The K-Space Green’s Functions for Decoupled Constant-Q Wave Equation and its Adjoint Equation

References

1. Carcione, J.M.
   [2009] Theory and modeling of constant-Q P- and S-waves using fractional time derivatives. Geophysics, 74(1), 1787–1795.
   [Google Scholar]
2. Carcione, J.M., Cavallini, F., Mainardi, F. and Hanyga, A.
   [2002] Time-domain Modeling of Constant-Q Seismic Waves Using Fractional Derivatives. Pure and Applied Geophysics, 159(7), 1719–1736.
   [Google Scholar]
3. Chen, H., Zhou, H., Li, Q. and Wang, Y.
   [2016] Two efficient modeling schemes for fractional Laplacian viscoacoustic wave equation. 81(5).
   [Google Scholar]
4. Kelly, J.F., Mcgough, R.J. and Meerschaert, M.M.
   [2008] Analytical time-domain Green’s functions for power-law media. Journal of the Acoustical Society of America, 124(5), 2861–72.
   [Google Scholar]
5. Kjartansson, E.
   [1979] Constant Q -wave propagation and attenuation. Journal of Geophysical Research Solid Earth, 84(B9), 4737–4748.
   [Google Scholar]
6. Li, Q., Zhou, H., Zhang, Q., Chen, H. and Sheng, S.
   [2016] Efficient reverse time migration based on fractional Laplacian viscoacoustic wave equation. Geophysical Journal International, 204(1), 488504.
   [Google Scholar]
7. Sun, J., Zhu, T. and Fomel, S.
   [2014] Viscoacoustic modeling and imaging using low-rank approximation. Geophysics, 80(5), 5183.
   [Google Scholar]
8. Treeby, B.E. and Cox, B.
   [2011] A k-space Green’s function solution for acoustic initial value problems in homogeneous media with power law absorption. The Journal ofthe Acoustical Society ofAmerica, 129(6), 3652–3660.
   [Google Scholar]
9. Treeby, B.E. and Cox, B.T.
   [2010] Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian. Journal of the Acoustical Society of America, 127(5), 2741–48.
   [Google Scholar]
10. Treeby, B.E. and Cox, B.T.
    [2014] Modeling power law absorption and dispersion in viscoelastic solids using a split-field and the fractional Laplaciana). Journal of the Acoustical Society of America, 136(4), 1499–510.
    [Google Scholar]
11. Treeby, B.E., Zhang, E.Z. and Cox, B.T.
    [2010] Photoacoustic tomography in absorbing acoustic media using time reversal. Inverse Problems, 26157(26), 115003–20.
    [Google Scholar]
12. Yang, P., Brossier, R., Métivier, L. and Virieux, J.
    [2016] A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium. Geophysical Journal International, 207(1).
    [Google Scholar]
13. Zhu, T.
    [2015] Viscoelastic time-reversal imaging. Geophysics, 80(2), A45–A50.
    [Google Scholar]
14. Zhu, T. and Harris, J.M.
    [2014] Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians. Geophysics, 79(3), T105–T116.
    [Google Scholar]
15. Zhu, T., Harris, J.M. and Biondi, B.
    [2014] Q-compensated reverse-time migration. Geophysics, 79(3), S77–S87.
    [Google Scholar]