多分量地震自适应极化滤波方法研究
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摘要
与常规单分量反射地震相比，多分量地震的波场信息更加丰富，联合利用纵波激发、多分量检波器接收的多波地震资料，可以解决复杂构造成像、裂隙描述及岩性勘探等难题。但是，由于多分量地震的波场比较复杂，根据不同的勘探目的，需要将不同的波场信息进行分离及去噪，为后续的资料处理和解释提供高质量的数据。
不同类型地震波的极化特性不同，实际采集到的地震波是不同类型、不同极化特性的振动相互干涉和叠加的结果。极化分析就是一种基于地震波的极化特性基础上的信号处理方法，通过测量各种类型地震波的极化属性来简化信息的提取，在特定波型的识别与分离、各类噪声的压制、横波分裂分析、多波震相识别和确定波至到时等方面都有很好的效果。因此，多分量地震极化分析研究对于多分量地震的理论研究和实际应用有着深远的意义。
本文针对多分量地震，在时间域和时频域分别研究了极化分析和滤波方法,取得了如下成果：
（1）在S变换的基础上，提出了一种改进的广义S变换（NGST）。改进的广义S变换主要针对窗函数进行改造，引入了一个以频率为自变量的调节函数，该时窗采用宽度可变的高斯函数，通过设置调节因子，使得窗函数的宽度可以随信号频率呈线性或指数变化。这样，不仅能使窗函数的时宽随频率变化的速率变快，同时，窗函数时宽大小随频率的变化不再受线性变化的约束，这更符合非平稳地震信号的特点。通过合成信号的S变换和NGST时频谱对比分析，NGST时频谱在各频率成份的能量中心的聚集性更好，时频分辨率得到了提高，为后续时频域极化分析方法的研究奠定了数学基础。
（2）标准协方差矩阵的时间域极化分析方法窗口长度固定，在实际应用中，时窗长度的选择完全依赖于经验判断，而且在给定长度的时窗内求得的极化参数不具有时变特性，因此，不可避免地会出现解释上的假象。另外，由于时窗长度的影响，无法确定记录开始和结束部分的极化参数。目前，该方法在实际应用中有很大的局限性。鉴于此，本文引入了自适应窗函数，该窗函数的长度自适应于三分量地震记录的瞬时频率，避免了在选择时窗长度时的人为影响。而且该极化分析方法是在三分量地震记录的每一个时间采样点上求极化特征参数的，因此不需要进行插值处理。
（3）将自适应协方差极化分析方法和时频分析方法相结合，研究了基于小波变换和广义S变换的时频域自适应协方差极化分析方法。该方法建立在协方差矩阵的基础上，用一个近似方程来计算时窗内的协方差矩阵，这个时窗是由多分量记录的瞬时频率确定的，其长度自适应于每个时频点处的地震波的优势周期；在每个时频点估计极化特征参数，不需要进行插值；明确地将极化分布和时频分析方法联系起来，在时频域设计中滤波器，进行波场识别和分离。处理结果表明，该方法可以在时频域中准确提取各个采样点的所有极化属性，具有一定的实用性。
（4）在广义S变换时频分析方法基础上，实现了一种时频域瞬时极化分析新方法。该方法不再依赖协方差矩阵，而是根据多分量信号的时频谱及瞬时相位来计算极化参数，例如极化主轴、极化次轴、极化率、平面化向量等。由于该方法在时频域中实现，结合了时频分析方法的优势，在波形识别方面更加准确。通过极化率可以识别并分离线性极化波和椭圆及圆形极化波，通过平面化向量与各分量之间的夹角大小，定性识别平面波和非平面波。
（5）结合广义S变换和谱分解方法，在时频域通过多分量地震数据时频谱的实部和虚部来表征极化椭圆，通过求取时频域中极化椭圆在每一个时频点的极化参数，将各分量信号分解为“线性”信号和“圆形”信号，再对各分量的“线性”信号和“圆形”信号进行广义S反变换，最终得到线性极化波和椭圆极化波，达到波场分离的目的。该方法的一个优点在于在压制具有某一种极化特性的地震波的同时不会影响其他极化特性的地震波的振幅，比如在压制椭圆极化波的时候，能够完全保留线性极化波。
由于各种极化分析方法在不同滤波目的情况下，效果也不尽相同。因此，在论文的结论部分，给出了针对不同处理目的的极化方法选择方案。
The multi-components Seismic data contain more information as compared withconventional single-component reflection seismic exploration. We can use the jointmulti-wave information to resolve many problems which cannot be realized with reflectionseismic. Meanwhile, because the wave-field of multi-wave Multi-component Seismic is morecomplex, in order to provide high-quality data for subsequent data processing andinterpretation, we need to separate and denoising according to specific exploration target.
