Retrieving the Green’s function of attenuating heterogeneous media by time-reversal modeling

The Green’s function between two locations within which seismograms that were not physically recorded, are retrieved by cross-correlation, convolution or deconvolution and summation of other recorded wavefields (also known as seismic interferometry). More recently seismic interferometry was applied in exploration seismology by Bakulin and Calvert (2006) and Schuster et al. (2004), in ultrasound by Weaver and Lobkis (2001), in crustal seismology by Campillo and Paul (2003), Sabra et al. (2005a, b), Roux et al. (2005) and Shapiro et al. (2005), and in helioseismology by Rickett and Claerbout (1999).

Theory of the retrieval of Green’s function can also be represented by time-reversal propagation because of time invariance of wave equations in the lossless media. In the presence of intrinsic attenuation in the media, however, the time invariance of wave equations is invalid. My previous work present methods of using novel viscoacoustic and viscoelastic wave equations to recover the time invariance property of such wave equations for viscoacoustic and viscoelastic time-reversal modeling. More importantly, attenuation effects are compensated for during time-reversal wave propagation. In this paper, I investigate the possibility of retrieving the Green’s function through time-reversal modeling techniques in attenuating media. I consider two different models to illustrate the feasibility of Green’s function retrieval in attenuating media. I consider the viscoacoustic as well as the viscoelastic situation. Numerical results show that the Green’s function can be retrieved in the correct amplitude and phase by time-reversal modeling with compensating both amplitude loss and dispersion effects.