Considering the difficulty of separating elastic vector wave-fields into different wave modes in anisotropic qP-wave modeling and imaging, acoustic approximation is an effective way. However in heterogeneous TTI media, setting shear velocity along the symmetry axis to zero can cause numerical solutions to be unstable, we solve this problem by introducing three different auxiliary functions including anisotropic parameter σ, and deduce three TTI second-order qP-wave equations and the corresponding first-order stress-velocity forms. Then, we solve the TTI first-order qP-wave equations by the improved RSFD method to avoid elastic modulus interpolation and enhance numerical accuracy. Numerical results show the validity and stability of the proposed method.


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