Seismic data interpolation based on the frequency-structure dual weighted threshold

Seismic data interpolation is a crucial part of seismic data processing. The quality of the interpolation is related to the subsequent inversion, denoising, deconvolution, migration, and other work. Conventional FK interpolation methods based on sparse inversion often use generalized thresholds. However, the missing seismic data in these methods only shows a sparse state along the wavenumber direction and a non-sparse state with a wavelet-like spectrum distribution along the frequency direction. The direct application of the generalized threshold based on the Lp norm will make it difficult to complete the high- and low-frequency information of the missing data, which is not conducive to the subsequent inversion that relies on low-frequency information and the development of high-resolution processing that relies on high frequency. To solve this problem, we design a frequency-weighted threshold that changes along the frequency direction and introduces a structure-weighted threshold along the wavenumber direction considering the aggregation distribution of complete seismic data in the wavenumber domain. Combining the above two points, we propose a frequency-structure dual weighted threshold to ensure the effective recovery of high- and low-frequency information while completing missing traces. By comparing with the generalized threshold, the model and actual data show that the frequencystructure dual weighted threshold can reduce the interpolation error and ensure the integrity of the high- and low-frequency information to the largest extent.