Full Waveform Inversion for Velocity Structure from Reflected Wave Seismic Data in the Frequency Domain

Full waveform inversion uses not only phase and amplitude information, but also waveform details, revealing precise details of the model. We use the LU factorization technique directly to solve the forward modeling, and show a preconditioned gradient method to inverse the velocity structure using the reflected wave from low-frequency to high-frequency in this study. The numerical structure of the finite difference method and back-propagation algorithm is exploited to develop an algorithm that explicitly calculates the Jacobin matrix utilizing a forward model solution. Furthermore, the diagonal elements of the false Hessian matrix are used as the preconditioned operator. Numerical tests on simple synthetic models find that a good velocity model can be obtained only by several frequency inversions, and the strategy of using low-frequency inversion result as the starting model in the high-frequency inversion can greatly reduce the non-uniqueness of their solutions. The initial model directly affects the imaging result. The smooth two-dimensional Gaussian model provides favorable low-frequency information for a better inversion result. The fast convergence can be achieved by using of the false Hessian matrix without any increase in the premise of computation.