Simulating propagation of separated wave modes in general anisotropic media, Part I: qP-wave propagators

2. Reverse-time migration of Hess VTI model

Our final example shows application of the pseudo-pure-mode qP-wave equation (i.e., equation 22 in its 2D form) to RTM of conventional seismic data representing mainly qP-wave energy using the synthetic data of SEG/Hess VTI model (Figure 10). In the original data set, there is no vertical velocity model for qSV-wave, namely $v_{s0}$ . For simplicity, we first get this parameter by setting $\frac{v_{s0}}{v_{p0}}=0.5$ anywhere. Figures 11a and 11b display the two components of the synthesized pseudo-pure-mode qP-wave fields, in which the source is located at the center of the windowed region of the original models. We observe that the summed wavefields (i.e., pseudo-pure-mode scalar qP-wave fields) contain quite weak residual qSV-wave energy (Figure 11c). For seismic imaging of qP-wave data, we try the finite nonzero $v_{s0}$ scheme (Fletcher et al., 2009) to suppress qSV-wave artifacts and enhance computation stability. Thanks to superposition of multi-shot migrated data, we obtain a good RTM result (Figure 12) using the common-shot gathers provided at http://software.seg.org, although spatial filtering has not been used to remove the residual qSV-wave energy. This example shows that the proposed pseudo-pure-mode qP-wave equation could be directly used for reverse-time migration of conventional single-component seismic data.

hessvp0,hessepsilon,hessdelta
Figure 10. Part of SEG/Hess VTI model with parameters of (a) vertical qP-wave velocity, Thomsen coefficients (b) $\epsilon$ and (c) $\delta$ .

PseudoPurePx,PseudoPurePz,PseudoPureP
Figure 11. Synthesized wavefields using the pseudo-pure-mode qP-wave equation in SEG/Hess VTI model: The three snapshots are synthesized by fixing the ratio of $v_{s0}$ to $v_{p0}$ as 0.5. The pseudo-pure-mode qP-wave fields (c) are the sum of the (a) x- and (b) z-components of the pseudo-pure-mode wavefields.

hessrtm
Figure 12. RTM of Hess VTI model using the pseudo-pure-mode qP-wave equation with nonzero finite $v_{s0}$ .

Simulating propagation of separated wave modes in general anisotropic media, Part I: qP-wave propagators