A preconditioned iterative solver for the 3D frequency-domain wave equation applied to seismic problems is evaluated. The preconditioner corresponds to an approximate inverse of a heavily damped wave equation deduced from the (undamped) wave equation. The approximate inverse is computed with one multigrid cycle. Numerical results show that the method is robust and that the number of iterations increases roughly linearly with frequency when the grid spacing is adapted to keep a constant number of discretization points per wavelength. To evaluate the relevance of this iterative solver, the number of floating-point operations required for two imaging problems are roughly evaluated. This rough estimate indicates that the time-domain migration approach is more than one order of magnitude faster. The full-wave-form tomography, based on a least-squares formulation and a scale separation approach, has the same complexity in both domains.

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