WANG Xiao-Kai,
GAO Jing-Huai,
CHEN Wen-Chao et al
.2016.Detecting method of seismic discontinuities based on high dimensional continuous wavelet transform.Chinese Journal Of Geophysics,59(9): 3394-3407,doi: 10.6038/cjg20160922
Detecting method of seismic discontinuities based on high dimensional continuous wavelet transform
WANG Xiao-Kai1,2,3, GAO Jing-Huai1,3, CHEN Wen-Chao3, YANG Chang-Chun2, ZHU Zhen-Yu4
1. Institute of wave and information, Xi'an Jiaotong University, Xi'an 710049, China; 2. Institute of Geology and Geophysics, The Chinese Academy of Sciences, Beijing 100029, China; 3. School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China; 4. Research Center of CNOOC, Beijing 100027, China
Abstract:Seismic discontinuous structures, such as faults, play an important role in seismic exploration. We first introduce the basic theory of high-dimensional continuous wavelet transform, including the definition of high-dimensional continuous wavelet transform, slices of high-dimensional continuous wavelet transform coefficients and the fast realization of high-dimensional continuous wavelet transform. We use a synthetic signal example to illustrate that the high-dimensional continuous wavelet transform has good angular resolution compared with high-dimensional separable wavelet transform. Then we introduce high-dimensional continuous wavelet transform to seismic discontinuity detection for the first time and propose a seismic discontinuities detecting method based on small-scale high-dimensional continuous wavelet transform coefficients. The realization procedures of the proposed method are also presented. Finally, synthetic signal examples and field examples confirm the effeteness of the proposed method.
Antoine J P, Demanet L, Hochedez J F, et al. 2002. Application of the 2-D wavelet transform to astrophysical images. Physicalia Mag., 24(1):93-116. Antoine J P, Murenzi R, Vandergheynst P. 1999. Directional wavelets revisited:Cauchy wavelets and symmetry detection in patterns. Applied and Computational Harmonic Analysis, 6(3):314-345. Antoine J P, Murenzi R, Vandergheynst P, et al. 2004. Two-Dimensional Wavelets and Their Relatives. Cambridge:Cambridge University Press. Antoine J P, Vandergheynst P, Bouyoucef K, et al. 1995a. Alternative representations of an image via the 2D wavelet transform:Application to character recognition.//Proceedings of the SPIE 2488, Visual Information Processing IV. Orlando, FL, United States:SPIE. Antoine J P, Vandergheynst P, Bouyoucef K, et al. 1995b. Target detection and recognition using two-dimensional isotropic and anisotropic wavelets.//Proceedings of the SPIE 2485, Automatic Object Recognition V. Orlando, FL, United States:SPIE. Bahorich M, Farmer S. 1995. 3-D seismic discontinuity for faults and stratigraphic features:The coherence cube. The Leading Edge, 14(10):1053-1058. Bahorich M S, Lopez J, Haskell N L, et al. 1995. Stratigraphic and structural interpretation with 3-D coherence.//SEG Technical Program Expanded Abstracts. SEG, 97-100. Bakker P. 2003. Image structure analysis for seismic interpretation[Ph. D]. Dutch:Technische Universiteit Delft. Bouchereau E B. 1997. Analyse d'images par transformées en ondelettes[Ph. D]. Français:Université Joseph Fourier-Grenoble I. Chen W C, Shi Z S, Wang W B, et al. 2000. Suppressing the direct wave noise in GPR data using the 2-D continue directional wavelets. Chinese Journal of Radio Science (in Chinese), 15(3):352-357. Chen W C, Wang W B, Zhao R C. 2003. Ground penetrating radar (GPR) wavelet constructing and application to high resolution processing of GPR data. Coal Geology & Exploration (in Chinese), 31(5):46-48. Choi Y, Koo J Y, Lee N Y. 2001. Image reconstruction using the wavelet transform for positron emission tomography. IEEE Transactions on Medical Imaging, 20(11):1188-1193. Chopra S, Marfurt K J. 2007. Seismic Attributes for Prospect Identification and