Wavefield reconstruction inversion with weak-total-variation constraint based on first arrival traveltime tomography

The objective function of full waveform inversion is a strong nonlinear function, the inversion process is not unique, and it is easy to fall into local minimum. Firstly, in the process of wavefield reconstruction, the wave equation is introduced into the construction of objective function as a penalty term to broaden the search space of solution and reduce the risk of falling into local minimum. In addition, there is no need to calculate the adjoint wavefield in the inversion process, which can significantly improve the calculation efficiency; Secondly, considering that the total variation constraint can effectively reconstruct the discontinuous interface in the velocity model, this paper introduces the weak total variation constraint to avoid the excessive smooth estimation of the model under the strong total variation constraint. The disadvantage of this strategy is that it is highly dependent on the initial model. In view of this, this paper takes the long wavelength initial model obtained by first arrival traveltime tomography as a prior model constraint, and proposes a weak total variation constrained wavefield reconstruction inversion method based on first arrival traveltime tomography. Numerical experimental results show that the new method reduces the dependence on the initial model, the interface description is more accurate, the error is reduced, and the iterative convergence efficiency is significantly improved.