隐马尔可夫模型平滑估计理论及其在压制地震资料随机噪声中的应用
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摘要
本论文在国内外学者一直从事的地震勘探资料随机噪声压制研究基础上,针对较强随机噪声背景下地震资料信噪比的提高以及在地震勘探领域的应用进行了系统而深入的研究。从单道记录建模角度出发,确立以下两个方面作为主要目标:一是实现信号和噪声有效分离以保证处理后信噪比达到比较理想水平;二是应努力避免一些常规方法在去噪过程中导致信号较大程度改变的现象,以期尽量降低恢复信号的畸变度。
论文在非线性/线性状态空间模型框架下构建合成记录道压制随机噪声的数学模型。根据地震信号具有的结构相似性和近似周期性,对信号短时段(帧)以建模方式描述其非平稳性。在统一考虑信号检测要求和状态估计目标并达到二者合理融合前提下,确立由噪声子模型和信号子模型构成的组合模型表征合成地震记录道数据变化规律的思想。论文提出用于压制地震资料随机噪声的隐马尔可夫模型平滑估计方法,并考察影响其去噪性能的因素。不但通过理论模型仿真实验更深层次地研究隐马尔可夫模型平滑估计去噪特点,而且探讨其在实际资料处理中的适用性,结果表明这种方法不仅仅停留于理论研究阶段,实际应用也已经达到抑制随机噪声的目的。
As far as seismic data are processed, enhancing signal-to-noise ratio(SNR) and the resolution indicating its quality simultaneously is the research subject holding prospector’s interest all the while. Raising SNR is the precondition and base of enhancing resolution, and whether the lengthways one or the transverse one depends on the seismic signal frequencies and the data’s SNR. Because of the diversity of the formation cause of stochastic noise acting as an important factor to deteriorate SNR and the complexity of the geologic structure of the exploration region, the underground reflection energy received by the detector is rather weak. Especially for the data area with the SNR lower than 0.5dB that the signal is comparatively feeble in the background of the strong stochastic noise, it is difficult for some common methods to obtain the ideal results of noise elimination. Nay, sometimes, noise suppression measures lead to the signal being damnified to the different extent. So the research trying for the robust technique of noise suppression is a challenging task all the same. In addition, most of the current means are based on the model of the multiple traces and the supposition that signal approximates the linearity within the some transverse range and the waveforms resemble each other, and the idea suprresssing stochastic noise based on the single trace model of one dimension time is waiting for the further development.
The dissertation commences with processing single trace and treats the following aspects as the main goal probing into the problem of stochastic noise suppression. One is to design a method implementing the effective separation between signal and noise and ensuring an ideal SNR level. The other is supposed to avoid the distinct aberration of the reconstructed signal incurred by some common methods and presume upon decreasing it as low as possible, if possible.
Founding on the above objects, the dissertation embraces the tasks summarized as follows,
a) Study the problem of stochastic noise suppression of seismic data, and construct its mathematical model within the framework of the nonlinear/linear state space model.
b) On the basis of the structure similarity and approximate periodicity of seismic signal, create the model for the short-time signal segment(frame) describing the non-stationarity of the seismic reflections. Premised by considering signal detection uniformly and state estimation and reaching the rational amalgamation, the combination model of noise submodel and signal frame submodel characterizes the data variation law of synthetical seismic records.
c) Apply the continuous hidden Markov models(HMM) smoothing estimate to stochastic noise suppression. By defining the state chain parameter corresponding to the main frequency of Ricker wavelet, discuss its influencing the performance of continuous HMM smoothing estimate.
d) Use continuous HMM smoothing estimate to deal with noisy synthetical seismic records with the events of the multiform types and do the emulation experiments of the theoretical models as well as give the performance contrast with other methods.
e) Apply continuous HMM smoothing estimate to the practical seismic section, and analyze its application effect.
The dissertation consists of six chapters, and the basic content of each one is as follows,
Chapter one reiterates the types of stochastic noise and explains many common classifications suppressing it after introducing the research background and significance of stochastic noise suppression of seismic data processing simply. Summarize the status quo of its current research according to the classification way of time-space domain and transformed domain. Finally elicit the substantial objects, the structure and the concrete contents of the dissertation.
Chapter two specifies the HMM principles and the algorithms of HMM filtering. Giving the example of the discrete HMM, explain such three basic problems as probability evaluation,‘optimal’state sequence extraction and model parameter estimation. Subsequently, elucidate the continuous HMM to which the dissertation attaches importance and the five problems which must be solved in the course of the application. Regarding the view that HMM is essentially a Bayesian finite state process as the cut-in, introduce the state space framework and Bayesian filtering principles along with HMM filtering algorithms.
Chapter three studies the stochastic noise suppression method of HMM smooting estimate(HMM-S) taking synthetical seismic records which play an important role in the geology property analysis of the reflection groups and geology layer determination as the object. Its primary expectation is to buck for an idea to remove the noise of the noisy records. Firstly laying the foundation for the application of Bayesian statitics inference, establish the state pace model of noisy synthetical seismic records and produce the noise-signal frame continuous HMM describing their data variation law. Secondly detail the parameter training flow of the wavelet frame continuous HMM. By comparing with the results of time-frequency peak filtering(TFPF) and Wiener filtering, evaluate the performance of HMM-S reducing noise. Discuss the varieties of the factors influencing its performance, the emulation experiments indicate the relations between the wavelet frame HMM state chain parameter settings and signal reconstruction accuracy.
Chapter four integrates constructing the many models of single hyperbolic reflection events or multiple hyperbolic reflection events and lucubrates HMM-S by the theoretical emulation experiments. First of all, make the models of single hyperbolic reflection events using zero-phase wavelet(Ricker wavelet) or mixed phase wavelet according to the different parameters such as wavelet frequency, arrival time and layer velocity, etc. By a series of experments, investigate HMM-S performance influenced by the intensity variation of stochastic noise, the absorption attenuation of seismic wave frequency, phase alteration arosed by souce wavelet traveling through the underground medium. Not only does HMM-S eliminate the noise of synthetical section with SNR lower to -0.236dB and improve its quality obviously, but also embodies the definite robustness while processing the sections whose quality is unbalanced in some local areas. In the next place, make synthetical seismic records using multiple horizontal and gradient events as well as hyperbolic events respectively, and analyze the HMM-S performance with multiple events coexisting in the same section. Experiments indicate that the components of the multiple events of the complex sections including the faultage, folium and incomeplete events, etc, are enhanced without exception, and their continuity is ameliorated with the favourable reconstruction effects for the section details.
Chapter five dicusses the noise suppression application of the practical seismic data for HMM-S. For the concrete data, introduce the implementation procedures orienting common shot point seismic record, the parameter settings, the results’comparison analysis and the problems demanding the solutions so as to attain high robustness.
In chapter six, a summary of the dissertation is given. The further research direction is illuminated.
To sum up, the author of the dissertation evolves the study and probe separately from the two aspects of theory and application addressing the problems that exist in the area of stochastic noise suppression area and wait for the further reseach based on systematicly learning HMM principles, and reaps some fruits also. The applicability for HMM-S to attenuate the noise doesn’t halt in the phase of the theory research at all, and it reaches the goal to suppress the noise when processing the practical seismic data. If letting it exert its particular advantage adequately in the extensive applications, it should be modified and perfected more delicately according to the actual.
论文在非线性/线性状态空间模型框架下构建合成记录道压制随机噪声的数学模型。根据地震信号具有的结构相似性和近似周期性,对信号短时段(帧)以建模方式描述其非平稳性。在统一考虑信号检测要求和状态估计目标并达到二者合理融合前提下,确立由噪声子模型和信号子模型构成的组合模型表征合成地震记录道数据变化规律的思想。论文提出用于压制地震资料随机噪声的隐马尔可夫模型平滑估计方法,并考察影响其去噪性能的因素。不但通过理论模型仿真实验更深层次地研究隐马尔可夫模型平滑估计去噪特点,而且探讨其在实际资料处理中的适用性,结果表明这种方法不仅仅停留于理论研究阶段,实际应用也已经达到抑制随机噪声的目的。
As far as seismic data are processed, enhancing signal-to-noise ratio(SNR) and the resolution indicating its quality simultaneously is the research subject holding prospector’s interest all the while. Raising SNR is the precondition and base of enhancing resolution, and whether the lengthways one or the transverse one depends on the seismic signal frequencies and the data’s SNR. Because of the diversity of the formation cause of stochastic noise acting as an important factor to deteriorate SNR and the complexity of the geologic structure of the exploration region, the underground reflection energy received by the detector is rather weak. Especially for the data area with the SNR lower than 0.5dB that the signal is comparatively feeble in the background of the strong stochastic noise, it is difficult for some common methods to obtain the ideal results of noise elimination. Nay, sometimes, noise suppression measures lead to the signal being damnified to the different extent. So the research trying for the robust technique of noise suppression is a challenging task all the same. In addition, most of the current means are based on the model of the multiple traces and the supposition that signal approximates the linearity within the some transverse range and the waveforms resemble each other, and the idea suprresssing stochastic noise based on the single trace model of one dimension time is waiting for the further development.