Reservoir Characterization. Tulsa:Society of Exploration Geophysicists and European Association of Geoscientists and Engineers. Cohen I, Coifman R R. 2002. Local discontinuity measures for 3-D seismic data. Geophysics, 67(6):1933-1945. Darrozes J, Gaillot P, De Saint-Blanquat M, et al. 1997. Software for multi-scale image analysis:The normalized optimized anisotropic wavelet coefficient method. Computers & Geosciences, 23(8):889-895. Gaillot P, Darrozes J, Bouchez J L. 1999. Wavelet transform:a future of rock fabric analysis? Journal of Structural Geology, 21(11):1615-1621. Gaillot P, Darrozes J, de Saint Blanquat M, et al. 1997. The normalised optimised anisotropic wavelet coefficient (NOAWC) method:An image processing tool for multi-scale analysis of rock fabric. Geophysical Research Letters, 24(14):1819-1822. Gao Z S, Li Q X, Liu C, et al. 1998. Application of 2D wavelet transform in coherent noise estimation. Journal of Changchun University of Science and Technology (in Chinese), 28(4):433-437. Gersztenkorn A, Marfurt K J. 1996. Eigenstructure based coherence computations.//1996 SEG Annual Meeting. Denver, Colorado:SEG, 328-331. Gersztenkorn A, Marfurt K J. 1999. Eigenstructure-based coherence computationsas an aid to 3-D structural and stratigraphic mapping. Geophysics, 64(5):1468-1479. Li C F, Liner C. 2008. Wavelet-based detection of singularities in acoustic impedances from surface seismic reflection data. Geophysics, 73(1):V1-V9. Liu C, Wang D, Yang B J, et al. 2003. Apply of 2-D wavelet transforms in surface wave eliminations of seismic exploration. Progress in Geophysics (in Chinese), 18(4):711-714. Li Y Y, Li Q C, Ding L B, et al. 2004. The iterative ground-roll suppressing method based on 2D wavelet transform. The 20th Annual Meeting of Chinese Geophysical Society, Xi'an, Chinese Geophysical Society. Lu W K, Li Y D, Zhang S W, et al. 2005. Higher-order-statistics and supertrace-based coherence-estimation algorithm. Geophysics, 70(3):P13-P18. Mallat S. 2008. A Wavelet Tour of Signal Processing:The Sparse Way. 3rd ed. New York:Academic Press. Mallat S, Hwang W L. 1992. Singularity detection and processing with wavelets. IEEE Transactions on Information Theory, 38(2):617-643. Marfurt K J, Kirlin R L. 2000. 3-D broad-band estimates of reflector dip and amplitude. Geophysics, 65(1):304-320. Marfurt K J, Kirlin R L, Farmer S L, et al. 1998. 3-D seismic attributes using a semblance-based coherency algorithm. Geophysics, 63(4):1150-1165. Marfurt K J, Sudhaker V, Gersztenkorn A, et al. 1999. Coherency calculations in the presence of structural dip. Geophysics, 64(1):104-111. Murenzi R. 1990. Ondelettes multidimensionnelles et applications à l'analyse d'images[Ph. D]. Belgique:Louvain-la-Neuve, Université Catholique de Louvain. Murenzi R, Kaplan L, Antoine J P, et al. 1997. Computational complexity of the continuous wavelet transform in two dimensions.//Proc. Army Research Laboratory Symp. on Sensors and Electron Devices, College Park. Murenzi R, Zhai W P, Namuduri K R, et al. 1999. Scale-angle CWT features:Application in object recognition.//Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VⅡ. Denver, CO, USA:SPIE, 16-27. Ouillon G, Castaing C, Sornette D. 1996. Hierarchical geometry of faulting. Journal of Geophysical Research-Solid Earth, 101(B3):5477-5487. Ouillon G, Sornette D, Castaing C. 1995. Organisation of joints and faults from 1 cm to 100 km scales revealed by optimized anisotropic wavelet coefficient methodand multifractal analysis. Nonlinear Processes in Geophysics, 2:158-177. Randen T, Monsen E, Signer C, et al. 2000. Three-dimensional texture attributes for seismic data analysis.