Seismic data reconstruction using Bregman iterative algorithm based on compressed sensing and discrete orthonormal wavelet transform.

Due to the limitations of the actual acquisition environment in the field, especially in ocean bottom seismometer (OBS) acquisition, the acquired seismic data are often irregular and incomplete, which affects the subsequent data imaging, interpretation and hydrocarbon‐bearing reservoir prediction. The interpolation reconstruction algorithm based on the compressive sensing theory can reconstruct the data without the limitation of Nyquist sampling interval. However, the reconstruction accuracy and effect are different for different sparse representations of the data. On the basis of compressed sensing theory, we propose a Bregman iterative seismic data reconstruction method based on the sparse decomposition of discrete orthonormal Coiflets and Symlets wavelet transforms. First, the discrete orthonormal matrix is constructed by using the above two wavelet functions to make the original seismic data sparse, then the Bregman iterative algorithm is used to reconstruct the sparse coefficients in the discrete wavelet domain, and finally the recovery matrix is used to reconstruct the seismic data. The discrete orthonormal Coiflets and Symlets wavelet transforms have good sparse representation ability and can compensate for the problem that discrete Fourier transform cannot well sparse representation of the data. After numerical experiments on horizontal‐layered model, Marmousi2 model and actual data, it is verified that the proposed method can reconstruct the missing seismic data under the regular observation system and under the irregular observation system with non‐uniform OBS distribution. Furthermore, this method can hardly bring the interference of random noise, and the reconstruction result is of high accuracy. [ABSTRACT FROM AUTHOR]