The dissertation commences with processing single trace and treats the following aspects as the main goal probing into the problem of stochastic noise suppression. One is to design a method implementing the effective separation between signal and noise and ensuring an ideal SNR level. The other is supposed to avoid the distinct aberration of the reconstructed signal incurred by some common methods and presume upon decreasing it as low as possible, if possible.
Founding on the above objects, the dissertation embraces the tasks summarized as follows,
a) Study the problem of stochastic noise suppression of seismic data, and construct its mathematical model within the framework of the nonlinear/linear state space model.
b) On the basis of the structure similarity and approximate periodicity of seismic signal, create the model for the short-time signal segment(frame) describing the non-stationarity of the seismic reflections. Premised by considering signal detection uniformly and state estimation and reaching the rational amalgamation, the combination model of noise submodel and signal frame submodel characterizes the data variation law of synthetical seismic records.
c) Apply the continuous hidden Markov models(HMM) smoothing estimate to stochastic noise suppression. By defining the state chain parameter corresponding to the main frequency of Ricker wavelet, discuss its influencing the performance of continuous HMM smoothing estimate.
d) Use continuous HMM smoothing estimate to deal with noisy synthetical seismic records with the events of the multiform types and do the emulation experiments of the theoretical models as well as give the performance contrast with other methods.
e) Apply continuous HMM smoothing estimate to the practical seismic section, and analyze its application effect.
The dissertation consists of six chapters, and the basic content of each one is as follows,
Chapter one reiterates the types of stochastic noise and explains many common classifications suppressing it after introducing the research background and significance of stochastic noise suppression of seismic data processing simply. Summarize the status quo of its current research according to the classification way of time-space domain and transformed domain. Finally elicit the substantial objects, the structure and the concrete contents of the dissertation.
Chapter two specifies the HMM principles and the algorithms of HMM filtering. Giving the example of the discrete HMM, explain such three basic problems as probability evaluation,‘optimal’state sequence extraction and model parameter estimation. Subsequently, elucidate the continuous HMM to which the dissertation attaches importance and the five problems which must be solved in the course of the application. Regarding the view that HMM is essentially a Bayesian finite state process as the cut-in, introduce the state space framework and Bayesian filtering principles along with HMM filtering algorithms.
Chapter three studies the stochastic noise suppression method of HMM smooting estimate(HMM-S) taking synthetical seismic records which play an important role in the geology property analysis of the reflection groups and geology layer determination as the object. Its primary expectation is to buck for an idea to remove the noise of the noisy records. Firstly laying the foundation for the application of Bayesian statitics inference, establish the state pace model of noisy synthetical seismic records and produce the noise-signal frame continuous HMM describing their data variation law. Secondly detail the parameter training flow of the wavelet frame continuous HMM. By comparing with the results of time-frequency peak filtering(TFPF) and Wiener filtering, evaluate the performance of HMM-S reducing noise. Discuss the varieties of the factors influencing its performance, the emulation experiments indicate the relations between the wavelet frame HMM state chain parameter settings and signal reconstruction accuracy.
Chapter four integrates constructing the many models of single hyperbolic reflection events or multiple hyperbolic reflection events and lucubrates HMM-S by the theoretical emulation experiments. First of all, make the models of single hyperbolic reflection events using zero-phase wavelet(Ricker wavelet) or mixed phase wavelet according to the different parameters such as wavelet frequency, arrival time and layer velocity, etc. By a series of experments, investigate HMM-S performance influenced by the intensity variation of stochastic noise, the absorption attenuation of seismic wave frequency, phase alteration arosed by souce wavelet traveling through the underground medium. Not only does HMM-S eliminate the noise of synthetical section with SNR lower to -0.236dB and improve its quality obviously, but also embodies the definite robustness while processing the sections whose quality is unbalanced in some local areas. In the next place, make synthetical seismic records using multiple horizontal and gradient events as well as hyperbolic events respectively, and analyze the HMM-S performance with multiple events coexisting in the same section. Experiments indicate that the components of the multiple events of the complex sections including the faultage, folium and incomeplete events, etc, are enhanced without exception, and their continuity is ameliorated with the favourable reconstruction effects for the section details.
Chapter five dicusses the noise suppression application of the practical seismic data for HMM-S. For the concrete data, introduce the implementation procedures orienting common shot point seismic record, the parameter settings, the results’comparison analysis and the problems demanding the solutions so as to attain high robustness.
In chapter six, a summary of the dissertation is given. The further research direction is illuminated.
To sum up, the author of the dissertation evolves the study and probe separately from the two aspects of theory and application addressing the problems that exist in the area of stochastic noise suppression area and wait for the further reseach based on systematicly learning HMM principles, and reaps some fruits also. The applicability for HMM-S to attenuate the noise doesn’t halt in the phase of the theory research at all, and it reaches the goal to suppress the noise when processing the practical seismic data. If letting it exert its particular advantage adequately in the extensive applications, it should be modified and perfected more delicately according to the actual.
引文
[1]刘光鼎.回顾与展望——21世纪的固体地球物理[J].地球物理进展, 2002, 17(2): 191-197.
[2] AMINZADEH F. Challenges direct future of geophysics[J]. The American Oil& Gas Reporter, 2000.
[3] AMINZADEH F. Applications of AI and soft computing for challenging problems in the oil industry[J]. Journal of Petroleum Science and Engineering, 2005, 47(1-2): 5-14.
[4] HUFFMAN A R. The future of pore-pressure prediction using geophysical methods[J]. The Leading Edge, 2002, 21(2): 199-205.
[5] ROBINSON E A. Geophysical exploration: Past and future[J]. The Leading Edge, 2006, 25(1): 96-99.
[6]刘喜武,刘洪.地球物理勘探技术所面临的挑战及可能的数学解决方案[J].中国海上油气(地质), 2003,17(2):145-148.
[7]滕吉文. 21世纪地球物理学的机遇与挑战[J].地球物理进展, 2004, 19 (2): 208-215.
[8]王典,刘财,刘洋,王培茂,许卓.反射法地震勘探噪声消除技术研究[J].地球物理进展, 2006, 21(3): 957-970.
[9]陆基孟.地震勘探原理[M].北京:石油大学出版社, 1993.
[10]李月,杨宝俊,赵雪平,张铭,林红波.检测地震勘探微弱同相轴的混沌振子算法[J].地球物理学报, 2005, 48 (6): 1428-1433.
[11]李庆忠.走向精确勘探道路——高分辨地震勘探系统工程剖析[M].北京:石油工业出版社, 1993.
[12]牛滨华.半空间介质与地震波传播[M].北京:石油工业出版社, 2002.
[13]林红波.时频峰值滤波随机噪声消减技术及其在地震勘探中的应用[D].长春:吉林大学通信工程学院, 2007.
[14]李卫忠,王成礼,马在田.叠前主分量重建随机噪声衰减[J].石油地球物理勘探, 2000, 35(2): 244-256.
[15]熊翥.地震数据数字处理应用技术[M].北京:石油工业出版社, 1993.
[16] QUINN R, BULL J M, DIX J K. Optimal processing of marine high-resolution seismic reflection (Chirp) data[J]. Marine Geophysical Researches, 1998, 20: 13–20.
[17] TYAPKIN Y, URSIN B. Optimum stacking of seismic records with irregular noise[J]. Journal of Geophysics and Engineering, 2005, 2: 177-187.
[18] ROBINSON J C. Statistically optimal stacking of seismic data[J]. Geophysics, 1970, 35(3): 436.
[19] WHITE R E. The performance of optimum stacking filters in suppressing uncorrelated noise[J]. Geophysical Prospecting, 1977, 25(1): 165-178.
[20]茅金根,刘雯林.非规则噪音地震记录的优化加权叠加[J].石油物探, 2002, 41(3): 309-311.
[21]裴江云,刘洪,李幼铭.在随机噪音背景下地震反射信号的增强[J].地球物理进展, 2002, 17(1): 91-95.
[22]刘俊峰,裴江云.利用扩大反射面元方法压制随机噪音[J].大庆石油地质与开发, 2002, 21(4): 78-79.
[23]俞寿朋.高分辨率地震勘探[M].北京:石油工业出版社, 1993.
[24] LIU X W, GOU L M. Suppressing random noise to broaden the useful bandwidth of seismic reflection data[J]. Applied Geophysics, 2007, 4(1): 37-44.
[25] GRECHKA V Y, MCMECHAN G A, VOLOVODENKO V A. Solving 1-D inverse problems by Chebyshev polynomial expansion[J]. Geophysics, 1996, 61(6): 1758–1768.
[26]俞寿朋,蔡希玲,苏永昌.用地震信号多项式拟合提高叠加剖面信噪比[J].石油地球物理勘探, 1988, 23(2): 131-139.
