Least-squares reverse-time migration (LSRTM) provides very accurate images of the subsurface. However, the computational cost of this technique is extremely high. One way to reduce that cost is to encode the sources using a random phase function and create a "super source". This encoding method introduces crosstalk artifacts that require averaging several realizations of the random encodings to suppress. I compare the convergence rates of the conventional and phase-encoded LSRTM for a fixed-spread geometry and show that the performance gain for the phase-encoded LSRTM far exceeds the loss due to the additional realizations. I also reduce the inversion cost by using the diagonal of the Hessian matrix as a preconditioner to the gradient. I also compare the convergence rates of different encoding methods used to estimate the true Hessian matrix. Then, I introduce a new source-based Hessian approximation and compare it to the other methods of approximating the Hessian matrix. Finally, I show the effect of each preconditioner on the LSRTM inversion. Results from the Marmousi synthetic model show that, for the same cost, preconditioning with the source-based Hessian gives the most accurate results.
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