Least-squares reverse time migration with an angle-dependent weighting factor

Least-squares reverse time migration (LSRTM) produces higher quality images than conventional RTM. However, directly using the standard gradient formula, the inverted images suffer from low-wavenumber noise. Using a simple high-pass filter on the gradient can alleviate the effect of the low-wavenumber noise. But, owing to the illumination issue, the amplitudes are not balanced and in the deep part they are often weak. These two issues can be mitigated by the iterative approach, but it needs more iterations. We introduced an angle-dependent weighting factor to weight the gradient of LSRTM to suppress the low-wavenumber noise and also to emphasize the gradient in the deep part. An optimal step length for the L2-norm objective function is also presented to scale the gradient to the right order. Two numerical examples performed with the data synthesized on the Sigsbee2A and Marmousi models indicate that when using this weighted gradient combined with the preconditioned l-BFGS algorithm with the optimal step length, only a few iterations can achieve satisfying results. © 2018 Society of Exploration Geophysicists.