Full waveform inversion (FWI) is a very important method for estimating the subsurface parameters. While it suffers from extensively computational cost, large memory requirements, slow convergence rate, cycle skipping, etc, which impede its practical application. In our implementation, a linear source encoding strategy is used for the gradient calculation in time-ray parameter domain. The plane wave encoding approach forms super-gathers by summing densely distributed individual shots, and can reduce the computational burden considerably. We also construct the diagonal part of the pseudo-Hessian using a hybrid source encoding method. The diagonal part of the encoded pseudo-Hessian is a good approximation to the full Hessian matrix, which preconditions the gradient. The preconditioning is equivalent applying a deconvolution imaging condition in prestack reverse time migration. To avoid the local minimum problem, a multi-scale approach in the time domain is employed, by (1) applying a low-pass filtering to the data residuals and (2) increasing the frequency bands step by step. This has been proved to be effective against cycle skipping. We assemble this suite of tools and carry out a numerical experiment with a modified Marmousi model, analyzing the effectiveness of this combination of strategies.
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