Applying the -method to viscoelastic forward modeling

The -method developed by Blanch et al. (1995) is an efficient and optimally inexpensive approach that allows for the input of a Q model for both pressure wave and shear wave and therefore calculates the stress and strain relaxation times to approximate a constant Q at each grid points. A staggered finite difference scheme of second-order accuracy in time and fourth-order accuracy in space is used to the isotropic viscoelastic wave equation with an unsplit convolutional perfectly matched layer (CPML). The numerical results show that the CPML efficiently absorb incoming energy in the case of waves impinging the CPML interfaces at near-grazing angles. Important differences in amplitudes and arrival times between elastic and viscoelastic wave are also appreciated.