探地雷达信号分辨率提高方法研究
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摘要
探地雷达作为一种高效的浅层地球物理探测技术，它的发展从20世纪初到现在，已经经历了一个世纪。随着探地雷达的进一步发展及应用，对于分辨率的要求越来越高。然而由于探地雷达的工作原理是通过向地下发射和接收高频电磁波从而实现对目标体的探测。与探空雷达电磁波在理想无耗介质中的传播所不同的是，探地雷达工作主要对象为有耗介质，探地雷达波在有耗介质中传播时会发生衰减和频散现象导致接收到的数据图像变得模糊失真，影响了探地雷达探测的深度和分辨率，这使得探地雷达的高分辨率这一优点受到了一定的限制，制约了高分辨率探地雷达技术的发展。鉴于衰减与频散对雷达波的影响，提高探地雷达分辨率的方法研究就显得非常有意义。高分辨率探地雷达技术的研究主要涉及到基本理论研究，方法研究和仪器研究三大方面。本文针对提高探地雷达分辨率技术主要进行的是方法研究，更确切是说本文进行的是提高探地雷达分辨率技术的信号处理算法的研究。围绕着提高探地雷达分辨率这一宗旨，本文的主要研究包括探地雷达品质因子Q值的估计，反Q滤波以及反褶积三个部分，这三部分主要研究内容简单介绍如下：
针对探地雷达品质因子Q的估计问题，本文对振幅谱比法求Q值算法进行了改进，把利用傅里叶变换求单一的频谱值转化成利用时频分析理论来求时频谱，利用这个时频谱的比值来估计Q值。
本文进一步发展了利用频率漂移法估计Q值的算法，并利用多层常Q模型对本算法进行了验证。
本文实现了利用探地雷达直达波的包络峰值处瞬时频率来估计Q值的方法。借鉴地震理论中的子波可以由四个参数：调制频率，子波的能量衰减因子，以及子波的幅度和相位来确定这一理论，在水平层状介质中,设每层的Q值为常数(即Q值和频率无关),从平面波的单程波传播理论的频率域方程出发,借助包络峰值处瞬时频率的定义，经过公式推导可知，Q值是由包络峰值处的瞬时频率的变化，传播时间以及子波能量衰减因子共同确定的，得到了利用探地雷达VRP资料直达波的包络峰值处瞬时频率来估计Q值的方法。并利用FDTD理论合成的实验数据以及野外实际数据对该算法的有效性和准确性进行了验证。
本文借鉴地震上的反Q滤波算法，把波场延拓理论结合广义S变换理论应用到探地雷达信号层状介质的反Q滤波数据处理中，假定地下Q模型为多层常Q结构，对每个常Q层，将地表波场记录直接延拓到当前层顶部；在常Q层内对延拓后的波场在时频域采用广义Ｓ变换，对信号进行反Q滤波；对滤波结果求广义Ｓ反变换，得到反Q滤波后的时域信号。最后利用本方法对基于波场延拓理论合成的层状探地雷达衰减记录和采用FDTD理论得到的两层探地雷达衰减记录进行了振幅和相位补偿，验证了该算法在探地雷达反Q滤波中的正确性和有效性。
本文把探地雷达吸收频散介质中的反Q滤波方法和介质的逆散射理论联系起来，根据散射场理论和格林函数理论的相关知识，把探地雷达中层状介质的反Q滤波转化为介质的逆散射问题。通过对逆散射问题的求解从而达到补偿电磁波在地下传播过程中幅值和相位所产生的畸变的目的。
本文对传统的探地雷达褶积模型进行了讨论，提出了用线性时变系统来描述雷达的回波信号，即把雷达回波信号描述成子波和地层两者的线性积分形式，为了验证该模型的正确性，本文把这个模型用到探地雷达子波提取的过程中，采用的地下介质分别为传统意义上的层状介质以及具有局部小尺度的非均匀特性的随机介质和野外实际数据，验证了这种线性时变系统比传统的线性时不变系统的褶积形式能够更好的来描述探地雷达回波信号。
在探地雷达子波提取的过程中，本文把分数阶傅里叶变换理论应用到探地雷达子波求取算法中，在提取子波的过程中，假设探地雷达信号满足分数阶傅里叶变换最优滤波的先验知识，利用分数阶傅里叶变换是酉变换，具有保范性这一特点，把子波的提取问题转化为在分数阶傅里叶变换域上的最优滤波问题。在分数阶傅里叶变换域上找到最优解，最后经过分数阶傅里叶变换反变换得到子波估计的时域信号。并针对单一的最优滤波效果不够理想以及信号受到噪声的影响时，单一的最优滤波不能满足需要的问题，本文提出了分数阶傅里叶域上的多级滤波的概念，以达到消除单一滤波的最优滤波效果不够理想和消除信号受到噪声的影响的目的。本文的子波提取算法对于子波的形状和特点没有做特殊的要求，所以本文所述的算法更具有普遍性。
建立在上面所述的线性时变地层系统响应模型基础之上，本文提出了基于地层频谱补偿因子探地雷达反褶积技术，本文通过分数阶傅里叶变换最优滤波算法在分数阶傅里叶变换域上来求取一个地层频谱校正因子以达到对原始记录的频谱进行校正,提高分辨率的目的。并且把本文提出的算法与建立在传统的褶积模型的基于地层频谱补偿因子探地雷达反褶积算法进行了对比，验证了本文所提出的算法比传统方法更加合理有效。
As an efficient shallow geophysical detection technology, the development of theground penetrating radar has experienced a century from the early20th century to now. Withthe further development and application of ground penetrating radar, the resolution isdemanded to improve itself higher and higher. However, the working principle of groundpenetrating radar is that the target body is detected through the ground penetrating radartransmitting and receiving high frequency electromagnetic wave to the underground. Themain work object of the ground penetrating radar is loss medium whereas the sky penetratingradar electromagnetic wave is transmitted in idea lossless medium. When the groundpenetrating