A nonlinear multigrid method for inversion of two-dimensional acoustic wave equation

We investigate the problem of estimating the velocity in a two-dimensional acoustic wave equation, which plays an important role in geological survey. The forward problem is discretized using finite-difference methods and the estimation is formulated as a least-square minimization problem with a regularization term. To reduce the computational burden, a nonlinear multigrid method is applied to solve this inverse problem. In the multigrid inversion process, in order to make the objective functionals at different scales compatible, they are dynamically adjusted. In this way, the necessary condition of "the optimal solution should be the fixed point of multigrid inversion" can be met. The stable and fast regularized Gauss-Newton method is applied to each grid. The results of numerical simulations indicate that the proposed method can effectively reduce the required computation, improve the inversion results, and have the anti-noise ability.