Joint seismic data reconstruction based on the accelerated Bregman method and threshold iteration method

The reconstruction of missing seismic data traces plays an important role in seismic data processing. However, the majority of the existing reconstruction algorithms, held back by their low convergence speed and high computational cost, can barely meet the needs of mass data processing. This paper proposed a rapid reconstruction method combining the accelerated linearized Bregman method (ALBM) with a threshold iteration method, namely the iterative shrinkage-thresholding algorithm (ISTA). Besides, multi-scale and multi-directional curvelet transform was adopted as the sparse basis. ALBM converges rapidly in the early stage of iteration as it can obtain more effective signals from unthresholded curvelet coefficients. Nevertheless, its reconstruction accuracy is weakened by the increasing noise brought by the unthresholded curvelet coefficients in the later stage. In contrast, ISTA needs to threshold the curvelet coefficients all along. Although its convergence speed is slow in the early stage of iteration as most of the effective coefficients are filtered out, its reconstruction accuracy is high in the later stage owing to the restoration of weak effective signals. To maximize the advantages of the two algorithms, this paper presented two weighting parameter formulas (linear and exponential) in the range of 0~1. In this way, ALBM and ISTA were effectively combined linearly to ensure that ALBM played a major role in the early stage of iteration while ISTA dominated the later stage of iteration and thereby to enable this joint algorithm to iterate rapidly and accurately. In the combination process, a soft thresholding formula was adopted, and an exponential thresholding parameter formula was introduced. The theoretical simulation results demonstrate that compared with ALBM, ISTA, and traditional joint methods, the proposed accelerated joint method delivers fast calculation and an evident reconstruction effect. © 2022, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.