radar wave transmits in the loss medium, the attenuation and dispersion can occur.It makes the data image received become fuzzy distortion and can affect the detection depthand resolution of ground penetrating radar. This makes the advantage of the high resolutionof ground penetrating radar be of restrictions and restricts the development of high resolutionground penetrating radar technology. In view of the influence of attenuation and dispersionon the radar wave, it is very meaningful to improve the resolution of ground penetrating radar.High resolution ground penetrating radar technology research involves basic theoreticalresearch, methods research and equipment three main areas. In this paper, aimed at improvingground penetrating radar resolution technology, methods research is the focus. More precisely,the study of signal processing algorithms to improve the ground penetrating radar resolutiontechnology is the focus in this paper. For improving the ground penetrating radar resolution,the main study contents involve the estimation of ground penetrating radar quality factor Q,the inverse Q filtering and deconvolution three parts. This three parts research contents areintroduced as follows:
Aiming at the problem of estimating ground penetrating radar quality factor Q, thealgorithm to obtain Q value using amplitude spectral ratio has been improved. Initially, asingle spectrum is obtained by using Fourier transform. But now, time frequency spectrum isobtained by using time-frequency analysis. The Q value is estimated by using the ratio oftime frequency spectrum.
The algorithm of estimating Q value by using frequency shift method is furtherdeveloped in this paper. this algorithm is validated by taking advantage of layered constant Q-model.
The wavelet is confirmed by modulation frequency, Energy attenuation factor of wavelet,the amplitude and phase of wavelet in seismic theory. Drawing lessons from this theory inthis paper, the Q value in each layer is set as a constant in horizontally layered medium (Qvalue is independent of frequency). And firstly the frequency-domain equation of the singlepass propagation theory of plane wave is solved. Through definition envelope peakinstantaneous frequency and discussing algorithm, it shows that Q value is confirmed by thechanges of envelope peak instantaneous frequency, travel time and the wavelet energyattenuation factor. So the method to estimate Q value using envelope peak instantaneousfrequency of ground penetrating radar VRP data direct wave is obtained. At last, theeffectiveness and accuracy of the algorithm is verified using synthetic VRP data andsynthesis experimental data applying FDTD theory and practical data.
