Amplitude Compensation for One-Way Wave Propagators in Inhomogeneous Media and Its Application to Seismic Imaging (Communications in Computational Physics, 2008)
The WKBJ solution for the one-way wave equations in media with smoothlyvarying velocity variation with depth, c(z), is reformulated from the principle of energy flux conservation for acoustic media. The formulation is then extended to generalheterogeneous media with local angle domain methods by introducing the concepts ofTransparent Boundary Condition (TBC) and Transparent Propagator (TP). The influence of the WKBJ correction on image amplitudes in seismic imaging, such as depthmigration in exploration seismology, is investigated in both smoothly varying c(z) andgeneral heterogeneous media. We also compare the effect of the propagator amplitude compensation with the effect of the acquisition aperture correction on the imageamplitude. Numerical results in a smoothly varying c(z) medium demonstrate thatthe WKBJ correction significantly improves the one-way wave propagator amplitudes,which, after compensation, agree very well with those from the full wave equationmethod. Images for a point scatterer in a smoothly varying c(z) medium show thatthe WKBJ correction has some improvement on the image amplitude, though it is notvery significant. The results in a general heterogeneous medium (2D SEG/EAGE saltmodel) show similar phenomena. When the acquisition aperture correction is applied,the image improves significantly in both the smoothly varying c(z) medium and the2D SEG/EAGE salt model. The comparisons indicate that although the WKBJ compensation for propagator amplitude may be important for forward modeling (especiallyfor wide-angle waves), its effect on the image amplitude in seismic imaging is muchless noticeable compared with the acquisition aperture correction for migration withlimited acquisition aperture in general heterogeneous media.