//SEG Technical Program Expanded Abstracts. SEG, 668-671. Song J G, Wang H K, Mu X. 2005. Research and implementation of cohere algorithm based on DOA. Progress in Geophysics (in Chinese), 25(5):1662-1669. Sun X P, Du S T. 2000. An application of power algorithm in the seismic attribute analysis. Computing Techniques for Geophysical and Geochemical Exploration (in Chinese), 22(4):316-321. Wang W, Gao J H, Chen W C, et al. 2012. Random seismic noise suppression via structure-adaptive median filter. Chinese J. Geophys. (in Chinese), 55(5):1732-1741. Wang X K, Gao J H, Chen W C, et al. 2012. An efficient implementation of eigenstructure-based coherence algorithm using recursion strategies and the power method. Journal of Applied Geophysics, 82:11-18. Wang X W, Du M J, Liu J Y, et al. 2002a. Computation of seismic coherence cube based on wavelet transform and its application. Geophysical Prospecting for Petroleum (in Chinese), 41(3):334-338. Wang X W, Yang K Q, Zhou L H, et al. 2002b. Methods of calculating coherence cube on the basis of wavelet transform. Chinese J. Geophys. (in Chinese), 45(6):847-852. Wu A D, Mou Y G. 1997. The use of 2D wavelet transform in imporving the resolution of seismic data. Geophysical Prospecting for Petroleum (in Chinese), 36(1):36-42. Yang L Q, Song H B, Hao T Y, et al. 2005. Method of 2-D wavelet transform in attenuating random noise. Geophysical Prospecting for Petroleum (in Chinese), 44(1):4-6. Ye Z L, He J J. 2006. The improvement of the coherency cube technique and its application. Computing Techniques for Geophysical and Geochemical Exploration (in Chinese), 28(2):121-123. Yuan S J. 2007. A review of seismic coherence techniques. Progress in Exploration Geophysics (in Chinese), 30(1):7-15. Zhang C J, Wang X D, Zhang H R, et al. 2006. Algorithm for image edge detection based on two-dimension continuous wavelet transform. Opto-Electronic Engineering (in Chinese), 33(4):93-96. Zhang H, Pan D M, Zhang X Y. 2007. Application of 2-D wavelet transformation in eliminating surface wave interference. Geophysical Prospecting for Petroleum(in Chinese), 46(2):147-150. Zhang J H, Dong M, Zhou Z X, et al. 2007. The coherence method based on GST and its application. Natural Gas Industry (in Chinese), 27(S1):381-383. Zhang J H, Wang Y Y, Zhao Y, et al. 2004. Detection of coherent data volume by wavelet multi resolution and application. Oil Geophysical Prospecting (in Chinese), 39(1):33-36. Zhou Y H, Gao J H. 2007. Application of local structural entropy measure on the detection of discontinuity of seismic data. Coal Geology & Exploration (in Chinese), 35(1):71-73. Zhou Y H, Gao J H, Chen W C. 2007. Local structural entropy based on frequency-division instantaneous phase for enhancing seismic discontinuities.//SEG Technical Program Expanded Abstracts. SEG, 846-850. Zhang B, Lin T F, Guo S G, et al. 2016. Noise suppression of time-migrated gathers using prestack structure-oriented filtering. Interpretation, 4(2):SG19-SG29. 陈文超, 师振盛, 汪文秉等. 2000. 小波变换在去除探地雷达信号直达波的应用. 电波科学学报, 15(3):352-357. 陈文超, 汪文秉, 赵荣椿. 2003. 探地雷达小波的构造及在提高雷达信号分辨率中的应用. 煤田地质与勘探, 31(5):46-48. 高振山, 李勤学, 刘财等. 1998. 二维小波变换在消除相干噪声中的应用. 长春科技大学学报, 28(4):433-437. 李媛媛, 李庆春, 丁梁波等. 2004. 二维小波变换迭代法去除地震面波.//中国地球物理学会第二十届年会. 西安:中国地球物理学会. 刘财, 王典, 杨宝俊等. 2003. 二维小波变换在地震勘探面波消除中的应用. 地球物理学进展, 18(4):711-714. 宋建国, 王海昆, 穆星. 2005. 基于DOA的相干算法研究与应用. 地球物理学进展, 25(5):1662-1669. 孙夕平, 杜世通. 2000. 乘幂法在地震属性分析中的应用. 物探化探计算技术, 22(4):316-321. 王伟, 高静怀, 陈文超等. 2012. 基于结构自适应中值滤波器的随机噪声衰减方法. 地球物理学报, 55(5):1732-1741. 王西文, 苏明军, 刘军迎等. 2002a. 基于小波变换的地震相干体算法及其应用. 石油物探, 41(3):334-338. 王西文, 杨孔庆, 周立宏等. 2002b. 基于小波变换的地震相干体算法研究. 地球物理学报, 45(6):847-852. 吴爱弟, 牟永光. 1997. 二维小波变换在提高地震资料分辨率中的应用. 石油物探, 36(1):36-42. 杨立强, 宋海斌, 郝天珧等. 2005. 基于二维小波变换的随机噪声压制方法研究. 石油物探, 44(1):4-6. 叶增炉, 何建军. 2006. 地震相干体算法的改进及应用. 物探化探计算技术, 28(2):121-123. 苑书金. 2007. 地震相干体技术的研究综述. 勘探地球物理进展, 30(1):7-15. [CM(29]张长江, 汪晓东, 张浩然等. 2006. 图像边缘检测的二维连续小波 变换法. 光电工程, 33(4):93-96. 张华, 潘冬明, 张兴岩. 2007. 二维小波变换在去除面波干扰中的应用. 石油物探, 46(2):147-150. 张军华, 王月英, 赵勇等. 2004. 小波多分辨率相干数据体的提取及应用. 石油地球物理勘探, 39(1):33-36. 张军华, 董猛, 周振晓等. 2007. 基于GST的相干体方法研究及应用. 天然气工业, 27(S1):381-383. 周艳辉, 高静怀. 2007. 局部结构熵算法在地震数据不连续性检测中的应用. 煤田地质与勘探, 35(1):71-73.