Reflectivity sparsity-constrained joint migration inversion for VTI media

Traditional joint migration inversion (JMI) algorithm for anisotropic media, rooted in one-way wave equation, simulate wave propagation in VTI media. VTI-JMI performs reflectivity migration and velocity models inversion by minimizing the mismatch between observed and modelled data. This paper integrates a reflectivity-constrained velocity estimation algorithm into the VTI-JMI framework to mitigate the impact of parameter trade-offs and noise accumulation in VTI-JMI. The proposed approach constructs a regularization constraint term by utilizing residual between iterative reflectivity and reflectivity approximated from the estimated velocity to refine velocity updates. Moreover, it incorporates the Non-subsampled Shearlet transform (NSST) to achieve multiscale sparse denoising of reflectivity image, for enhancing constraint quality. The constraint does not require large extra computational costs and accurate initial models. Compared to traditional VTI-JMI, the proposed method significantly reduces noise in reflectivity image, while achieving higher precision in velocity models with sharper reflectors. Numerical experiments demonstrate the validity of our proposed algorithm.