A study of seismic data reconstruction based on complex-valued curvelet transform
XU Wei1,2, ZHANG Hua3, ZHANG Luo-Yi3
1. School of Geosciences and Info-physics, Central South University, Changsha 410083, China;
2. Geophysical Prospecting, Surveying and Mapping Institute, Shanxi Coal Geological Exploration, Jinzhong 030600, China;
3. Fundamental Science on Radioactive Geology and Exploration Technology Laboratory, East China Institute of Technology, Nanchang 344000, China
Traditional seismic data sampling must follow the Nyquist sampling theorem;nevertheless, the field data acquisition can't meet the sampling theorem due to missing traces or exploration cost limits, so we need to reconstruct prestack data to meet the requirements for subsequent processing.A seismic data reconstruction method based on the Projections Onto Convex Sets (POCS) algorithm and a complex-valued curvelet transform (CCT) has been introduced in the paper.Firstly, the Projections Onto Convex Sets (POCS) and complex-valued curvelet transform to characterize the local features of seismic data have been introduced.To tackle the disadvantage of slow convergence in traditional threshold parameter during the reconstruction process, the authors also propose an exponential square root decreased threshold and process 2-D seismic data reconstruction with the hard thresholding, which can reduce iterations and improve reconstruction efficiency.The case study of synthetic seismic data shows that the effect of this method is fairly good.The authors applied this technology in real seismic data and obtained a good result.
徐卫, 张华, 张落毅. 基于复值曲波变换的地震数据重建方法[J]. 物探与化探, 2016, 40(4): 750-756.
XU Wei, ZHANG Hua, ZHANG Luo-Yi. A study of seismic data reconstruction based on complex-valued curvelet transform. Geophysical and Geochemical Exploration, 2016, 40(4): 750-756.
[1] Herrmann F J.Randomized sampling and sparsity:Getting more information from fewer samples[J].Geophysics,2010,75(6):173-187.
[2] Trad D O.Five-dimensional interpolation:Recovering from acquisition constraints[J]. Geophysics, 2009, 74(6):123-132.
[3] Gao J,Sacchi M,Chen X H.A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions[J].Geophysics,2013,78(2):21-30.
[4] 路交通,曹思远,董建华,等.基于稀疏变换的地震数据重构方法[J].物探与化探,2013,37(1):175-179.
[5] 黄小刚,王一博,刘伊克,等.半径-斜率域加权反假频地震数据重建[J].地球物理学报,2014,57(7):2278-2290.
[6] 张华,陈小宏. 基于jitter采样和曲波变换的三维地震数据重建[J].地球物理学报,2013,56(5):1637-1649.
[7] Trad D,Ulryeh T,Sacchi M.Latest view of sparse radon transform[J].Geophysics,2003,68(1):386-399.
[8] 石颖,柯璇,王维红.一种加权抛物Radon变换地震波场重建方法[J].物探与化探,2012,36(5):846-850.
[9] 张振波,轩义华.高分辨率抛物线拉冬变换多次波压制技术[J].物探与化探,2014,38(5):981-988.
[10] 唐欢欢,毛伟建.3D高阶抛物Radon变换地震数据保幅重建[J].地球物理学报,2014,57(9):2918-2927.
[11] Wang J F,Ng M,Perz M.Seismic data interpolation by greedy local Radon transform[J]. Geophysics,2010,75(6):225-234.
[12] 薛亚茹,唐欢欢,陈小宏.高阶高分辨率Radon变换地震数据重建方法[J].石油地球物理勘探,201,49(1):95-101.
[13] Jin S.5D seismic data regularization by a damped least-norm Fourier inversion[J].Geophysics,2010,75(6):103-111.
[14] Herrmann F J,Hennenfent G.Non-parametric seismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
[15] 白兰淑,刘伊克,卢回忆,等.基于压缩感知的Curvelet域联合迭代地震数据重建[J].地球物理学报,2014,57(9):2937-2945.
[16] 冯飞, 王德利,张亚红,等.结合曲波变换的焦点变换在地震数据去噪和插值中的应用[J].物探与化探,2013,37(3):480-487.
[17] 薛永安,王勇,李红彩,等.改进的曲波变换及全变差联合去噪技术[J].物探与化探,2014,38(1):81-86.
[18] 张广智,郑静静,印兴耀,等.基于Curvelet变换的角度流体因子提取技术[J].物探与化探,2011,35(4):505-510.
[19] 张华,陈小宏,贺宗斌. 基于频率域复值曲波变换的三维地震数据重建[C]//北京:中国地球科学联合学术年会,2014:1114-1118.
[20] Abma R,Kabir N.3D interpolation of irregular data with a POCS algorithm[J].Geophysics, 2006,71(6):E91-E97.
[21] Gao J J,Chen X H,Li J Y,et al.Irregular seismic data reconstruction based on exponential threshold model of POCS method[J].Applied Geophysics,2010,7(3):229-238.
[22] 刘国昌,陈小宏, 郭志峰,等.基于curvelet变换的缺失地震数据插值方法[J].石油地球物理勘探,2011,46(2):237-245.
[23] Candès E,Demanet L,Donoho D,et al. Fast discrete curvelet transforms[J]. SIAM Multiscale Modeling and Simulation,2006,5(1):861-899.
[24] Neelamani R,Baumstein A,Ross W S.Adaptive subtraction using complex-valued curvelet transforms[J].Geophysics,2010,75(4):51-60.
[25] 王本锋,陈小宏,李景叶,等.POCS联合改进的Jitter采样理论曲波域地震数据重建[J]. 石油地球物理勘探,2015,50(1):20-28.
[26] Zhang H, Chen X H,Li H X.3D seismic data reconstruction based on complex-valued curvelet transform in frequency domain[J].Journal of Applied Geophysics,2015,113(6):64-73.