Different type of seismic wave has different polarization properties. The actuallycollected seismic wave is interfered and superimposed by vibrations with different type anddifferent polarization property. Polarization analysis is a signal processing method based onpolarization characteristic of seismic wave. It can simplify the extraction of information bymeasuring the polarization properties of the various types of seismic waves. Thus, it havegood effects on specific wave-type identification and separation, separation of various typesof noise, noise suppression, multi-wave seismic phase identification and wave arrival timedetermination. With that said, researches of polarization analysis for multi-wavemulti-component Seismic has profound significance to the theoretical study and practicalapplication of the multi-wave multi-component seismic exploration.
In this paper, we respectively studied polarization analysis and filtering methods in timedomain and time-frequency domain for the multi-wave multi-component seismic data, and gotthe following achievements:
(1) An improved generalized S transform (NGST) is put forward based on S transform.The NGST introduces a tuning function whose independent variable is frequency in timewindow named variable-width Gaussian function. The width of the window function linearlyor exponentially changes with the frequency of signal by setting the adjustable factor. In thisway, On the one hand, we can make the rate of window function width with a frequencybecomes faster, On the other hand, the change of the window function width with thefrequency is no longer bounded by the linear changes, that is more correspond with thecharacteristics of the non-stationary seismic signals. Through comparing time-frequencyspectra of synthesized signal by S transform and NGST, we can find that NGST has a good aggregation in the energy center of the every frequency component and has a higherresolution, which has laid the mathematical foundation for the subsequent polarizationanalysis method in time-frequency domain.
(2) The window length in Polarization analysis method based on standard covariancematrix in time domain is fixed. In the practical application, the selection of time windowlength of the standard covariance method is entirely dependent on the experience, and thepolarization attributions in given length window don’t have time-varying characteristic. So itwill inevitably appear gloss in interpretation. In addition, due to the impact of time windowlength, we cannot determine the beginning and end part of the polarization parameters, thatlead to this method has great limitation in the practical application. For this reason, the paperintroduces an adaptive window function, whose length adapts to instantaneous frequency ofthree-component seismic data and it reduces the factitious impact of the window lengthselection. Even more the polarization analysis method calculates the polarization parametersat each time sampling point of three-component seismic data without interpolation.
(3) Combing the adaptive covariance matrix polarization analysis and time-frequencyanalysis method, we propose the adaptive covariance matrix polarization analysis based onwavelet transform and generalized S transform in time-frequency domain. Established oncovariance matrix, this method uses an approximate equation to calculate the covariancematrix within the time window. This time window is determined by the instantaneousfrequency of multi-component records and its length adapts to advantage cycle of wave ateach time-frequency point. It estimates the polarization characteristic parameters in eachtime-frequency point and don’t require interpolation, and it definitely links the polarizationdistributions and time-frequency analysis methods. We can design filter in time-frequencydomain and separate the wave fields. The results show that this method can accurately extractall polarization properties of each sampling point in time-frequency domain and is very usefulin practical applications.
(4) Based on the generalized S transform, we propose a new polarization analysismethod in time-frequency domain. This method no longer depends on the covariance matrix,calculates the polarization parameters by the time-frequency spectrum and instantaneousphase of multi-component signals, such as semi-major axis, semi-minor axis, polarization ratio, planarity vector and so on. Because it combines the advantages of time-frequencyanalysis method in time-frequency domain, it is more accurate in waveform recognition. Wecan judge and separate linear polarized wave and ellipse and circular polarized wave bypolarization ratio, also can qualitatively identify the plane wave and out-of-plane wave by thecorresponding cosine direction of the planarity vector.
(5) We characterize the polarization ellipse in time-frequency domain by combininggeneralized S transform and spectral decomposition technique. The signal of each componentis decomposed into “linear” and “circular” signal trough calculating polarization parametersof polarization ellipse at each time-frequency point, then the “linear” and “circular” signal ofeach component is done with the generalized S inverse transform and get linearly polarizedwaves and elliptically polarized waves at the end, to achieve the purpose of the wave fieldseparation. One of the advantages of the method is that it doesn’t affect the amplitude ofseismic wave having other polarization characteristics when suppressing a certain kind ofseismic wave, for example, the linear part can be fully retained when suppressing the circularpart of polarization ellipse.