[27]万海涛,苏永昌,俞寿朋. 3-D叠后地震资料多项式拟合提高信噪比和道内插[J].石油地球物理勘探, 1994, 29(2): 208-212.
[28] JOHANSEN T A, BRULAN L, LUTRO J. Tracking the AVO by using orthogonal polynomials[J]. Geophysical prospecting, 1995, 43(2): 245-261.
[29]陆文凯,张学工,李衍达,何汉猗,温书亮,刘永江.时频域零炮检距地震道拟合[J].石油地球物理勘探, 2001, 36(1): 56-59+71.
[30]钟伟,杨宝俊,张智.多项式拟合技术在强噪声地震资料中的应用研究[J].地球物理进展, 2006, 21(1): 184-189.
[31]夏洪瑞,董江伟,邹少峰,刘艳峰.常规二次多项式拟合地震数据[J].石油地球物理勘探, 2006, 45 (5): 492-496.
[32]薛亚茹,陆文凯,陈小宏,黄饶,马继涛.基于正交多项式变换的CMP动校正道集随机噪声压制[J].地球物理学进展, 2009, 24(1): 159-163.
[33] REITER E C, TOKSOZ M N, PURDY G M. A semblance-guided median filter[J]. Geophysical Prospecting, 1992, 41: 15-41.
[34] RABINER L R, SAMBUR M R, SCHMIDT C E. Applications of a nonlinear smoothing algorithm for speech[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1975, 23(6): 552-557.
[35]李承楚.关于中值滤波的理论基础[J].石油地球物理勘探, 1986, 21(4): 372-379.
[36] DUNCAN G, BERESFORD G. Median filter behavior with seismic data[J]. Geophysical Prospecting, 1995, 43(3): 329-345.
[37] BROWNRIGG D R. The weighted median filter[J]. Communications of the Association for Computing Machinery, 1984, 27(8): 204-208.
[38]夏洪瑞,陈德刚,周开明,刘新强.中值约束下的矢量分解去噪[J].石油物质, 2001, 40(3): 29-33.
[39]王宏伟.矢量分解法去噪[J].石油地球物理勘探, 1989, 24(1): 16-29.
[40] LIU C, LIU Y, YANG B J, WANG D, SUN J G. A 2D multistage median filter to reduce random seismic noise[J]. Geophysics, 2006, 71(5): 105-110.
[41] WANG X. Adaptive multistage median filter[J]. IEEE Transactions on Signal Processing, 1992, 40(4): 1015-1017.
[42] BEKARA M, VAN DER BAAN M. Local singular value decomposition for signal enhancement of seismic data[J]. Geophysics, 2007, 72(2): 59-65.
[43] SONG L P, ZHANG S Y. Singular value decomposition-based reconstruction algorithm for seismic traveltime tomography[J]. IEEE Transactions on Image Processing, 1999, 8(8): 1152-1154.
[44] URSIN B, ZHENG Y. Identification of seismic reflections using singular value decomposition[J]. Geophysical Prospecting, 1985, 33(6): 773-799.
[45]谢凤兰,赵改善.利用SVD法重建地震剖面[J].石油物探, 1990, 29(4): 33-40.
[46]徐伯勋,白应甫,白旭滨,孙茵.奇异值分解在垂直地震剖面中的应用[J].石油物探, 1993, 32(3): 60-72.
[47] FREIRE S L M, ULRYCH T J. Application of singular value decomposition to vertical seismicprofiling[J]. Geophysics, 1988, 53(6): 778-785.
[48]吴亚东,符溪,文鹏飞,王宏语,谭绍泉,任富新,姜维财.奇异值分解压制随机噪声的方法及应用[J].新疆石油地质, 2003, 24(2): 144-145.
[49]刘婉莹,孟凡顺,刘喜武,张宁,高伟,李达.地震数据分数阶域空间预测滤波方法研究[J].中国海洋大学学报, 2008, 38(6): 1008-1012.
[50] JUTTEN C, HERAULT J. Blind separation of sources,Part I: An adaptive algorithm based on neuro mimetic architecture[J]. Signal Processing, 1991, 24: 1-10.
[51]刘喜武,刘洪,李幼铭.独立分量分析及其在地震信息处理中应用初探[J].地球物理进展, 2003, 18(1): 90-96.
[52]彭才,朱仕军,孙建库,陈俊华,夏凌,黄东山.基于独立成分分析的地震数据去噪[J].勘探地球物理进展, 2007, 30(1): 30-32+68.
[53] SERRA J. Image Analysis and Mathematical Morphology[M]. London: Academic Press, 1982.
[54]王润秋,郑桂娟,付洪洲,李青.地震资料处理中的形态滤波去噪方法[J].石油地球物理勘探, 2005, 40(3): 277-282.
[55]夏洪瑞,陈德刚,周开明.地震资料处理中随机干扰消除方法分析[J].石油物探, 2003, 42(1): 93-96.
[56]尹成,伍志明,邓怀群.高阶统计量方法在地震勘探中的应用[J].地球物理进展, 2003, 18(3): 546-550.
[57]邓小英,李月.基于Ricker子波核的支持向量回归方法及其在地震勘探记录去噪处理中的应用[J].吉林大学学报(地球科学版), 2007, 37(4): 821-827.
[58]李月,杨宝俊,林红波,袁野,郝雪,刘晓华.地震勘探时空域双曲滤波因子的特点与提高信噪比的能力[J].地球物理学报, 2008, 51(5): 1557-1566.
[59]于海超,吴涛,刘继承.非线性滤波技术在地震信号处理中的应用[J].佳木斯大学学报(自然科学版), 2007, 25(1): 25-27.
[60] AL-YAHYA K M. Application of the partial Karhunen-Loève transform to suppress random noise in seismic sections[J]. Geophysical Prospecting, 1991, 39(1): 77-93.
[61] DJEDDI M, MIHOUBI A, AITOUCHE M A, DJEDDI M, BENIDIR M. Using the Karhunen-Loeve transform in the sources separation: application for the separaration of field waves in a vertical seismic profile and in the attenuation of multiples (SVP). Proceedings of the Conference: 2004-Dynamical Systems and Applications, 2004[C]. Dehli: GBS Publishers & Distributors, 2005.
[62] HEMON C H, MACE D. Use of the Karhunen-Loeve transformation in seismic data processing[J]. Geophysical Prospecting, 1978, 26: 600-626.
[63]傅才芳,罗国安.应用KL滤波提高地震记录的信噪比[J].石油地球物理勘探, 1986, 21(5): 486-493.
[64] JONES I F, LEVY S. Signal-to-noise ratio enhancement in multichannel seismic data via the Karhumen-Loeve transform[J]. Geophysical Prospecting, 1987, 35: 12-32.
[65]付燕,赵荣椿.应用时空变—倾角扫描叠加KL变换提高地震资料信噪比[J].物探化探计算技术, 2001, 23(4): 303-307.
[66]付燕,赵荣椿.应用改进的KL变换提高叠后地震记录信噪比[J].煤田地质与勘探, 2002, 30(3): 49-54.
[67]刘保童,朱光明.地震记录快速KL滤波的自组织神经网络方法[J].石油地球物理勘探, 2005,40(6): 632-636.
[68] CANALES L L. Random noise reduction. 54th Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts[C]. 1984, 3: 525–527.
[69]国九英.叠前ω-x域算子外推法去噪[J].石油地球物理勘探, 1995, 30(4): 487-494.
[70]蔡加铭,周兴元,吴律. f-x域算子外推去噪技术研究[J].石油地球物理勘探, 1999, 34(3): 325-331.
[71]康冶,于承业,贾卧,王春梅,陈颖. f-x域去噪方法研究[J].石油地球物理勘探, 2003, 38(2): 136-138.
[72]赵德斌,黄真萍,王春梅. F-X域奇异值分解预测滤波法随机噪声衰减[J].石油物探, 1998, 37(3): 29-33.
[73]国九英,周兴元,杨慧珠. f-x,y域随机噪音衰减[J].石油地球物理勘探, 1995, 30(2): 207-215.
[74]苏贵士,周兴元,李承楚.频率空间三维F-XYZ域预测去噪技术[J].石油地球物理勘探, 1998, 33(1): 95-103.
[75] CLAERBOUT J F. Earth Soundings Analysis: Processing Versus Inversion[M]. Oxford: Blackwell Scientific Publications, 1992.
[76] ZHOU B Z, Greenhalgh S A. Linear and parabolicτ-p transforms revisited[J]. Geophysics, 1994, 59(7): 1133-1149.
[77] BENOLIEL S D, SCHNEIDER W A, SHURTLEFF R N. Frequency wavenumber approach of theτ-p transform——Some applications in seismic data processing[J]. Geophysical Prospecting, 1987, 35(5): 517-538.
