This website uses cookies to improve your experience. If you continue without changing your settings, you consent to our use of cookies in accordance with our cookie policy. You can disable cookies at any time.

×
The SEG Library is experiencing unexpected technical problems preventing users from logging into their accounts.
Please contact us if you need immediate access to your publications. We apologize for the inconvenience.

Wavefield decomposition for viscoelastic anisotropic media

Authors:

Separating wave modes on seismic records is an essential step in imaging of multicomponent seismic data. Viscoelastic anisotropic models provide a realistic description of subsurface formations that exhibit anisotropy of velocity and attenuation. However, mode separation has not been extended to viscoelastic anisotropic media yet. Here, we propose an efficient approach to wavefield decomposition that takes velocity and attenuation anisotropy into account. Our algorithm operates in the frequency-wavenumber domain and, therefore, is suitable for general dissipative models. We present exact equations for wavefield decomposition in arbitrarily anisotropic attenuative homogeneous media. Then the proposed approach is applied to viscoelastic constant-Q VTI (transversely isotropic with a vertical symmetry axis) models. Numerical examples demonstrate the accuracy and efficiency of our approach for piecewise-homogeneous media characterized by pronounced velocity and attenuation anisotropy.

REFERENCES

  • Apostol, T. M., 1974, Mathematical analysis, 2nd ed.: Addison-Wesley.
  • Bai, T., and I. Tsvankin, 2016, Time-domain finite-difference modeling for attenuative anisotropic media: Geophysics, 81, no. 2, C69–C77, doi: 10.1190/geo2015-0424.1.GPYSA70016-8033
  • Behura, J., I. Tsvankin, E. Jenner, and A. Calvert, 2012, Estimation of interval velocity and attenuation anisotropy from reflection data at coronation field: The Leading Edge, 31, 580–587, doi: 10.1190/tle31050580.1.
  • Borcherdt, R. D., 2009, Viscoelastic waves in layered media: Cambridge University Press.
  • Carcione, J. M., 2014, Wave fields in real media: Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media, 3rd ed.: Elsevier, Handbook of Geophysical Exploration.
  • Červený, V., 2001, Seismic ray theory: Cambridge University Press.
  • Červený, V., and I. Pšencík, 2005, Plane waves in viscoelastic anisotropic media — I. Theory: Geophysical Journal International, 161, 197–212, doi: 10.1111/j.1365-246X.2005.02589.x.GJINEA0956-540X
  • Červený, V., and I. Pšencík, 2006, Particle motion of plane waves in visco-elastic anisotropic media: Russian Geology and Geophysics, 47, 551–562.RGEGEZ1068-7971
  • Červený, V., and I. Pšencík, 2009, Perturbation Hamiltonians in heterogeneous anisotropic weakly dissipative media: Geophysical Journal International, 178, 939–949, doi: 10.1111/j.1365-246X.2009.04218.x.GJINEA0956-540X
  • Chen, Y., and S. Fomel, 2023, 3D true-amplitude elastic wave-vector decomposition in heterogeneous anisotropic media: Geophysics, 88, no. 3, C79–C89, doi: 10.1190/geo2022-0361.1.GPYSA70016-8033
  • Cheng, J., and S. Fomel, 2014, Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media: Geophysics, 79, no. 4, C97–C110, doi: 10.1190/geo2014-0032.1.GPYSA70016-8033
  • Clark, R. A., P. M. Benson, A. J. Carter, and C. A. G. Moreno, 2009, Anisotropic P-wave attenuation measured from a multi-azimuth surface seismic reflection survey: Geophysical Prospecting, 57, 835–845, doi: 10.1111/j.1365-2478.2008.00772.x.GPPRAR0016-8025
  • Dellinger, J., 1991, Anisotropic seismic wave propagation: Ph.D. thesis, Stanford University.
  • Dellinger, J., and J. Etgen, 1990, Wavefield separation in two-dimensional anisotropic media: Geophysics, 55, 914–919, doi: 10.1190/1.1442906.GPYSA70016-8033
  • Devaney, A. J., and M. L. Oristaglio, 1986, A plane-wave decomposition for elastic wave fields applied to the separation of P-waves and S-waves in vector seismic data: Geophysics, 51, 419–423, doi: 10.1190/1.1442102.GPYSA70016-8033
  • Gurtin, M. E., and E. Sternberg, 1962, On the linear theory of viscoelasticity: Archive for Rational Mechanics and Analysis, 11, 291–356, doi: 10.1007/BF00253942.AVRMAW0003-9527
  • Hao, Q., and S. Greenhalgh, 2021a, Nearly constant Q dissipative models and wave equations for general viscoelastic anisotropy: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477, 20210170, doi: 10.1098/rspa.2021.0170.