Drawing lessons from inverse Q filtering algorithm in the seismic theory, the theory ofwavefield downward continuation is combined with generalized S transform and the jointtheory is applied to the data processing of inverse Q filtering of ground penetrating radarsignal horizontally layered medium. The underground Q model is assumed to layeredconstant Q structure and for each constant Q layer, the earth’s surface wavefield records isdirectly prolonged the top of current layer; the wave domain prolonged is done generalized Stransform in time frequency domain in constant Q layer and the signal is done inverse Qfiltering; the filtering result is done generalized S inverse transform and the time domainsignal after being inverse Q filtering is obtained. Finally, the complex layered groundpenetrating radar attenuation records based on the theory of wavefield downwardcontinuation and the two layer ground penetrating radar attenuation records obtained fromFDTD theory are done amplitude and phase compensation. It verifies the effectiveness andaccuracy of the algorithm in ground penetrating radar inverse Q filtering.
Inverse Q filtering method in ground penetrating radar absorption dispersion mediumand the inverse scattering theory of medium are combined in this paper. The problem ofinverse Q filtering of layered medium in ground penetrating radar is transformed into theproblem of inverse scattering of medium according to scattering domain theory and greenfunction knowledge. The distortion of amplitude and phase generated in communicationprocess of electromagnetic waves in the underground is compensated by solving inversescattering problem.
The traditional ground penetrating radar convolution model is discussed in this paper. Itproposes to use linear time-varying systems to describe the radar return signal. Namely, theradar return signal is described to linear integral form between wavelet and formation. For validating the correctness of this model, the model is used in the process of extracting groundpenetrating radar wavelet in this paper. In this process, the underground medium used aretraditional layered medium and random medium possessing local small scale inhomogeneouscharacter. The final result shows that this kind of linear time-varying systems can be better todescribe the ground penetrating radar return signal than the convolution form of thetraditional linear time invariant system.
Fractional Fourier transform theory is applied to ground penetrating radar waveletextraction algorithm in the process of ground penetrating radar wavelet extraction in thispaper. It assumes that ground penetrating radar signal meets the prior knowledge of fractionalFourier transform optimal filtering in the process of wavelet extraction. The problem ofwavelet extraction can be transformed the problem of optimal filtering in fractional Fouriertransform domain since fractional Fourier transform is a unitary transform and has normconserving. The optimal solution is found in fractional Fourier transform domain and finallythe time domain signal of wavelet estimation is obtained after fractional Fourier transforminverse transform. In addition, when the single optimal filter is not ideal and the signal isaffected by noise, single optimal filter can not meet the needs. Thus a concept of multilevelfilter in the fractional Fourier transform domain is proposed. The shape and characteristics ofwavelet have no special requirements in the wavelet extraction algorithm in this paper. So,the algorithm described in this article is more universal.
Ground penetrating radar deconvolution technology based on formation spectrumcompensation factor and linear time varying formation system response model is proposed inthis paper. A formation spectrum correction factor in the fractional Fourier transform domainis solved using fractional Fourier transform optimal filtering algorithm to verify the originalrecords of the spectrum and improve resolution. The algorithm proposed in this paper iscompared with ground penetrating radar deconvolution algorithm built on the traditionalconvolution model and based on formation spectrum correction factor. The result verifies theproposed algorithm is more reasonable and effective than the traditional methods.