[78]牛滨华,孙春岩,张中杰,沈操,李英才,吕景贵,王宏语.多项式Radon变换[J].地球物理学报, 2001, 44(2): 263-271.
[79]刘喜武,刘洪,李幼铭.高分辨率Radon变换方法及其在地震信号处理中的应用[J].地球物理学进展, 2004, 19(1): 8-15.
[80] RUSSELL B, HAMPSON D, CHUN J. Noise elimination and the Radon transform, Part1[J]. The Leading Edge, 1990, 9 (9): 18-23.
[81] RUSSELL B, HAMPSON D, CHUN J. Noise elimination and the Radon transform, Part2[J]. The Leading Edge, 1990, 9 (11): 31-37.
[82] SPITZER R, NIETZSCHE F O, GREEN A G. Reducing source-generated noise in shallow seismic data using linear and hyperbolic & tau-p transformations[J]. Geophysics, 2001, 66(5): 1612-1621.
[83] MALLAT S. A Wavelet Tour of Signal Processing[M]. 2nd ed. New York: Academic Press, 1999.
[84] YOUNG R K. Wavelet Theory and its Applications[M]. 1st ed. Dordrecht: Kluwer Academic Publishers, 1993.
[85] GOUPILLAUD P, GROSSMANN A, MORLET J. Cycle-octave and related transforms in seismic analysis[J]. Geoexploration, 1984, 23: 85-102.
[86]章珂,刘贵忠,邹大文,钱俊生,李风岐.二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报, 1996, 39(2): 265-270.
[87]李鲲鹏,刘业新,李衍达,范存奎.小波变换的过零点特性与地震勘探信号的信噪比和分辨率[J].地球物理学报, 1997, 40(4): 561-568.
[88]宗涛,孟鸿鹰,贾玉兰,刘贵忠.小波包F-X域前后向预测去噪[J].地球物理学报, 1998, 41(增刊): 337-346.
[89]王振国,周熙襄,李晶.基于小波变换的最小光滑滤波去噪[J].石油地球物理勘探, 2002, 37(6): 594-600.
[90]张宇,张关泉.小波变换用于去除高频噪声[J].石油地球物理勘探, 1997, 32 (3): 327-337.
[91]吴爱弟,牟永光.地震信号的小波包分解压噪方法[J].石油地球物理勘探, 1998, 33 (4): 558-562.
[92]吴爱弟,曹思远.用正交多小波压制地震信号的随机噪声[J].石油地球物理勘探, 2002, 37(5):473-476.
[93]王振国,汪恩华.小波包相关阀值去噪[J].石油物探, 2002, 41(4): 400-405.
[94]杨立强,宋海斌,郝天珧,江为为.基于二维小波变换的随机噪声压制方法研究[J].石油物探, 2005, 44(1): 4-6.
[95]彭才,常智,朱仕军.基于曲波变换的地震数据去噪方法[J].石油物探, 2008, 47(5): 461-464.
[96]彭才,常智,韩朝军,朱仕军.基于Contourlet变换的地震噪声衰减[J].勘探地球物理进展, 2008, 31(4): 274-277.
[97]高静怀,毛剑,满蔚仕,陈文超,郑庆庆.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报, 2006, 49(4): 1155-1163.
[98]黄德芹,贾玉亮,方江雪.模型约束方法在低信噪比地震资料处理中的应用[J].工程地球物理学报, 2006, 3(3): 167-171.
[99]王珺,杨长春,乔玉雷.用稳定高效的反Q滤波技术提高地震资料分辨率[J].地球物理进展, 2008, 23(2): 456-463.
[100] HARGREAVES N D, CALVERT A J. Inverse Q-filtering by Fourier transform[J]. Geophysics, 1991, 56(1): 519-527.
[101] HARGREAVES N D. Similarity and the inverse Q filter: some simple algorithms for inverse Q filtering[J]. Geophysics, 1992, 57(2): 944-947.
[102] STOLT R H. Migration by Fourier transform[J]. Geophysics, 1978, 43(1): 23-48.
[103] HALE D. An inverse Q-filter[R]. Stanford Exploration Project, 1981.
[104] WANG Y H. Quantifying the effectiveness of stabilized inverse Q filtering[J]. Geophysics, 2003, 68(1): 337-345.
[105] WANG Y H. Inverse Q-filter for seismic resolution enhancement[J]. Geophysics, 2006, 71(1): 51-60.
[106]金雷,李月,杨宝俊.用时频峰值滤波方法消减地震勘探资料中随机噪声的初步研究[J].地球物理学进展, 2005, 20(3): 724-728.
[107]林红波,李月,叶文海,潘伟.时频峰值滤波去噪技术及其应用[J].地球物理学进展, 2008, 23(6): 1953-1957.
[108] ZHANG Z J, WANG G J, HARRIS J M. Multi-component wavefield simulation in viscous extensively dilatancy anisotropic media[J]. Physics of the Earth and Planetary Interiors, 1999, 114: 25-38.
[109] ZHANG Z J, WANG G J, TENG J W, et al. CDP mapping to obtain the fine structure of the crust and upper mantle from seismic sounding data: an example for the southeastern China[J]. Physics of the Earth and Planetary Interiors, 2000, 122: 133-146.
[110]张军华,吕宁,田连玉,陆文志,钟磊.地震资料去噪方法、技术综合评述[J].地球物理进展, 2005, 20(4): 1083-1091.
[111]刘建红,孟小红,程玉坤.针对叠前反演的去噪技术[J].石油勘探与开发, 2007, 34(6): 718-723.
[112] RABINER L R, JUANG B H. Fundamentals of Speech Recognition[M]. 1st ed. New York: Prentice-Hall, 1993.
[113] RABINER L R. A tutorial on hidden Markov models and selected applications in speech recognition[J]. Proceedings of the IEEE, 1989, 77(2): 257-286.
[114] VASEGHI S V. Advanced Digital Signal Processing and Noise Reduction[M]. 3rd ed. New York: John Wiley & Sons, 2006.
[115] BAUM L E, PéTRIE T. Statistical inference for probabilistic functions of finite state Markov chains[J]. The Annals of Mathematical Statistics, 1966, 37: 1554-1563.
[116] BAUM L E, EAGON J A. An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology[J]. The Bulletin of the American Mathematical Society, 1967, 73: 360-363.
[117] BAUM L E, SELL G R. Growth transformations for functions on manifolds[J]. The Pacific Journal of Mathematics, 1968, 27(2): 211-217.
[118] BAUM L E, PéTRIE T, SOULES G, WEISS N. A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains[J]. The Annals of Mathematical Statistics, 1970, 41(1):164-171.
[119] BAUM L E. An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes[J]. Inequalities, 1972, 3:1-8.
[120] BAKER J K. The DRAGON system—An overview[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1975, 23(1): 24-29.
[121] JELINEK F. Fast sequential decoding algorithm using a stack[J]. IBM Journal of Research and Development, 1969, 13: 675-685.
[122] BAHL L R, JELINEK F. Decoding for channels with insertions, deletions, and substitutions with applications to speech recongnition[J]. IEEE Transactions on Information Theory, 1975, 21: 404-411.
[123] JELINEK F, BAHL L R, MERCER R L. Design of a linguistic statistical decoder for the recognition of continuous speech[J]. IEEE Transactions on Information Theory, 1975, 21: 250-256.
[124] JELINEK F. Continuous speech recognition by statistical methods[J]. Proceedings of the IEEE, 1976, 64: 532-536.
[125] BAKIS R. Continuous speech recognition via centisecond acoustic states[J]. The Journal of the Acoustical Society of America, 1976, 59(1): 97.
[126] BAHL L R, JELINEK F, MERCER R L. A maximum likelihood approach to continuous speech recognition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, 5: 179-190.
[127] HUANG X D, ARIKI Y, JACK M A. Hidden Markov Models for Speech Recognition[M]. 1st ed. Edinburgh: Edinburgh University Press, 1990.
[128] RABINER L R, JUANG B H. An introduction to hidden Markov models[J]. IEEE ASSP Magazine, 1986, 1: 4-15.
[129] EPHRAIM Y. Statistical-model-based speech enhancement systems[J]. Proceedings of the IEEE, 1992, 80(10): 1526-1555.
[130] JEFFREY H. Scientific Inference[M]. 3rd ed. Cambridge: Cambridge University Press, 1961.
[131] LARSON H J, BRUNO O S. Probabilitic Models in Engeering Sciences. I and II[M]. New York: Wiley, 1979.
[132] SCHARF L L. Statistical Signal Processing: Detection, Estimation, and Time Series Analysis[M]. MA: Addison Wesley, 1991.
[133] CRAMER H. Mathematical Methods of Statistics[M]. NJ: Princeton University Press, 1974.
[134] BERNARDO J M, SMITH A F M. Bayesian Theory[M]. New York: Wiley, 1998.
[135] PRESS S J. Subjective and Objective Bayesian Statistics: Principles, Models, and Applications[M].2nd ed. New York: Wiley, 2003.
