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

Authors

  • E.S. Efimova Trofimuk Institute of Petroleum Geology and Geophysics of SB RAS

DOI:

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

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.

Author Biography

E.S. Efimova

References

  1. Алексеев А.С., Костин В.И., Хайдуков В.Г., Чеверда В.А. Восстановление двумерных возмущений скорости вертикально-неоднородной акустической среды по данным многократного перекрытия (линеаризованная постановка) // Геология и геофизика. 1997. 38, № 12. 1980-1992.
  2. Вишневский Д.М., Лисица В.В., Решетова Г.В. Численное моделирование распространения сейсмических волн в средах с вязкоупругими включениями // Вычислительные методы и программирование. 2013. 14. 155-165.
  3. Гадыльшин К.Г., Чеверда В.А. Обращение полных волновых полей нелинейным методом наименьших квадратов: SVD-анализ // Вычислительные методы и программирование. 2014. 15. 499-513.
  4. Романов В.Г. Двумерная обратная задача для уравнения вязкоупругости // Сибирский математический журнал. 2012. 53, № 6. 1401-1412.
  5. Assous F., Collino F. A numerical method for the explanation of sensitivity: the case of the identification of the 2D stratified elastic medium // Inverse Problems. 1990. 6, N 4. 487-513.
  6. Blanch J.O., Robertsson J.O. A., Symes W.W. Modeling of a constant Q: methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique // Geophysics. 1995. 60, N 1. 176-184.
  7. Carcione J.M., Picotti S. P-wave seismic attenuation by slow-wave diffusion: effects of inhomogeneous rock properties // Geophysics. 2006. 71, N 3. O1-O8.
  8. Carcione J.M. Seismic modeling in viscoelastic media // Geophysics. 1993. 58, N 1. 110-120.
  9. Cheverda V.A., Kostin V.I. R-pseudoinverses for compact operators in Hilbert spaces: existence and stability // Journal of Inverse and Ill-Posed Problems. 1995. 3, N 2. 131-148.
  10. Christensen R.M. Theory of viscoelasticity: an introduction. Academic Press: New York, 1982.
  11. Coleman B.D., Noll W. Foundations of linear viscoelasticity // Review of Modern Physics. 1961. 33, N 2. 239-249.
  12. Efimova E.S., Cheverda V.A. Reliability of attenuation properties recovery for viscoelastic media // Open Journal of Applied Sciences. 2013. 3, N 1B. 84-88.
  13. Futterman W.I. Dispersive body waves // J. Geophysics Res. 1962. 67, N 13. 5279-5291.
  14. Hak B., Mulder W.A. Seismic attenuation imaging with causality // Geophys. J. Int. 2011. 184, N 1. 439-451.
  15. Hicks G.J., Pratt R.G. Reflection waveform inversion using local descent methods: Estimating attenuation and velocity over a gas-sand deposit // Geophysics. 2001. 66, N 2. 598-612.
  16. Liu H.-P., Anderson D.L., Kanamori H. Velocity dispersion due to anelasticity; implications for seismology and mantle composition // Geophys. J. Int. 1976. 47, N 1. 41-58.
  17. Mulder W.A., Hak B. An ambiguity in attenuation scattering imaging // Geophys. J. Int. 2009. 178, N 3. 1614-1624.
  18. Mulder W.A., Hak B. Velocity and attenuation perturbations can hardly be determined simultaneously in acoustic attenuation scattering // SEG Technical Program Expanded Abstracts. 2009. 3078-3082.
  19. Tarantola A. A strategy for nonlinear elastic inversion of seismic reflection data // Geophysics. 1986. 51, N 10. 1893-1903.

Published

2016-07-29

How to Cite

Ефимова Е.С. A Study of Coupling Between Viscoelastic Parameters Using the Singular Value Decomposition Analysis // Numerical methods and programming. 2016. 17. 309-317. doi 10.26089/NumMet.v17r329

Issue

Section

Section 1. Numerical methods and applications