基于Seislet域改进POCS算法的地震数据重构  

Improve POCS algorithm based on compressed sensing for seismic data reconstruction in Seislet domain

作　　者：张入化 苟其勇 黄建平[2] 张洞君 陈飞 ZHANG Ruhua;GOU Qiyong;HUANG Jianping;ZHANG Dongjun;CHEN Fei(Shale Gas Institute,PetroChina Southwest Oil&Gasfield Company,Chengdu 610056,China;School of Geoscience,China University of Petroleum(East China),Qingdao 266580,China;CCDC Safety Environment Quality Supervision&Testing Research Institute,Chongqing 401120,China)

机构地区：[1]中国石油西南油气田分公司页岩气研究院,成都610056 [2]中国石油大学(华东)地球科学与技术学院,青岛266580 [3]中国石油川庆钻探工程公司安全环保质量监督检测研究院,重庆401120

出　　处：《物探化探计算技术》2022年第5期578-589,共12页Computing Techniques For Geophysical and Geochemical Exploration

基　　金：西南油气田科技项目(20210304-02)。

摘　　要：压缩感知理论突破了奈奎斯特采样理论的局限性,可用于地震数据的重建。凸集投影(POCS)是基于压缩感知重建地震数据的主要算法之一。凸集投影(POCS)算法的主要参数包括阈值函数和阈值模型。针对传统硬阈值函数和软阈值函数的不足,这里结合Riemann-Liouville分数阶积分理论,提出了分数阶阈值函数。与硬阈值函数相比,分数阶阈值函数增强了阈值点的连续性,与软阈值函数相比,分数阶阈值函数减小了与原始系数的偏差。阈值模型能确定阈值函数所使用的阈值在线性阈值模型和数据驱动阈值模型之间添加了加权因子,然后获得加权阈值模型。最后将分数阶阈值函数和加权阈值模型应用于Seislet域中的POCS算法,以获得改进的Seislet域POCS算法。在模型测试和实际地震数据测试中,分数阶阈值函数与传统阈值函数相比,可以有效地提高地震数据的重构精度,而加权阈值模型可以在保证地震数据重建精度的前提下提高重构效率。The compression sensing breaks the limitation of the Nyquist sampling theorem in the discrete sampling of the signal,so that it can be used in the reconstruction of seismic data.In reconstruction of the seismic data using compression sensing the main parameters of the projection onto convex set(POCS)reconstruction algorithm include the threshold function and the threshold model.Because of the shortcomings of the traditional hard-threshold function and the soft-threshold function,we put forward the fractional-order threshold function in combination with the Riemann-Liouville fractional-order integral theory.This function enhances the continuity at the threshold end point compared with hard threshold function,and reduces the deviation from the original coefficient liken to soft threshold function.The threshold model determines the threshold value used by the threshold function.We add the weighting factor between the linear threshold model and the data-driven threshold model,and then the weighted threshold model is obtained.Finally,we apply the fractional-order threshold function and the weighted threshold model to the POCS algorithm in the Seislet domain to get the improved POCS algorithm of the Seislet domain.In the real seismic data test,fractional-order threshold function can effectively improve the reconstruction precision of the seismic data compared with the traditional threshold function,and the weighted threshold model can improve the reconstruction efficiency on the premise of ensuring the data reconstruction precision.

关 键 词：地震资料处理 地震数据重建 压缩感知 阈值函数 分数阶积分理论 阈值模型 

分 类 号：P631.4[天文地球—地质矿产勘探]