[136]冯长建. HMM动态模式识别理论、方法以及在旋转机械故障诊断中的应用[D].杭州:浙江大学机械与能源工程学院, 2002.
[137]赵力.语音信号处理[M].北京:机械工业出版社, 2003.
[138]杨行峻,迟惠生.语音信号数字处理[M].北京:电子工业出版社, 1995.
[139] VITERBI A J. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm[J]. IEEE Transactions on Information Theory, 1967, 13(2): 260-269.
[140] FORNEY G D. The viterbi algorithm[J]. Proceedings of the IEEE, 1973, 61(3): 268-278.
[141] DEMPSTER A P, LAIRD M L, RUBIN D B. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society, 1977, 39(1): 1-38.
[142] LEVINSON S E, RABINER L R, SONDHI M M. An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition[J]. The Bell System Technical Journal, 1983, 62(4): 1035-1074.
[143] FEDER M, WEINSTEIN E. Parameter estimation of superimposed signals using EM algorithm[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1988, 36(4): 477-489.
[144] RENDER R A, WALKER H F. Mixture densities, maximum likelihood and the EM algorithm[J]. SIAM Rev. 1984, 26: 195-239.
[145] LIPORACE L A. Maximum likelihood estimation for multivariate observations of Markov sources[J]. IEEE Transactions on Information Theory, 1982, 28(5): 729-734.
[146] JUANG B H. Maximum likelihood estimation for mixture multivariate stochastic observation of Markov chains[J]. AT&T Technical Journal, 1985, 64(6): 1235-1249.
[147] JUANG B H, LEVINSON S E, SONDHI M M. Maximum likelihood estimation for multivariate mixture observations of markov chains[J]. IEEE Transactions on Information Theory, 1986, 32(2): 307-309.
[148] RABINER L R, JUANG B H, LEVINSON S E, SONDHI M M. Recognition of isolated digits using hidden Markov models with continuous mixture densities[J]. AT&T Technical Journal, 1985, 64(6): 1211-1234.
[149] BAHL L R, BROWN P F, DE SOUZA P V, MERCER L R. Maximum mutual information estimation of hidden Markov model parameters for speech recognition. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing[C]. 1986, 11:49:52.
[150] EPHRAIM Y, DEMBO A, RABINER L R. A minimum discrimination information approach for hidden Markov modeling[J]. IEEE Transactions on Information Theory, 1989, 35(5): 1001-1003.
[151] EPHRAIM Y, RABINER L R. On the relations between modeling approaches for speech recognition[J]. IEEE Transactions on Information Theory, 1990, 36(2): 372-380.
[152]何强,毛士艺,张有为.多观察序列连续隐含马尔柯夫模型的无溢出参数重估[J].电子学报, 2000, 28(10): 98-101.
[153] JELINEK F, MERCER R L. Interpolated estimation of Markov source parameters from sparse data. Pattern Recognition in Practice[M]. Gelesma E S, Kanal L N. 1st ed. Netherlands: North-Holland, 1980.
[154] HARVEY A C, KOOPMAN S J, SHEPHARD N. State space and unobserved component models[M]. Cambridge: Cambridge University Press, 2004.
[155] KIM S, SHEPHARD N, CHIB S. Stochastic volatility: Likelihood inference and comparison with ARCH models[J]. Review of Economics Studies, 1998, 65:361-393.
[156] WEST M, HARRISON J. Bayesian forecasting and dynamic models[M]. 2nd ed. New York:Springer-Verlag, 1999.
[157] LAVIELLE M. Bayesian deconvolution of Bernoulli-Gaussian processes[J]. Signal Processing, 1993, 33: 67-79.
[158] FARHMEIR L, TUTZ G. Multivariate statistical modelling based on generalzed linear models. Springer Series in Statistics[M]. 2nd ed. New York: Springer, 2001.
[159] CHEN Z. Bayesian fitering: From Kalman filters to particle filters, and beyond. Technical Report[R]. Hamilton: Adaptive Systems Lab, McMaster University, 2003.
[160]陈学华.状态空间模型理论与算法及其在金融计量中的应用[D].广州:暨南大学经济学院, 2007.
[161] KITAGAWA G. Non-Gaussian state-space modeling of nonstationary time series[J]. Journal of the American Statistical Association, 1987, 82(400): 1032-1041.
[162] GODSILL S J, DOUCET A, WEST M. Monte Carlo smoothing for nonlinear time series[J]. Journal of the American Statistical Association, 2004, 99(465): 156-167.
[163] GILKS W R, BERZUINI C. Following a moving target-Monte Carlo inference for dynamic Bayesian models[J]. Journal of the Royal Statistical Society, Ser. B. 2000, 63: 1-20.
[164] KITAGAWA G. A self organizing state space model[J]. Jounal of the American Statistical Association, 1998, 93: 1203-1215.
[165] SHEPARD N, PITT M K. Likelihood analyis of non-Gaussian measurement time series[J]. Biometrika, 1997, 84:653-667.
[166] ARULAMPALAM M S, MASKELL S, GORDON N, CLAPP T. A tutorial on particle filters for online nonlinear/Non-Gaussian Bayesian tracking[J]. IEEE Transactions on Signal Processing, 2002, 50(2): 174-188.
[167] DOUCET A, GODSILL S, ANDRIEU C. On sequential Monte Carlo sampling methods for Bayesian filtering[J]. Statistics and Computing, 2000, 10: 197-208.
[168] QUATIERI T F. Discrete-Time Speech Signal Processing: Principles and Practice[M]. 1st ed. New York: Prentice-Hall, 2002.
[169]刘喜武,刘洪.地震盲反褶积综述[J].地球物理学进展, 2003, 18(2): 203-209.
[170]刘财,陈业全,刘洋,王典,李勤学,苗广文.勘探地震资料处理新方法及新技术[M].北京:科学出版社, 2006.
[171] RICKER N. The form and nature of seismic waves and the structure of seismograms[J]. Geophysics, 5: 348-366.
[172] TANAKA M, SAKAWA M, SHIROMARU M, MATSUMOTO T. Application of Kohonen's self-organizing netwok to the diagnosis system for rotating machinary. Systems, Man and Cybernetics. Proceedings of IEEE International Conference on Intelligent Systems for the 21st Century[C]. 1995, 5: 4039-4044.
[173]王庆海.浅层地震勘探记录信号的特点及消除干扰方法[J].物探与化探, 1991, 15(3): 237-240.
[174]高静怀,汪文秉,朱光明,彭玉华,王玉贵.地震资料处理中小波函数的选取研究[J].地球物理学报, 1996, 39(3): 392-399.
[175]付燕.人工地震信号去噪方法研究[D].西安:西北工业大学计算机科学与工程系, 2002.
[176]长春地质学院、成都地质学院、武汉地质学院合编.地震勘探——原理和方法[M].北京:地质出版社, 1980.
[177]李玉新.地震相干技术在断层与沉积相解释中的应用[J].沉积与特提斯地质, 2006, 26(3): 67-71.
[2] AMINZADEH F. Challenges direct future of geophysics[J]. The American Oil& Gas Reporter, 2000.
[3] AMINZADEH F. Applications of AI and soft computing for challenging problems in the oil industry[J]. Journal of Petroleum Science and Engineering, 2005, 47(1-2): 5-14.
[4] HUFFMAN A R. The future of pore-pressure prediction using geophysical methods[J]. The Leading Edge, 2002, 21(2): 199-205.
[5] ROBINSON E A. Geophysical exploration: Past and future[J]. The Leading Edge, 2006, 25(1): 96-99.
[6]刘喜武,刘洪.地球物理勘探技术所面临的挑战及可能的数学解决方案[J].中国海上油气(地质), 2003,17(2):145-148.
[7]滕吉文. 21世纪地球物理学的机遇与挑战[J].地球物理进展, 2004, 19 (2): 208-215.
[8]王典,刘财,刘洋,王培茂,许卓.反射法地震勘探噪声消除技术研究[J].地球物理进展, 2006, 21(3): 957-970.
[9]陆基孟.地震勘探原理[M].北京:石油大学出版社, 1993.
[10]李月,杨宝俊,赵雪平,张铭,林红波.检测地震勘探微弱同相轴的混沌振子算法[J].地球物理学报, 2005, 48 (6): 1428-1433.
[11]李庆忠.走向精确勘探道路——高分辨地震勘探系统工程剖析[M].北京:石油工业出版社, 1993.
[12]牛滨华.半空间介质与地震波传播[M].北京:石油工业出版社, 2002.
[13]林红波.时频峰值滤波随机噪声消减技术及其在地震勘探中的应用[D].长春:吉林大学通信工程学院, 2007.
[14]李卫忠,王成礼,马在田.叠前主分量重建随机噪声衰减[J].石油地球物理勘探, 2000, 35(2): 244-256.
[15]熊翥.地震数据数字处理应用技术[M].北京:石油工业出版社, 1993.
