Spectrum decomposition based on three-parameter wavelet
(2.China University of Petroleum (Beijing) , Beijing, China 102200)
【Abstract】We first describe the basic principle of spectrum decomposition, then introduce three-parameter (TP) wavelet, and study the influence of each parameter on wavelet. After that, we conduct time-frequency analysis with three parameters based on forward modeling. Finally, we perform reservoir characterization with TP wavelet. It is found that subtle geological information can be highlighted. The following understanding are obtained based on model and real data tests: ① the TP wavelet has high flexibility, the modulation frequency σ of the wavelet affects the vibration degree of the wavelet, the energy attenuation parameter τ controls attenuation speed of attenuation function. When the value of τ is relatively big, the σ has less influence on the wavelet. The influence of the energy lag parameter β on the wavelet shape is more complex. When β is an integer multiple of trigonometric function period, only wavelet time shift occurs, it can be used to match the zero phase wavelet; when the β is not an integer multiple of trigonometric function period, wavelet time shift and deformation are generated, it can be used to match the non-zero phase wavelet. Deeply buried channels may be misinterpreted when β is not equal to zero; ② compared with Morlet wavelet, TP wavelet can more precisely depict subtle sedimentary structures in thin interbeds; ③ in real data processing, the optimal parameter combinations can be obtained according to the correlation of various forms of basic wavelets with the real wavelet extracted from targets.
【Keywords】 spectrum decomposition; three-parameter wavelet ; wavelet transform ; time-frequency analysis ; reservoir characterization ;
 Widess M B. How thin is a thinbed? Geophysics, 1973, 38 (6): 1176–1180.
 Neidell N S, Poggiagliolmi E. Seismcc Stratigraphy-Applications to Hydrocarbon Exploration: AAPG Special Volumes, 1977: 389–416.
 Partyka G. Interpretational applications of spectral decomposition in reservoir characterization. The Leading Edge, 1999, 18 (3): 173–184.
 Liu Feng, Mou Zhonghai, Jiang Yuqiang et al. Seismic identification of small fault. Progress in Geophysics, 2011, 26 (6): 2210–2215 (in Chinese with English abstract).
 Li Wei, Yue Daii, Hu Guangyi et al. Frequency-segmented seismic attribute optimization and sandbody distribution prediction: An example in North Block, Qinghuangdao 32–6 Oilfield. OGP, 2017, 52 (1): 121–130 (in Chinese with English abstract).
 Yu Hao, Li Jinsong, Zhang Yan et al. Spectral decomposition in fault and reservoir identifications. OGP, 2013, 48 (6): 954–959 (in Chinese with English abstract).
 Zhu Zhenyu, Lü Dingyou, Sang Shuyun et al. Research of spectrum decomposition method based on physical wavelet transform and its application. Chinese Journal of Geophysics, 2009, 52 (8): 2152–2157 (in Chinese with English abstract).
 Li Bin, Yue Youxi, Wen Mingming. Reservoir predication based on synchrosqueezing wavelet transform. Natural Gas Geoscience, 2017, 28 (2): 341–348 (in Chinese with English abstract).
 Liu Shunlan, Qian Huisheng, Xu Pingyuan. Application of the Morlet wavelet transform to detection of transient signals. Journal of Hangzhou Institute of Electronic Engineering, 1999, 19 (3): 29–36 (in Chinese with English abstract).
 Harrop J D, Taraskin S N, Elliott S R. Instantaneous frequency and amplitude identification using wavelets: application to glass structure. Statistical Nonlinear & Soft Matter Physics, 2002, doi: 10.1103/PhysRevE.66.026703.
 Gao Jinghuai, Wan Tao, Chen Wenchao et al. Three parameter wavelet and its application in seismic data analysis. Chinese Journal of Geophysics, 2006, 49 (6): 1802–1812 (in Chinese with English abstract).
 Feng Bin, Zhao Fenghua, Wang Shuhua. Application of spectral decomposition technique in fluvial sand body prediction. Advances in Earth Science, 2012, 27 (5): 510–514 (in Chinese with English abstract).
 Marfurt K J, Kirlin R L. Narrow-band spectral analysis and thin-bed tuning. Geophysics, 2001, 66 (4): 1274–1283.
 Ma Yuehua, Wu Shuyan, Bai Yuhua et al. River sedimentary microfacies prediction based on spectral decomposition. OGP, 2015, 50 (3): 502–509 (in Chinese with English abstract).
 Zhu Qiuying, Wei Guoqi, Yang Wei et al. Favorable sand body prediction based on the time-frequency analysis in Iraqi Structure. OGP, 2017, 52 (3): 538–547 (in Chinese with English abstract).
 Ma Debo, JiaJinhua, ShenYinmin et al. Seismic prediction of Donghe sandstone pinch-out line in Jilake, Tarim Basin. OGP, 2017, 52 (1): 94–104 (in Chinese with English abstract).
 Chen Yuhong, Yang Changchun, Cao Qifang et al. The comparison of some time-frequency analysis methods. Progress in Geophysics, 2006, 21 (4): 1180–1185 (in Chinese with English abstract).
 Grossmann A, Morlet J. Decomposition of Hardy functions into square integrable wavelets of constant shape. Siam Journal on Mathematical Analysis, 1984, 15 (4): 723–736.
 Huang Handong, Zhang Ruwei, Guo Yingchun. Wavelet frequency-division process for seismic signals. Journal of Oil & Gas Technology, 2008, 30 (3): 87–91 (in Chinese with English abstract).
 Gao Jinghuai, Wang Wenbing, Zhu Guangming et al. On the choice of wavelet functions for seismic data processing. Chinese Journal of Geophysics, 1996, 39 (3): 392–400 (in Chinese with English abstract).
 Xiong Xiaojun, Wang Fei, Mi Hong et al. Frequency attenuation analysis based on time-frequency three-parameter wavelet transform. OGP, 2015, 50 (4): 699–705 (in Chinese with English abstract).
 Jiang Xiudi, Weng Bin, Liu Yaru et al. Application of spectral decomposition RGB plotting technique for spectral components in high accuracy seismic interpretation. Progress in Geophysics, 2013, 28 (2): 882–888 (in Chinese with English abstract).