Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media

Abstract

A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen’s anisotropic parameters [Formula: see text] and [Formula: see text], and the tilt angle. The finite-difference discretization relies on a parsimonious mixed-grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at the source or at seismic discontinuities when [Formula: see text]. In frequency-domain modeling with absorbing boundary conditions, the unstable S-wave mode is not excited when [Formula: see text], allowing stable simulations of the P-wave mode for such anisotropic media. Some S-wave instabilities are seen in the PMLs when the symmetry axis is tilted and [Formula: see text]. These instabilities are consistent with previous theoretical analyses of PMLs in anisotropic media; they are removed if the grid interval is matched to the P-wavelength that leads to dispersive S-waves. Comparisons between seismograms computed with the frequency-domain acoustic TTI method and a finite-difference, time-domain method for the vertical transversely isotropic elastic equation show good agreement for weak to moderate anisotropy. This suggests the method can be used as a forward problem for viscoacoustic anisotropic full-waveform inversion.