[16] QUINN R, BULL J M, DIX J K. Optimal processing of marine high-resolution seismic reflection (Chirp) data[J]. Marine Geophysical Researches, 1998, 20: 13–20.
[17] TYAPKIN Y, URSIN B. Optimum stacking of seismic records with irregular noise[J]. Journal of Geophysics and Engineering, 2005, 2: 177-187.
[18] ROBINSON J C. Statistically optimal stacking of seismic data[J]. Geophysics, 1970, 35(3): 436.
[19] WHITE R E. The performance of optimum stacking filters in suppressing uncorrelated noise[J]. Geophysical Prospecting, 1977, 25(1): 165-178.
[20]茅金根,刘雯林.非规则噪音地震记录的优化加权叠加[J].石油物探, 2002, 41(3): 309-311.
[21]裴江云,刘洪,李幼铭.在随机噪音背景下地震反射信号的增强[J].地球物理进展, 2002, 17(1): 91-95.
[22]刘俊峰,裴江云.利用扩大反射面元方法压制随机噪音[J].大庆石油地质与开发, 2002, 21(4): 78-79.
[23]俞寿朋.高分辨率地震勘探[M].北京:石油工业出版社, 1993.
[24] LIU X W, GOU L M. Suppressing random noise to broaden the useful bandwidth of seismic reflection data[J]. Applied Geophysics, 2007, 4(1): 37-44.
[25] GRECHKA V Y, MCMECHAN G A, VOLOVODENKO V A. Solving 1-D inverse problems by Chebyshev polynomial expansion[J]. Geophysics, 1996, 61(6): 1758–1768.
[26]俞寿朋,蔡希玲,苏永昌.用地震信号多项式拟合提高叠加剖面信噪比[J].石油地球物理勘探, 1988, 23(2): 131-139.
[27]万海涛,苏永昌,俞寿朋. 3-D叠后地震资料多项式拟合提高信噪比和道内插[J].石油地球物理勘探, 1994, 29(2): 208-212.
[28] JOHANSEN T A, BRULAN L, LUTRO J. Tracking the AVO by using orthogonal polynomials[J]. Geophysical prospecting, 1995, 43(2): 245-261.
[29]陆文凯,张学工,李衍达,何汉猗,温书亮,刘永江.时频域零炮检距地震道拟合[J].石油地球物理勘探, 2001, 36(1): 56-59+71.
[30]钟伟,杨宝俊,张智.多项式拟合技术在强噪声地震资料中的应用研究[J].地球物理进展, 2006, 21(1): 184-189.
[31]夏洪瑞,董江伟,邹少峰,刘艳峰.常规二次多项式拟合地震数据[J].石油地球物理勘探, 2006, 45 (5): 492-496.
[32]薛亚茹,陆文凯,陈小宏,黄饶,马继涛.基于正交多项式变换的CMP动校正道集随机噪声压制[J].地球物理学进展, 2009, 24(1): 159-163.
[33] REITER E C, TOKSOZ M N, PURDY G M. A semblance-guided median filter[J]. Geophysical Prospecting, 1992, 41: 15-41.
[34] RABINER L R, SAMBUR M R, SCHMIDT C E. Applications of a nonlinear smoothing algorithm for speech[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1975, 23(6): 552-557.
[35]李承楚.关于中值滤波的理论基础[J].石油地球物理勘探, 1986, 21(4): 372-379.
[36] DUNCAN G, BERESFORD G. Median filter behavior with seismic data[J]. Geophysical Prospecting, 1995, 43(3): 329-345.
[37] BROWNRIGG D R. The weighted median filter[J]. Communications of the Association for Computing Machinery, 1984, 27(8): 204-208.
[38]夏洪瑞,陈德刚,周开明,刘新强.中值约束下的矢量分解去噪[J].石油物质, 2001, 40(3): 29-33.
[39]王宏伟.矢量分解法去噪[J].石油地球物理勘探, 1989, 24(1): 16-29.
[40] LIU C, LIU Y, YANG B J, WANG D, SUN J G. A 2D multistage median filter to reduce random seismic noise[J]. Geophysics, 2006, 71(5): 105-110.
[41] WANG X. Adaptive multistage median filter[J]. IEEE Transactions on Signal Processing, 1992, 40(4): 1015-1017.
[42] BEKARA M, VAN DER BAAN M. Local singular value decomposition for signal enhancement of seismic data[J]. Geophysics, 2007, 72(2): 59-65.
[43] SONG L P, ZHANG S Y. Singular value decomposition-based reconstruction algorithm for seismic traveltime tomography[J]. IEEE Transactions on Image Processing, 1999, 8(8): 1152-1154.
[44] URSIN B, ZHENG Y. Identification of seismic reflections using singular value decomposition[J]. Geophysical Prospecting, 1985, 33(6): 773-799.
[45]谢凤兰,赵改善.利用SVD法重建地震剖面[J].石油物探, 1990, 29(4): 33-40.
[46]徐伯勋,白应甫,白旭滨,孙茵.奇异值分解在垂直地震剖面中的应用[J].石油物探, 1993, 32(3): 60-72.
[47] FREIRE S L M, ULRYCH T J. Application of singular value decomposition to vertical seismicprofiling[J]. Geophysics, 1988, 53(6): 778-785.
[48]吴亚东,符溪,文鹏飞,王宏语,谭绍泉,任富新,姜维财.奇异值分解压制随机噪声的方法及应用[J].新疆石油地质, 2003, 24(2): 144-145.
[49]刘婉莹,孟凡顺,刘喜武,张宁,高伟,李达.地震数据分数阶域空间预测滤波方法研究[J].中国海洋大学学报, 2008, 38(6): 1008-1012.
[50] JUTTEN C, HERAULT J. Blind separation of sources,Part I: An adaptive algorithm based on neuro mimetic architecture[J]. Signal Processing, 1991, 24: 1-10.
[51]刘喜武,刘洪,李幼铭.独立分量分析及其在地震信息处理中应用初探[J].地球物理进展, 2003, 18(1): 90-96.
[52]彭才,朱仕军,孙建库,陈俊华,夏凌,黄东山.基于独立成分分析的地震数据去噪[J].勘探地球物理进展, 2007, 30(1): 30-32+68.
[53] SERRA J. Image Analysis and Mathematical Morphology[M]. London: Academic Press, 1982.
[54]王润秋,郑桂娟,付洪洲,李青.地震资料处理中的形态滤波去噪方法[J].石油地球物理勘探, 2005, 40(3): 277-282.
[55]夏洪瑞,陈德刚,周开明.地震资料处理中随机干扰消除方法分析[J].石油物探, 2003, 42(1): 93-96.
[56]尹成,伍志明,邓怀群.高阶统计量方法在地震勘探中的应用[J].地球物理进展, 2003, 18(3): 546-550.
[57]邓小英,李月.基于Ricker子波核的支持向量回归方法及其在地震勘探记录去噪处理中的应用[J].吉林大学学报(地球科学版), 2007, 37(4): 821-827.
[58]李月,杨宝俊,林红波,袁野,郝雪,刘晓华.地震勘探时空域双曲滤波因子的特点与提高信噪比的能力[J].地球物理学报, 2008, 51(5): 1557-1566.
[59]于海超,吴涛,刘继承.非线性滤波技术在地震信号处理中的应用[J].佳木斯大学学报(自然科学版), 2007, 25(1): 25-27.
[60] AL-YAHYA K M. Application of the partial Karhunen-Loève transform to suppress random noise in seismic sections[J]. Geophysical Prospecting, 1991, 39(1): 77-93.
[61] DJEDDI M, MIHOUBI A, AITOUCHE M A, DJEDDI M, BENIDIR M. Using the Karhunen-Loeve transform in the sources separation: application for the separaration of field waves in a vertical seismic profile and in the attenuation of multiples (SVP). Proceedings of the Conference: 2004-Dynamical Systems and Applications, 2004[C]. Dehli: GBS Publishers & Distributors, 2005.
[62] HEMON C H, MACE D. Use of the Karhunen-Loeve transformation in seismic data processing[J]. Geophysical Prospecting, 1978, 26: 600-626.
[63]傅才芳,罗国安.应用KL滤波提高地震记录的信噪比[J].石油地球物理勘探, 1986, 21(5): 486-493.
[64] JONES I F, LEVY S. Signal-to-noise ratio enhancement in multichannel seismic data via the Karhumen-Loeve transform[J]. Geophysical Prospecting, 1987, 35: 12-32.
[65]付燕,赵荣椿.应用时空变—倾角扫描叠加KL变换提高地震资料信噪比[J].物探化探计算技术, 2001, 23(4): 303-307.
[66]付燕,赵荣椿.应用改进的KL变换提高叠后地震记录信噪比[J].煤田地质与勘探, 2002, 30(3): 49-54.
[67]刘保童,朱光明.地震记录快速KL滤波的自组织神经网络方法[J].石油地球物理勘探, 2005,40(6): 632-636.
