The full-waveform inversion is a high accurate imaging method which deduces physical parameters by using the wavefield observed on surface or in cross well. In this paper, we investigate the numerical methods of the frequency-domain full-waveform inversion. The forward problem is solved by the 9-point difference scheme with PML absorbing boundary conditions. The inversion is an optimization iterative process to minimize the residual between the synthetic data and the observed data. Several numerical optimization methods are compared in detail in this paper. They include the steepest descent method, the conjugate gradient method, the LBFGS method, the Gauss-Newton method and the preconditioned methods. The inversion is implemented from low frequency to high frequency successively. Furthermore, the inversion result of present frequency is used as the initial model for the inversion of the next frequency. This strategy overcomes the difficulty that the inversion falls into the local minimum or may be divergence. The forward and inverse methods are described detailly in this paper. Numerical computations based on MPI parallelization for a simple mode and two international benchmark models called Marmousi model and Overthrust model are completed. The computational results show that the Newton-type method and the preconditioned methods can yield very high accurate inversion results for complicated models.
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