A variety of polarization analysis methods have different effect due to different filteringpurposes. So, this paper gives the options of polarization methods based on different filteringpurpose.
不同类型地震波的极化特性不同，实际采集到的地震波是不同类型、不同极化特性的振动相互干涉和叠加的结果。极化分析就是一种基于地震波的极化特性基础上的信号处理方法，通过测量各种类型地震波的极化属性来简化信息的提取，在特定波型的识别与分离、各类噪声的压制、横波分裂分析、多波震相识别和确定波至到时等方面都有很好的效果。因此，多分量地震极化分析研究对于多分量地震的理论研究和实际应用有着深远的意义。
本文针对多分量地震，在时间域和时频域分别研究了极化分析和滤波方法,取得了如下成果：
（1）在S变换的基础上，提出了一种改进的广义S变换（NGST）。改进的广义S变换主要针对窗函数进行改造，引入了一个以频率为自变量的调节函数，该时窗采用宽度可变的高斯函数，通过设置调节因子，使得窗函数的宽度可以随信号频率呈线性或指数变化。这样，不仅能使窗函数的时宽随频率变化的速率变快，同时，窗函数时宽大小随频率的变化不再受线性变化的约束，这更符合非平稳地震信号的特点。通过合成信号的S变换和NGST时频谱对比分析，NGST时频谱在各频率成份的能量中心的聚集性更好，时频分辨率得到了提高，为后续时频域极化分析方法的研究奠定了数学基础。
（2）标准协方差矩阵的时间域极化分析方法窗口长度固定，在实际应用中，时窗长度的选择完全依赖于经验判断，而且在给定长度的时窗内求得的极化参数不具有时变特性，因此，不可避免地会出现解释上的假象。另外，由于时窗长度的影响，无法确定记录开始和结束部分的极化参数。目前，该方法在实际应用中有很大的局限性。鉴于此，本文引入了自适应窗函数，该窗函数的长度自适应于三分量地震记录的瞬时频率，避免了在选择时窗长度时的人为影响。而且该极化分析方法是在三分量地震记录的每一个时间采样点上求极化特征参数的，因此不需要进行插值处理。
（3）将自适应协方差极化分析方法和时频分析方法相结合，研究了基于小波变换和广义S变换的时频域自适应协方差极化分析方法。该方法建立在协方差矩阵的基础上，用一个近似方程来计算时窗内的协方差矩阵，这个时窗是由多分量记录的瞬时频率确定的，其长度自适应于每个时频点处的地震波的优势周期；在每个时频点估计极化特征参数，不需要进行插值；明确地将极化分布和时频分析方法联系起来，在时频域设计中滤波器，进行波场识别和分离。处理结果表明，该方法可以在时频域中准确提取各个采样点的所有极化属性，具有一定的实用性。
（4）在广义S变换时频分析方法基础上，实现了一种时频域瞬时极化分析新方法。该方法不再依赖协方差矩阵，而是根据多分量信号的时频谱及瞬时相位来计算极化参数，例如极化主轴、极化次轴、极化率、平面化向量等。由于该方法在时频域中实现，结合了时频分析方法的优势，在波形识别方面更加准确。通过极化率可以识别并分离线性极化波和椭圆及圆形极化波，通过平面化向量与各分量之间的夹角大小，定性识别平面波和非平面波。
（5）结合广义S变换和谱分解方法，在时频域通过多分量地震数据时频谱的实部和虚部来表征极化椭圆，通过求取时频域中极化椭圆在每一个时频点的极化参数，将各分量信号分解为“线性”信号和“圆形”信号，再对各分量的“线性”信号和“圆形”信号进行广义S反变换，最终得到线性极化波和椭圆极化波，达到波场分离的目的。该方法的一个优点在于在压制具有某一种极化特性的地震波的同时不会影响其他极化特性的地震波的振幅，比如在压制椭圆极化波的时候，能够完全保留线性极化波。
由于各种极化分析方法在不同滤波目的情况下，效果也不尽相同。因此，在论文的结论部分，给出了针对不同处理目的的极化方法选择方案。
The multi-components Seismic data contain more information as compared withconventional single-component reflection seismic exploration. We can use the jointmulti-wave information to resolve many problems which cannot be realized with reflectionseismic. Meanwhile, because the wave-field of multi-wave Multi-component Seismic is morecomplex, in order to provide high-quality data for subsequent data processing andinterpretation, we need to separate and denoising according to specific exploration target.
