Researches On Adaptive Polarization Filtering For Multi-component Seismic Data

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.