Optimal mini-batch shot selection for target-oriented least-squares reverse time migration

We present an accelerated least-squares reverse time migration (LSRTM) approach based on optimal mini-batch shot selection. This selection strategy uses an illumination metric to select subsets (mini-batches) of shots that are critical to illuminating an area of interest. Illumination is the diagonal of the Hessian of the linearized Born modeling operator. We derive a low-cost Hessian matrix using the ultra-wide-band phase-space beam summation method, where beams are the local basis functions. This approach enables a target-oriented Hessian and also leads to an a-priori sparse representation of the beam propagators. By deriving the shot effectiveness metric over a target region, we cluster all the selected shots that contribute to the image using the K-means clustering technique. We sort the resulting clusters (mini-batches) in descending order based on the shot-effectiveness of the cluster center. The optimal mini-batch approach has many advantages: 1) Adaptive mini-batch size ensures that in each iteration an optimal number of sources are used, thus potentially leading to significant cost savings in target-oriented imaging; 2) Mini-batches are combined with the Adam stochastic optimization method where the previous gradients information is accumulated and exploited for faster convergence. We demonstrate the potential of the proposed method using the 2D Marmousi model.