Usually the computational cost of the quasi-P simulation depends on the complexity of the medium, and specifically the anisotropy. The effective-model method splits the anisotropic dispersion relation to an isotropic background and a correction factor that depends on the gradient of the wavefields. As a result, the computational cost is independent of the nature of anisotropy, which makes the extrapolation efficient. A dynamic implementation of this approach decomposes the original pseudo-differential operator into a Laplacian, handled using the low-rank approximation of the spectral operator, and an angular dependent correction factor applied in the space domain to correct for anisotropy. We analyze the role played by the correction factor and propose a new spherical decomposition. The proposed method provides accurate wavefields in phase and a more balanced amplitude. Also, it is free of SV-wave artifacts. Applications to a simple homogeneous VTI model and the revised Hess VTI model demonstrate the effectiveness of the approach.


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