Reverse-Time Migration for Pure qP-Wave Based on Elliptical Decomposition Vector Equation

Anisotropic reverse-time migration (RTM) yields more accurate images for subsurface medium than isotropic migration. However, conventional qP-wave (quasi-P-wave) RTM in transversely isotropic (TI) medium with vertical symmetry axis (VTI) suffers from the crosstalk which is caused by residual SV waves and the instabilities when
$\varepsilon $
is less than
$\delta $
. To overcome these drawbacks, we present a new wave equation to characterize the propagation of seismic waves in the acoustic VTI medium. This new wave equation is described as the first-order velocity-stress vector wave equation that has specific physical meaning and is dynamically accurate. By decomposing the conventional qP-wave equation, we derive an elliptically anisotropic wave equation along with a non-elliptical operator. The latter is derived from an accurate phase velocity formulation using the acoustic approximation. Our solution is robust against S waves and remains numerically stable even for complex models, without the constraint of
$\varepsilon \ge \delta $
. Moreover, it exhibits high accuracy in both travel time and amplitude. The numerical tests demonstrate that our approach is attractive and promising when we perform qP-wave forward modeling and RTM. The comparison of images indicates the advantages of the proposed pure qP-wave on stability and accuracy.