Different type of seismic wave has different polarization properties. The actuallycollected seismic wave is interfered and superimposed by vibrations with different type anddifferent polarization property. Polarization analysis is a signal processing method based onpolarization characteristic of seismic wave. It can simplify the extraction of information bymeasuring the polarization properties of the various types of seismic waves. Thus, it havegood effects on specific wave-type identification and separation, separation of various typesof noise, noise suppression, multi-wave seismic phase identification and wave arrival timedetermination. With that said, researches of polarization analysis for multi-wavemulti-component Seismic has profound significance to the theoretical study and practicalapplication of the multi-wave multi-component seismic exploration.
In this paper, we respectively studied polarization analysis and filtering methods in timedomain and time-frequency domain for the multi-wave multi-component seismic data, and gotthe following achievements:
(1) An improved generalized S transform (NGST) is put forward based on S transform.The NGST introduces a tuning function whose independent variable is frequency in timewindow named variable-width Gaussian function. The width of the window function linearlyor exponentially changes with the frequency of signal by setting the adjustable factor. In thisway, On the one hand, we can make the rate of window function width with a frequencybecomes faster, On the other hand, the change of the window function width with thefrequency is no longer bounded by the linear changes, that is more correspond with thecharacteristics of the non-stationary seismic signals. Through comparing time-frequencyspectra of synthesized signal by S transform and NGST, we can find that NGST has a good aggregation in the energy center of the every frequency component and has a higherresolution, which has laid the mathematical foundation for the subsequent polarizationanalysis method in time-frequency domain.
(2) The window length in Polarization analysis method based on standard covariancematrix in time domain is fixed. In the practical application, the selection of time windowlength of the standard covariance method is entirely dependent on the experience, and thepolarization attributions in given length window don’t have time-varying characteristic. So itwill inevitably appear gloss in interpretation. In addition, due to the impact of time windowlength, we cannot determine the beginning and end part of the polarization parameters, thatlead to this method has great limitation in the practical application. For this reason, the paperintroduces an adaptive window function, whose length adapts to instantaneous frequency ofthree-component seismic data and it reduces the factitious impact of the window lengthselection. Even more the polarization analysis method calculates the polarization parametersat each time sampling point of three-component seismic data without interpolation.
(3) Combing the adaptive covariance matrix polarization analysis and time-frequencyanalysis method, we propose the adaptive covariance matrix polarization analysis based onwavelet transform and generalized S transform in time-frequency domain. Established oncovariance matrix, this method uses an approximate equation to calculate the covariancematrix within the time window. This time window is determined by the instantaneousfrequency of multi-component records and its length adapts to advantage cycle of wave ateach time-frequency point. It estimates the polarization characteristic parameters in eachtime-frequency point and don’t require interpolation, and it definitely links the polarizationdistributions and time-frequency analysis methods. We can design filter in time-frequencydomain and separate the wave fields. The results show that this method can accurately extractall polarization properties of each sampling point in time-frequency domain and is very usefulin practical applications.
(4) Based on the generalized S transform, we propose a new polarization analysismethod in time-frequency domain. This method no longer depends on the covariance matrix,calculates the polarization parameters by the time-frequency spectrum and instantaneousphase of multi-component signals, such as semi-major axis, semi-minor axis, polarization ratio, planarity vector and so on. Because it combines the advantages of time-frequencyanalysis method in time-frequency domain, it is more accurate in waveform recognition. Wecan judge and separate linear polarized wave and ellipse and circular polarized wave bypolarization ratio, also can qualitatively identify the plane wave and out-of-plane wave by thecorresponding cosine direction of the planarity vector.
(5) We characterize the polarization ellipse in time-frequency domain by combininggeneralized S transform and spectral decomposition technique. The signal of each componentis decomposed into “linear” and “circular” signal trough calculating polarization parametersof polarization ellipse at each time-frequency point, then the “linear” and “circular” signal ofeach component is done with the generalized S inverse transform and get linearly polarizedwaves and elliptically polarized waves at the end, to achieve the purpose of the wave fieldseparation. One of the advantages of the method is that it doesn’t affect the amplitude ofseismic wave having other polarization characteristics when suppressing a certain kind ofseismic wave, for example, the linear part can be fully retained when suppressing the circularpart of polarization ellipse.
A variety of polarization analysis methods have different effect due to different filteringpurposes. So, this paper gives the options of polarization methods based on different filteringpurpose.
引文
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