Accelerated and automatic sparse parabolic Radon transform in the mixed frequency-time domain with alternating split Bregman algorithm

摘要

Parabolic Radon transform (PRT) can separate seismic wavefields based on their residual moveout difference. The mixed frequency-time domain sparse PRT (MSPRT) can not only implement the forward and inverse Radon transform in the frequency domain but also impose the sparse constraint along the temporal direction of the Radon model. Generally, MSPRT needs to solve the unconstrained optimization problem with L1 norm minimization constraint of the Radon model and L2 norm minimization constraint of the data fitting. By using the generalized cross-validation (GCV) function the unconstrained MSPRT solves the original optimization problem multiple times to determine the regularization parameter and is computationally expensive. In this paper we define the constrained optimization problem for MSPRT and solve it with the alternating split Bregman (ASB) algorithm. For constrained MSPRT the ASB algorithm can enforce the estimated Radon model in every iteration to converge to the true Radon model. So the iteration number can be determined automatically with respect to the minimum value of the GCV function. Therefore, constrained MSPRT circumvents excessive computations of multiple optimizations to determine the minimum value of the GCV function. Compared with unconstrained MSPRT, the proposed constrained MSPRT takes less time to achieve similar Radon model estimation results and similar multiple removal results. In addition, the proposed constrained MSPRT can better focus seismic events in the Radon domain and remove multiples more effectively than least squares based PRT.