pore fluids and seismic attenuation in rocks.” Geophys. Res. Lett., 6, 1–4.
Zhao, H., Ursin, B., and Amundsen, L.(1994). “Frequency-wavenumber elastic inversion of marine seismic data.” Geophysics, 59, 1868–1881.
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Copyright © 2002 American Society of Civil Engineers.
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Received: Aug 10, 2000
Accepted: Jul 30, 2001
Published online: Apr 1, 2002
Published in print: Apr 2002
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