DOI: https://doi.org/10.26089/NumMet.v17r329

A study of coupling between viscoelastic parameters using the singular value decomposition analysis

Authors

  • E.S. Efimova

Keywords:

viscoelasticity
seismic attenuation
singular value decomposition
inverse problems
ambiguity of solution

Abstract

The solution of a linearized inverse seismic problem of viscoelasticity is studied. The generalized standard linear solid model and the τ-method are used to describe media with attenuation. If the heterogeneity of one of the sought parameters influence the variability of another one during the process of numerical solution, then such parameters are said to be called coupled. Such a coupling is a sign of ill-posedness of the original problem. A regularization is necessary to overcome this difficulty. To accomplish this, we propose the truncation of the singular value decomposition to simultaneously determine the P-velocity and its attenuation. A combination of the Lame parameters and the quality factor are used as the parametrization of the medium under consideration.

New computational technologies

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Published

2016-07-29

Issue

Vol. 17 (2016): Issue 3.

Section

Section 1. Numerical methods and applications

Author Biography

E.S. Efimova

Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS
• Engineer

References

  1. A. S. Alekseev, V. I. Kostin, V. G. Khaidukov, and V. A. Cheverda, “Recovery of Two-Dimensional Perturbations of the Velocity of a Vertically Inhomogeneous Medium from Multicoverage Data (Linearized Formulation),” Geolog. Geofiz. 38 (12), 1980-1992 (1997) [Russ. Geol. Geophys. 38 (12), 2012-2025 (1997)].
  2. D. M. Vishnevsky, V. V. Lisitsa, and G. V. Reshetova, “Numerical Simulation of Seismic Wave Propagation in Media with Viscoelastic Intrusions,” Vychisl. Metody Programm. 14, 155-165 (2013).
  3. K. G. Gadylshin and V. A. Tcheverda, “Nonlinear Least-Squares Full Waveform Inversion: SVD Analysis,” Vychisl. Metody Programm. 15, 499-513 (2014).
  4. V. G. Romanov, “A Two-Dimensional Inverse Problem for the Viscoelasticity Equation,” Sib. Mat. Zh. 53 (6), 1401-1412 (2012) [Sib. Math. J. 53 (6), 1128-1138 (2012)].
  5. F. Assous and F. Collino, “A Numerical Method for the Explanation of Sensitivity: The Case of the Identification of the 2D Stratified Elastic Medium,” Inverse Probl. 6 (4), 487-513 (1990).
  6. J. O. Blanch, J. O. A. Robertsson, and W. W. Symes, “Modeling of a Constant Q: Methodology and Algorithm for an Efficient and Optimally Inexpensive Viscoelastic Technique,” Geophysics 60 (1), 176-184 (1995).
  7. J. M. Carcione and S. Picotti, “P-Wave Seismic Attenuation by Slow-Wave Diffusion: Effects of Inhomogeneous Rock Properties,” Geophysics 71 (3), O1-O8 (2006).
    doi 10.1190/1.2194512
  8. J. M. Carcione, “Seismic Modeling in Viscoelastic Media,” Geophysics 58 (1), 110-120 (1993).
  9. V. A. Cheverda and V. I. Kostin, “R-Pseudoinverses for Compact Operators in Hilbert Spaces: Existence and Stability,” J. Inverse Ill-Posed Probl. 3 (2), 131-148 (1995).
  10. R. M. Christensen, Theory of Viscoelasticity: An Introduction (Academic, New York, 1982).
  11. B. D. Coleman and W. Noll, “Foundations of Linear Viscoelasticity,” Rev. Mod. Phys. 33 (2), 239-249 (1961).
  12. E. Efimova and V. Cheverda, “Reliability of Attenuation Properties Recovery for Viscoelastic Media,” Open J. Appl. Sci. 3 (1B), 84-88 (2013).
  13. W. I. Futterman, “Dispersive Body Waves,” J. Geophys. Res. 67 (13), 5279-5291 (1962).
  14. B. Hak and W. A. Mulder, “Seismic Attenuation Imaging with Causality,” Geophys. J. Int. 184 (1), 439-451 (2011).
  15. G. J. Hicks and R. G. Pratt, “Reflection Waveform Inversion Using Local Descent Methods: Estimating Attenuation and Velocity over a Gas-Sand Deposit,” Geophysics 66 (2), 598-612 (2001).
  16. H.-P. Liu, D. L. Anderson, and H. Kanamori, “Velocity Dispersion due to Anelasticity; Implications for Seismology and Mantle Composition,” Geophys. J. Int. 47 (1), 41-58 (1976).
  17. W. A. Mulder and B. Hak, “An Ambiguity in Attenuation Scattering Imaging,” Geophys. J. Int. 178 (3), 1614-1624 (2009).
  18. W. A. Mulder and B. Hak, “Velocity and Attenuation Perturbations Can Hardly Be Determined Simultaneously in Acoustic Attenuation Scattering,” SEG Technical Program Expanded Abstracts, 3078-3082 (2009).
    doi 10.1190/1.3255494
  19. A. Tarantola, “A Strategy for Nonlinear Elastic Inversion of Seismic Reflection Data,” Geophys. 51 (10), 1893-1903 (1986).