Summary
P and S decomposition is an essential step in isotropic viscoelastic reverse time migration (VRTM). Separation using divergence and curl operators doesn’t preserve the phase or amplitude of the input viscoelastic wavefield, so an alternative decomposition that preserves the vector components of the P- and S-waves in the input wavefield is desired. With a decoupled assumption, we rearrange the memory variables in the elastodynamic equations based on the standard linear solid. The vector components of the propagating P- and S-wave can be can be decomposed in isotropic viscoelastic media without losing accuracy. Synthetic tests show that the P- and S-waves can be decomposed with no distortion of the amplitude or phase, and have the same vector components of particle velocity that exist in the viscoelastic wavefield before decomposition.
Introduction
Anelastic effects have been widely observed in wave propagation in the Earth (Carcione et al., 1988b). To simulate viscoelastic wave propagation, the theory of linear viscoelasticity based on Boltzmann’s superposition principle has been proposed and shown to be effective (Liu et al., 1976). Carcione et al. (1988a; 1988b; 1993) replace the time convolution in the viscoelastic constitutive equation by introducing memory variables, which allow the simulation of wavefields for models with arbitrary quality factor (Q) distributions, thus making viscoelastic computations practical and affordable in the time domain. This approach was extended to the stressparticle velocity formulation by Robertsson et al. (1994), that is used in this paper. Earth materials have been shown to have a nearly constant Q over the exploration seismic frequency range (McDonal et al., 1958; Bourbie et al., 1987). To achieve realistic simulation, Blanch et al. (1995) proposed a quick procedure for modeling constant Q behavior; Hestholm et al. (2006) combined the method of Blanch et al. (1995) and the Nelder - Mead algorithm (Powell, 1973) and improved Q estimation. Xu and McMechan (1995) improved the efficiency of the viscoelastic stress-particle velocity formulation by using composite memory variables, where the shear and compressional memory variables are combined by vector components to reduce RAM storage. With the linear viscoelastic formulation, attenuation loss can be compensated during both forward (source) and backward (receiver) wavefield extrapolations, which is used in true-amplitude migrations (Deng and McMechan, 2008).
