Goal-Oriented Inversion-Based NMO Correction Using a Convex $l_{2,1}$ -Norm

Abstract

Normal moveout (NMO) correction is a routine step in seismic data processing, which has an important impact on other seismic processing procedures, seismic inversion, and interpretation. We propose a goal-oriented inversion-based NMO correction method using a convex $l_{2,1}$ -norm. The proposed method corrects the superresolution multichannel offset-dependent reflectivity rather than the bandlimited data itself sample by sample, block by block, or wavelet by wavelet. Therefore, the proposed method can essentially reduce the amplitude and even phase distortion introduced by data-based NMO correction methods in the presence of strong wavelet interference. We impose two goal-oriented constraints including both the temporal sparsity and the horizontal continuity of reflectivity, which are approximately represented by a convex $l_{2,1}$ -norm, on the geometric moveout relationship from offset-dependent trajectories to zero offsets to build a new objective function for NMO correction. The goal-desired temporal sparsity of reflectivity can induce the superresolution solution; meanwhile, the goal-desired horizontal continuity introduces a reasonable intrinsic structure to further limit the solution space and is particularly suitable to processing interfering reflections. Attributing to these two additional constraints, the new NMO correction method can flatten the interfering events and the intersecting events with favorable offset-dependent amplitude and phase variations even in the presence of noise. Synthetic and real data examples are adopted to verify the performance of our method. The results show that goal-oriented inversion-based NMO correction using the $l_{2,1}$ -norm is a potentially effective, stable, and high-quality NMO correction tool, especially for strong wavelet interference and at far offsets.