[68] CANALES L L. Random noise reduction. 54th Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts[C]. 1984, 3: 525–527.
[69]国九英.叠前ω-x域算子外推法去噪[J].石油地球物理勘探, 1995, 30(4): 487-494.
[70]蔡加铭,周兴元,吴律. f-x域算子外推去噪技术研究[J].石油地球物理勘探, 1999, 34(3): 325-331.
[71]康冶,于承业,贾卧,王春梅,陈颖. f-x域去噪方法研究[J].石油地球物理勘探, 2003, 38(2): 136-138.
[72]赵德斌,黄真萍,王春梅. F-X域奇异值分解预测滤波法随机噪声衰减[J].石油物探, 1998, 37(3): 29-33.
[73]国九英,周兴元,杨慧珠. f-x,y域随机噪音衰减[J].石油地球物理勘探, 1995, 30(2): 207-215.
[74]苏贵士,周兴元,李承楚.频率空间三维F-XYZ域预测去噪技术[J].石油地球物理勘探, 1998, 33(1): 95-103.
[75] CLAERBOUT J F. Earth Soundings Analysis: Processing Versus Inversion[M]. Oxford: Blackwell Scientific Publications, 1992.
[76] ZHOU B Z, Greenhalgh S A. Linear and parabolicτ-p transforms revisited[J]. Geophysics, 1994, 59(7): 1133-1149.
[77] BENOLIEL S D, SCHNEIDER W A, SHURTLEFF R N. Frequency wavenumber approach of theτ-p transform——Some applications in seismic data processing[J]. Geophysical Prospecting, 1987, 35(5): 517-538.
[78]牛滨华,孙春岩,张中杰,沈操,李英才,吕景贵,王宏语.多项式Radon变换[J].地球物理学报, 2001, 44(2): 263-271.
[79]刘喜武,刘洪,李幼铭.高分辨率Radon变换方法及其在地震信号处理中的应用[J].地球物理学进展, 2004, 19(1): 8-15.
[80] RUSSELL B, HAMPSON D, CHUN J. Noise elimination and the Radon transform, Part1[J]. The Leading Edge, 1990, 9 (9): 18-23.
[81] RUSSELL B, HAMPSON D, CHUN J. Noise elimination and the Radon transform, Part2[J]. The Leading Edge, 1990, 9 (11): 31-37.
[82] SPITZER R, NIETZSCHE F O, GREEN A G. Reducing source-generated noise in shallow seismic data using linear and hyperbolic & tau-p transformations[J]. Geophysics, 2001, 66(5): 1612-1621.
[83] MALLAT S. A Wavelet Tour of Signal Processing[M]. 2nd ed. New York: Academic Press, 1999.
[84] YOUNG R K. Wavelet Theory and its Applications[M]. 1st ed. Dordrecht: Kluwer Academic Publishers, 1993.
[85] GOUPILLAUD P, GROSSMANN A, MORLET J. Cycle-octave and related transforms in seismic analysis[J]. Geoexploration, 1984, 23: 85-102.
[86]章珂,刘贵忠,邹大文,钱俊生,李风岐.二进小波变换方法的地震信号分时分频去噪处理[J].地球物理学报, 1996, 39(2): 265-270.
[87]李鲲鹏,刘业新,李衍达,范存奎.小波变换的过零点特性与地震勘探信号的信噪比和分辨率[J].地球物理学报, 1997, 40(4): 561-568.
[88]宗涛,孟鸿鹰,贾玉兰,刘贵忠.小波包F-X域前后向预测去噪[J].地球物理学报, 1998, 41(增刊): 337-346.
[89]王振国,周熙襄,李晶.基于小波变换的最小光滑滤波去噪[J].石油地球物理勘探, 2002, 37(6): 594-600.
[90]张宇,张关泉.小波变换用于去除高频噪声[J].石油地球物理勘探, 1997, 32 (3): 327-337.
[91]吴爱弟,牟永光.地震信号的小波包分解压噪方法[J].石油地球物理勘探, 1998, 33 (4): 558-562.
[92]吴爱弟,曹思远.用正交多小波压制地震信号的随机噪声[J].石油地球物理勘探, 2002, 37(5):473-476.
[93]王振国,汪恩华.小波包相关阀值去噪[J].石油物探, 2002, 41(4): 400-405.
[94]杨立强,宋海斌,郝天珧,江为为.基于二维小波变换的随机噪声压制方法研究[J].石油物探, 2005, 44(1): 4-6.
[95]彭才,常智,朱仕军.基于曲波变换的地震数据去噪方法[J].石油物探, 2008, 47(5): 461-464.
[96]彭才,常智,韩朝军,朱仕军.基于Contourlet变换的地震噪声衰减[J].勘探地球物理进展, 2008, 31(4): 274-277.
[97]高静怀,毛剑,满蔚仕,陈文超,郑庆庆.叠前地震资料噪声衰减的小波域方法研究[J].地球物理学报, 2006, 49(4): 1155-1163.
[98]黄德芹,贾玉亮,方江雪.模型约束方法在低信噪比地震资料处理中的应用[J].工程地球物理学报, 2006, 3(3): 167-171.
[99]王珺,杨长春,乔玉雷.用稳定高效的反Q滤波技术提高地震资料分辨率[J].地球物理进展, 2008, 23(2): 456-463.
[100] HARGREAVES N D, CALVERT A J. Inverse Q-filtering by Fourier transform[J]. Geophysics, 1991, 56(1): 519-527.
[101] HARGREAVES N D. Similarity and the inverse Q filter: some simple algorithms for inverse Q filtering[J]. Geophysics, 1992, 57(2): 944-947.
[102] STOLT R H. Migration by Fourier transform[J]. Geophysics, 1978, 43(1): 23-48.
[103] HALE D. An inverse Q-filter[R]. Stanford Exploration Project, 1981.
[104] WANG Y H. Quantifying the effectiveness of stabilized inverse Q filtering[J]. Geophysics, 2003, 68(1): 337-345.
[105] WANG Y H. Inverse Q-filter for seismic resolution enhancement[J]. Geophysics, 2006, 71(1): 51-60.
[106]金雷,李月,杨宝俊.用时频峰值滤波方法消减地震勘探资料中随机噪声的初步研究[J].地球物理学进展, 2005, 20(3): 724-728.
[107]林红波,李月,叶文海,潘伟.时频峰值滤波去噪技术及其应用[J].地球物理学进展, 2008, 23(6): 1953-1957.
[108] ZHANG Z J, WANG G J, HARRIS J M. Multi-component wavefield simulation in viscous extensively dilatancy anisotropic media[J]. Physics of the Earth and Planetary Interiors, 1999, 114: 25-38.
[109] ZHANG Z J, WANG G J, TENG J W, et al. CDP mapping to obtain the fine structure of the crust and upper mantle from seismic sounding data: an example for the southeastern China[J]. Physics of the Earth and Planetary Interiors, 2000, 122: 133-146.
[110]张军华,吕宁,田连玉,陆文志,钟磊.地震资料去噪方法、技术综合评述[J].地球物理进展, 2005, 20(4): 1083-1091.
[111]刘建红,孟小红,程玉坤.针对叠前反演的去噪技术[J].石油勘探与开发, 2007, 34(6): 718-723.
[112] RABINER L R, JUANG B H. Fundamentals of Speech Recognition[M]. 1st ed. New York: Prentice-Hall, 1993.
[113] RABINER L R. A tutorial on hidden Markov models and selected applications in speech recognition[J]. Proceedings of the IEEE, 1989, 77(2): 257-286.
[114] VASEGHI S V. Advanced Digital Signal Processing and Noise Reduction[M]. 3rd ed. New York: John Wiley & Sons, 2006.
[115] BAUM L E, PéTRIE T. Statistical inference for probabilistic functions of finite state Markov chains[J]. The Annals of Mathematical Statistics, 1966, 37: 1554-1563.
[116] BAUM L E, EAGON J A. An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology[J]. The Bulletin of the American Mathematical Society, 1967, 73: 360-363.
[117] BAUM L E, SELL G R. Growth transformations for functions on manifolds[J]. The Pacific Journal of Mathematics, 1968, 27(2): 211-217.
[118] BAUM L E, PéTRIE T, SOULES G, WEISS N. A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains[J]. The Annals of Mathematical Statistics, 1970, 41(1):164-171.
[119] BAUM L E. An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes[J]. Inequalities, 1972, 3:1-8.
[120] BAKER J K. The DRAGON system—An overview[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1975, 23(1): 24-29.
[121] JELINEK F. Fast sequential decoding algorithm using a stack[J]. IBM Journal of Research and Development, 1969, 13: 675-685.
[122] BAHL L R, JELINEK F. Decoding for channels with insertions, deletions, and substitutions with applications to speech recongnition[J]. IEEE Transactions on Information Theory, 1975, 21: 404-411.
