Angle-domain least-squares Kirchhoff migration with angle-dependent L1 regularization

ABSTRACT Least-squares migration (LSM) is a highly ill-posed inverse problem because of undersampled seismic acquisition and the band-limited property of recorded data. The inverted solution from the iteration solvers may suffer from migration artifacts and low spatial resolution. Total variation (TV) and L1 regularization methods can be used to mitigate these undesired effects present in the inverted LSM solution. However, the LSM method formulated in the angle-domain, which is denoted as angle-domain LSM, will become a more ill-posed inverse problem than standard LSM, due to angle-dependent wavelet stretching effects and migration artifacts in the migrated angle-domain common-image gathers (ADCIGs). To mitigate these artifacts and improve the quality of ADCIGs, an angle-domain least-squares Kirchhoff migration with angle-dependent L1 regularization was developed. There are two key points in the proposed method. The first key point is that the angle-domain Hessian matrix was explicitly computed by angle-domain Kirchhoff migration. The second key point is that angle-dependent L1 regularization was used to mitigate the angle-dependent stretching effects in the migrated and inverted ADCIGs. Meanwhile, the TV regularization along the spatial direction and a smooth constraint along the angle direction are incorporated to mitigate the migration artifacts. The alternating direction method of multipliers was used to resolve this optimization problem. Through numerical experiments with synthetic and field data, the effectiveness of the proposed method was tested, and two key benefits were highlighted. First, the proposed angle-dependent L1 regularization can effectively mitigate the angle-dependent stretching effects in the inverted ADCIGs. Second, the proposed least-squares Kirchhoff migration method can efficiently and effectively recover high-resolution and high-fidelity ADCIGs in the case of inhomogeneous velocity. In addition, the proposed method remains effective even in the presence of migration velocity errors and sparse recorded data.