  • Hao, Q., and S. Greenhalgh, 2021b, Nearly constant Q models of the generalized standard linear solid type and the corresponding wave equations: Geophysics, 86, no. 4, T239–T260, doi: 10.1190/geo2020-0548.1.GPYSA70016-8033
  • Hao, Q., S. Greenhalgh, X. Huang, and H. Li, 2022, Viscoelastic wave propagation for nearly constant Q transverse isotropy: Geophysical Prospecting, 70, 1176–1192, doi: 10.1111/1365-2478.13230.GPPRAR0016-8025
  • Hao, Q., and I. Tsvankin, 2023, Thomsen-type parameters and attenuation coefficients for constant-Q transverse isotropy: Geophysics, 88, no. 5, C123–C134, doi: 10.1190/geo2022-0575.1.GPYSA70016-8033
  • Hosten, B., M. Deschamps, and B. R. Tittmann, 1987, Inhomogeneous wave generation and propagation in lossy anisotropic solids. Application to the characterization of viscoelastic composite materials: The Journal of the Acoustical Society of America, 82, 1763–1770, doi: 10.1121/1.395170.
  • Hudson, J. A., 1980, The excitation and propagation of elastic waves: Cambridge University Press.
  • Kaur, H., S. Fomel, and N. Pham, 2021, A fast algorithm for elastic wave-mode separation using deep learning with generative adversarial networks (GANS): Journal of Geophysical Research: Solid Earth, 126, e2020JB021123, doi: 10.1029/2020JB021123.
  • Kjartansson, E., 1979, Constant Q-wave propagation and attenuation: Journal of Geophysical Research, 84, 4737–4748, doi: 10.1029/JB084iB09p04737.JGREA20148-0227
  • Sripanich, Y., S. Fomel, J. Sun, and J. Cheng, 2017, Elastic wave-vector decomposition in heterogeneous anisotropic media: Geophysical Prospecting, 65, 1231–1245, doi: 10.1111/1365-2478.12482.GPPRAR0016-8025
  • Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966, doi: 10.1190/1.1442051.GPYSA70016-8033
  • Tsvankin, I., 2012, Seismic signatures and analysis of reflection data in anisotropic media, 3rd ed.: SEG.
  • Tsvankin, I., and V. Grechka, 2011, Seismology of azimuthally anisotropic media and seismic fracture characterization: SEG.
  • Wang, W., B. Hua, G. A. McMechan, and B. Duquet, 2018, P- and S-decomposition in anisotropic media with localized low-rank approximations: Geophysics, 83, no. 1, C13–C26, doi: 10.1190/geo2017-0138.1.GPYSA70016-8033
  • Wang, X., Y. Lu, and J. Zhang, 2021, Elastic wave-mode separation in 2D transversely isotropic media using optical flow: Geophysical Prospecting, 69, 349–371, doi: 10.1111/1365-2478.13061.GPPRAR0016-8025
  • Yan, J., and P. Sava, 2009, Elastic wave-mode separation for VTI media: Geophysics, 74, no. 5, WB19–WB32, doi: 10.1190/1.3184014.GPYSA70016-8033
  • Yan, J., and P. Sava, 2011, Improving the efficiency of elastic wave-mode separation for heterogeneous tilted transverse isotropic media: Geophysics, 76, no. 4, T65–T78, doi: 10.1190/1.3581360.GPYSA70016-8033
  • Yang, J., H. Zhang, Y. Zhao, and H. Zhu, 2019, Elastic wavefield separation in anisotropic media based on eigenform analysis and its application in reverse-time migration: Geophysical Journal International, 217, 1290–1313, doi: 10.1093/gji/ggz085.GJINEA0956-540X
  • Zhang, L., L. Liu, F. Niu, J. Zuo, D. Shuai, W. Jia, and Y. Zhao, 2022, A novel and efficient engine for P-/S-wave-mode vector decomposition for vertical transverse isotropic elastic reverse time migration: Geophysics, 87, no. 4, S185–S207, doi: 10.1190/geo2021-0609.1.GPYSA70016-8033
  • Zhang, Q., and G. A. McMechan, 2010, 2D and 3D elastic wavefield vector decomposition in the wavenumber domain for VTI media: Geophysics, 75, no. 3, D13–D26, doi: 10.1190/1.3431045.GPYSA70016-8033
  • Zhou, Y., and H. Wang, 2017, Efficient wave-mode separation in vertical transversely isotropic media: Geophysics, 82, no. 2, C35–C47, doi: 10.1190/geo2016-0191.1.GPYSA70016-8033
  • Zhu, Y., and I. Tsvankin, 2006, Plane-wave propagation in attenuative transversely isotropic media: Geophysics, 71, no. 2, T17–T30, doi: 10.1190/1.2187792.GPYSA70016-8033
  • Zhu, Y., I. Tsvankin, P. Dewangan, and K. van Wijk, 2007a, Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media: Geophysics, 72, no. 1, D1–D7, doi: 10.1190/1.2374797.GPYSA70016-8033
  • Zhu, Y., I. Tsvankin, and I. Vasconcelos, 2007b, Effective attenuation anisotropy of thin-layered media: Geophysics, 72, no. 5, D93–D106, doi: 10.1190/1.2754185.GPYSA70016-8033
  • Zhubayev, A., M. E. Houben, D. M. Smeulders, and A. Barnhoorn, 2016, Ultrasonic velocity and attenuation anisotropy of shales, Whitby, United Kingdom: Geophysics, 81, no. 1, D45–D56, doi: 10.1190/geo2015-0211.1.GPYSA70016-8033