Surface-consistency forms the basis for short-wavelength statics estimation. When raypaths in the near-surface diverge from normal-incidence or when the normal moveout (NMO) velocity is inaccurate, surface-consistent methods may fail to estimate accurate statics. Existing non-surface-consistent techniques can be prone to errors due to the need to construct pilot traces or pick horizons, while imposing additional computational costs. To overcome these limitations and correct for the surface- and non-surface-consistent statics, we propose a low-rank-based residual statics (LR-ReS) estimation and correction framework. The method makes use of the redundant-nature of seismic data by utilizing its low-rank structure in the midpoint-offset-frequency domain. Due to the near-surface effect, the low-rank structure gets destroyed. Therefore, we estimate the statics by means of low-rank approximation and cross-correlation. To alleviate the need for accurate rank selection for low-rank approximation and for improved statics estimation, we implement the method in an iterative and multi-scale fashion. Since the low-rank approximation deteriorates at high frequencies, we utilize its better performance at low frequencies and exploit the common statics amongst the different frequency bands. The LR-ReS estimation and correction can be applied to data without NMO correction, which makes statics estimation independent of the NMO velocity errors. Consequently, it can reduce the multiple iterations of NMO velocity estimation and short-wavelength statics correction commonly needed for conventional methods to improve their performance. Moreover, the LR-ReS estimation does not require windowing of a noise-free area containing aligned primaries nor mute to avoid the NMO stretch effect, which enables statics correction of the wavefield of all offsets. To evaluate the performance of our proposed method, we apply it to simulated data and a challenging field data set affected by complex weathering layers and noise, which show substantial improvement compared to conventional short-wavelength statics correction.