[123] JELINEK F, BAHL L R, MERCER R L. Design of a linguistic statistical decoder for the recognition of continuous speech[J]. IEEE Transactions on Information Theory, 1975, 21: 250-256.
[124] JELINEK F. Continuous speech recognition by statistical methods[J]. Proceedings of the IEEE, 1976, 64: 532-536.
[125] BAKIS R. Continuous speech recognition via centisecond acoustic states[J]. The Journal of the Acoustical Society of America, 1976, 59(1): 97.
[126] BAHL L R, JELINEK F, MERCER R L. A maximum likelihood approach to continuous speech recognition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, 5: 179-190.
[127] HUANG X D, ARIKI Y, JACK M A. Hidden Markov Models for Speech Recognition[M]. 1st ed. Edinburgh: Edinburgh University Press, 1990.
[128] RABINER L R, JUANG B H. An introduction to hidden Markov models[J]. IEEE ASSP Magazine, 1986, 1: 4-15.
[129] EPHRAIM Y. Statistical-model-based speech enhancement systems[J]. Proceedings of the IEEE, 1992, 80(10): 1526-1555.
[130] JEFFREY H. Scientific Inference[M]. 3rd ed. Cambridge: Cambridge University Press, 1961.
[131] LARSON H J, BRUNO O S. Probabilitic Models in Engeering Sciences. I and II[M]. New York: Wiley, 1979.
[132] SCHARF L L. Statistical Signal Processing: Detection, Estimation, and Time Series Analysis[M]. MA: Addison Wesley, 1991.
[133] CRAMER H. Mathematical Methods of Statistics[M]. NJ: Princeton University Press, 1974.
[134] BERNARDO J M, SMITH A F M. Bayesian Theory[M]. New York: Wiley, 1998.
[135] PRESS S J. Subjective and Objective Bayesian Statistics: Principles, Models, and Applications[M].2nd ed. New York: Wiley, 2003.
[136]冯长建. HMM动态模式识别理论、方法以及在旋转机械故障诊断中的应用[D].杭州:浙江大学机械与能源工程学院, 2002.
[137]赵力.语音信号处理[M].北京:机械工业出版社, 2003.
[138]杨行峻,迟惠生.语音信号数字处理[M].北京:电子工业出版社, 1995.
[139] VITERBI A J. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm[J]. IEEE Transactions on Information Theory, 1967, 13(2): 260-269.
[140] FORNEY G D. The viterbi algorithm[J]. Proceedings of the IEEE, 1973, 61(3): 268-278.
[141] DEMPSTER A P, LAIRD M L, RUBIN D B. Maximum Likelihood from Incomplete Data via the EM Algorithm[J]. Journal of the Royal Statistical Society, 1977, 39(1): 1-38.
[142] LEVINSON S E, RABINER L R, SONDHI M M. An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition[J]. The Bell System Technical Journal, 1983, 62(4): 1035-1074.
[143] FEDER M, WEINSTEIN E. Parameter estimation of superimposed signals using EM algorithm[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1988, 36(4): 477-489.
[144] RENDER R A, WALKER H F. Mixture densities, maximum likelihood and the EM algorithm[J]. SIAM Rev. 1984, 26: 195-239.
[145] LIPORACE L A. Maximum likelihood estimation for multivariate observations of Markov sources[J]. IEEE Transactions on Information Theory, 1982, 28(5): 729-734.
[146] JUANG B H. Maximum likelihood estimation for mixture multivariate stochastic observation of Markov chains[J]. AT&T Technical Journal, 1985, 64(6): 1235-1249.
[147] JUANG B H, LEVINSON S E, SONDHI M M. Maximum likelihood estimation for multivariate mixture observations of markov chains[J]. IEEE Transactions on Information Theory, 1986, 32(2): 307-309.
[148] RABINER L R, JUANG B H, LEVINSON S E, SONDHI M M. Recognition of isolated digits using hidden Markov models with continuous mixture densities[J]. AT&T Technical Journal, 1985, 64(6): 1211-1234.
[149] BAHL L R, BROWN P F, DE SOUZA P V, MERCER L R. Maximum mutual information estimation of hidden Markov model parameters for speech recognition. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing[C]. 1986, 11:49:52.
[150] EPHRAIM Y, DEMBO A, RABINER L R. A minimum discrimination information approach for hidden Markov modeling[J]. IEEE Transactions on Information Theory, 1989, 35(5): 1001-1003.
[151] EPHRAIM Y, RABINER L R. On the relations between modeling approaches for speech recognition[J]. IEEE Transactions on Information Theory, 1990, 36(2): 372-380.
[152]何强,毛士艺,张有为.多观察序列连续隐含马尔柯夫模型的无溢出参数重估[J].电子学报, 2000, 28(10): 98-101.
[153] JELINEK F, MERCER R L. Interpolated estimation of Markov source parameters from sparse data. Pattern Recognition in Practice[M]. Gelesma E S, Kanal L N. 1st ed. Netherlands: North-Holland, 1980.
[154] HARVEY A C, KOOPMAN S J, SHEPHARD N. State space and unobserved component models[M]. Cambridge: Cambridge University Press, 2004.
[155] KIM S, SHEPHARD N, CHIB S. Stochastic volatility: Likelihood inference and comparison with ARCH models[J]. Review of Economics Studies, 1998, 65:361-393.
[156] WEST M, HARRISON J. Bayesian forecasting and dynamic models[M]. 2nd ed. New York:Springer-Verlag, 1999.
[157] LAVIELLE M. Bayesian deconvolution of Bernoulli-Gaussian processes[J]. Signal Processing, 1993, 33: 67-79.
[158] FARHMEIR L, TUTZ G. Multivariate statistical modelling based on generalzed linear models. Springer Series in Statistics[M]. 2nd ed. New York: Springer, 2001.
[159] CHEN Z. Bayesian fitering: From Kalman filters to particle filters, and beyond. Technical Report[R]. Hamilton: Adaptive Systems Lab, McMaster University, 2003.
[160]陈学华.状态空间模型理论与算法及其在金融计量中的应用[D].广州:暨南大学经济学院, 2007.
[161] KITAGAWA G. Non-Gaussian state-space modeling of nonstationary time series[J]. Journal of the American Statistical Association, 1987, 82(400): 1032-1041.
[162] GODSILL S J, DOUCET A, WEST M. Monte Carlo smoothing for nonlinear time series[J]. Journal of the American Statistical Association, 2004, 99(465): 156-167.
[163] GILKS W R, BERZUINI C. Following a moving target-Monte Carlo inference for dynamic Bayesian models[J]. Journal of the Royal Statistical Society, Ser. B. 2000, 63: 1-20.
[164] KITAGAWA G. A self organizing state space model[J]. Jounal of the American Statistical Association, 1998, 93: 1203-1215.
[165] SHEPARD N, PITT M K. Likelihood analyis of non-Gaussian measurement time series[J]. Biometrika, 1997, 84:653-667.
[166] ARULAMPALAM M S, MASKELL S, GORDON N, CLAPP T. A tutorial on particle filters for online nonlinear/Non-Gaussian Bayesian tracking[J]. IEEE Transactions on Signal Processing, 2002, 50(2): 174-188.
[167] DOUCET A, GODSILL S, ANDRIEU C. On sequential Monte Carlo sampling methods for Bayesian filtering[J]. Statistics and Computing, 2000, 10: 197-208.
[168] QUATIERI T F. Discrete-Time Speech Signal Processing: Principles and Practice[M]. 1st ed. New York: Prentice-Hall, 2002.
[169]刘喜武,刘洪.地震盲反褶积综述[J].地球物理学进展, 2003, 18(2): 203-209.
[170]刘财,陈业全,刘洋,王典,李勤学,苗广文.勘探地震资料处理新方法及新技术[M].北京:科学出版社, 2006.
[171] RICKER N. The form and nature of seismic waves and the structure of seismograms[J]. Geophysics, 5: 348-366.
[172] TANAKA M, SAKAWA M, SHIROMARU M, MATSUMOTO T. Application of Kohonen's self-organizing netwok to the diagnosis system for rotating machinary. Systems, Man and Cybernetics. Proceedings of IEEE International Conference on Intelligent Systems for the 21st Century[C]. 1995, 5: 4039-4044.
[173]王庆海.浅层地震勘探记录信号的特点及消除干扰方法[J].物探与化探, 1991, 15(3): 237-240.
[174]高静怀,汪文秉,朱光明,彭玉华,王玉贵.地震资料处理中小波函数的选取研究[J].地球物理学报, 1996, 39(3): 392-399.
[175]付燕.人工地震信号去噪方法研究[D].西安:西北工业大学计算机科学与工程系, 2002.
[176]长春地质学院、成都地质学院、武汉地质学院合编.地震勘探——原理和方法[M].北京:地质出版社, 1980.
[177]李玉新.地震相干技术在断层与沉积相解释中的应用[J].沉积与特提斯地质, 2006, 26(3): 67-71.
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