基于快速凸集投影與周期正弦延遲時間編碼的混源數據分離方法

中圖分類號：P631 文獻標識碼：A DOI：10.13810/j.cnki.issn.1000-7210.20240276

Abstract： The traditional method of seismic data acquisition involves separate excitation between shots，leading to low construction eficiency. The simultaneous-source acquisition technique，which involves simultaneous or delayed excitation of multiple shots， has significantly improved construction efficiency.To process multi-source seismic data conventionally，it is essential to separate the mixed data into single-source data. However， traditional data separation methods sufer from low eficiency. On the basis of the separation method using sparse inversion，this paper develops fast projection onto convex sets（FPOCS） algorithm through ntroducing an inertial parameter into the conventional POCS algorithm.Additionally，to address the problem that random time-delay encoding causes local continuity of aliasing noise and thus reduces separation accuracy，this paper proposes a method of periodic sinusoidal time-delay encoding. During the iterative process，the curvelet transform is used as a sparse basis，the soft thresholding function as the threshold model，and the exponential threshold formula as the threshold update formula.As aresult，the blending interference from other sources becomes more discrete，and the aliasing noise is distributed uniformly within a certain delay time，which reduces the dificultyin simultaneous-sourcedata separation.The results obtained from theoretical analysis and processing of measured data demonstrate that the two methods proposed in this paper not only greatly improve the con

vergence speed but also effectively enhance the accuracy of simultaneous-source data separation and have good anti-noise performance.

Keywords： simultaneous-source acquisition，curvelet transform，fast projection onto convex sets（FPOCS） algo rithm，periodic time-delay encoding

楊熙熙，張華，付立恒，等．基于快速凸集投影與周期正弦延遲時間編碼的混源數據分離方法[J].石油地球物 理勘探，2025，60（4）：923-936.

YANG Xixi，ZHANG Hua，FU Liheng，et al. Simultaneous-source data separation method based on fast projection onto convex sets and periodic sinusoidal time-delay encoding[J]. Oil Geophysical Prospecting，2025，60（4）： 923-936.

0 引言

傳統的地震數據采集方式與當前日益增加的勘探需求相矛盾，既要考慮震源激發的時間間隔，又要考慮震源之間的距離。為了提高地震勘探的采集效率，Silverman在1979年通過專利發表了多震源混采技術，Beasley2在1998年應用脈沖型震源實現了海上多震源采集，利用疊加濾波和偏移成像技術分離混采數據，證明了多震源采集技術的可行性和優勢。多震源混采技術不僅提高了地震勘探的效率，還改善了地震數據的質量，較傳統地震采集方式優勢大。

多震源混采獲得的地震數據，除了包含主震源的地震記錄，還存在來自其他震源較強的混疊干擾。針對多震源混采數據的分離，研究者們一開始利用最小二乘法進行偽分離，得到了兩張重復的地震剖面，但偽分離數據并不等同于單震源數據。為了將多震源混合數據分離成單震源數據，Chen等[3首次提出使用整形正則化迭代的方法分離混采地震數據，為后續研究提供了一種新的分離思路；2016年，Zu 等4使用線性周期變化的時間延遲編碼代替隨機時間延遲編碼對多震源數據進行分離，進一步提高了分離結果的精度;同年，Qu等[5結合軟閾值函數與硬閾值函數的特點，提出了新的firm閾值函數，通過改進閾值函數的方式改善了數據分離效果。后來，Gan等利用一種面向結構的中值濾波方法成功分離出單個震源數據；……