An iterative multilevel method for computing wavefields in frequency-domain seismic inversion

We describe an iterative multilevel method for solving linear systems representing forward modeling and back propagation of wavefields in frequency-domain seismic inversions. The workhorse of the method is the so-called multilevel Krylov method, applied to a multigrid-preconditioned linear system, and is called multigrid-multilevel Krylov (MKMG) method. Numerical experiments are presented for 2D Marmousi synthetic model for a range of frequencies. The convergence of the method is fast, and depends only mildly on frequency. The method can be considered as the first viable alternative to LU factorization, which is practically prohibitive for 3D seismic inversions.