Wave-equation migration velocity analysis for VTI media using optimized implicit finite difference

Conclusions and discussions

In this paper, I use an optimized implicit finite difference one-way propagation engine to improve both the efficiency and accuracy for anisotropic WEMVA. By precomputing the tables for the finite difference coefficients, the cost of this VTI extrapolation is similar to an isotropic implicit finite difference scheme. With the optimized coefficients, the dispersion relation is accurate up to $60^\circ$ . To compute the disturbed wave fields due to the perturbation in the models, the numerical derivatives of the optimized coefficients with respect to $\eta$ are also precomputed.

I test the VTI implicit finite difference scheme by impulse responses in both 2D and 3D. These impulse responses of the adjoint anisotropic WEMVA operator from a spike perturbation in the image space have a familiar banana-donut sensitivity kernel shape for both $v_v$ and $\eta$ . The amplitudes in these impulse responses show different sensitivities for different parameters with different source-receiver geometries. The waves traveling vertically have higher sensitivity to $v_v$ and the waves traveling at large angles have higher sensitivity to $\eta$ . Therefore, the 3D sensitivity kernels can also be used for acquisition design before exploration when specific parameters are under consideration.

Wave-equation migration velocity analysis for VTI media using optimized implicit finite difference