针对探地雷达品质因子Q的估计问题，本文对振幅谱比法求Q值算法进行了改进，把利用傅里叶变换求单一的频谱值转化成利用时频分析理论来求时频谱，利用这个时频谱的比值来估计Q值。
本文进一步发展了利用频率漂移法估计Q值的算法，并利用多层常Q模型对本算法进行了验证。
本文实现了利用探地雷达直达波的包络峰值处瞬时频率来估计Q值的方法。借鉴地震理论中的子波可以由四个参数：调制频率，子波的能量衰减因子，以及子波的幅度和相位来确定这一理论，在水平层状介质中,设每层的Q值为常数(即Q值和频率无关),从平面波的单程波传播理论的频率域方程出发,借助包络峰值处瞬时频率的定义，经过公式推导可知，Q值是由包络峰值处的瞬时频率的变化，传播时间以及子波能量衰减因子共同确定的，得到了利用探地雷达VRP资料直达波的包络峰值处瞬时频率来估计Q值的方法。并利用FDTD理论合成的实验数据以及野外实际数据对该算法的有效性和准确性进行了验证。
本文借鉴地震上的反Q滤波算法，把波场延拓理论结合广义S变换理论应用到探地雷达信号层状介质的反Q滤波数据处理中，假定地下Q模型为多层常Q结构，对每个常Q层，将地表波场记录直接延拓到当前层顶部；在常Q层内对延拓后的波场在时频域采用广义Ｓ变换，对信号进行反Q滤波；对滤波结果求广义Ｓ反变换，得到反Q滤波后的时域信号。最后利用本方法对基于波场延拓理论合成的层状探地雷达衰减记录和采用FDTD理论得到的两层探地雷达衰减记录进行了振幅和相位补偿，验证了该算法在探地雷达反Q滤波中的正确性和有效性。
本文把探地雷达吸收频散介质中的反Q滤波方法和介质的逆散射理论联系起来，根据散射场理论和格林函数理论的相关知识，把探地雷达中层状介质的反Q滤波转化为介质的逆散射问题。通过对逆散射问题的求解从而达到补偿电磁波在地下传播过程中幅值和相位所产生的畸变的目的。
本文对传统的探地雷达褶积模型进行了讨论，提出了用线性时变系统来描述雷达的回波信号，即把雷达回波信号描述成子波和地层两者的线性积分形式，为了验证该模型的正确性，本文把这个模型用到探地雷达子波提取的过程中，采用的地下介质分别为传统意义上的层状介质以及具有局部小尺度的非均匀特性的随机介质和野外实际数据，验证了这种线性时变系统比传统的线性时不变系统的褶积形式能够更好的来描述探地雷达回波信号。
在探地雷达子波提取的过程中，本文把分数阶傅里叶变换理论应用到探地雷达子波求取算法中，在提取子波的过程中，假设探地雷达信号满足分数阶傅里叶变换最优滤波的先验知识，利用分数阶傅里叶变换是酉变换，具有保范性这一特点，把子波的提取问题转化为在分数阶傅里叶变换域上的最优滤波问题。在分数阶傅里叶变换域上找到最优解，最后经过分数阶傅里叶变换反变换得到子波估计的时域信号。并针对单一的最优滤波效果不够理想以及信号受到噪声的影响时，单一的最优滤波不能满足需要的问题，本文提出了分数阶傅里叶域上的多级滤波的概念，以达到消除单一滤波的最优滤波效果不够理想和消除信号受到噪声的影响的目的。本文的子波提取算法对于子波的形状和特点没有做特殊的要求，所以本文所述的算法更具有普遍性。
建立在上面所述的线性时变地层系统响应模型基础之上，本文提出了基于地层频谱补偿因子探地雷达反褶积技术，本文通过分数阶傅里叶变换最优滤波算法在分数阶傅里叶变换域上来求取一个地层频谱校正因子以达到对原始记录的频谱进行校正,提高分辨率的目的。并且把本文提出的算法与建立在传统的褶积模型的基于地层频谱补偿因子探地雷达反褶积算法进行了对比，验证了本文所提出的算法比传统方法更加合理有效。
As an efficient shallow geophysical detection technology, the development of theground penetrating radar has experienced a century from the early20th century to now. Withthe further development and application of ground penetrating radar, the resolution isdemanded to improve itself higher and higher. However, the working principle of groundpenetrating radar is that the target body is detected through the ground penetrating radartransmitting and receiving high frequency electromagnetic wave to the underground. Themain work object of the ground penetrating radar is loss medium whereas the sky penetratingradar electromagnetic wave is transmitted in idea lossless medium. When the groundpenetrating radar wave transmits in the loss medium, the attenuation and dispersion can occur.It makes the data image received become fuzzy distortion and can affect the detection depthand resolution of ground penetrating radar. This makes the advantage of the high resolutionof ground penetrating radar be of restrictions and restricts the development of high resolutionground penetrating radar technology. In view of the influence of attenuation and dispersionon the radar wave, it is very meaningful to improve the resolution of ground penetrating radar.High resolution ground penetrating radar technology research involves basic theoreticalresearch, methods research and equipment three main areas. In this paper, aimed at improvingground penetrating radar resolution technology, methods research is the focus. More precisely,the study of signal processing algorithms to improve the ground penetrating radar resolutiontechnology is the focus in this paper. For improving the ground penetrating radar resolution,the main study contents involve the estimation of ground penetrating radar quality factor Q,the inverse Q filtering and deconvolution three parts. This three parts research contents areintroduced as follows:
Aiming at the problem of estimating ground penetrating radar quality factor Q, thealgorithm to obtain Q value using amplitude spectral ratio has been improved. Initially, asingle spectrum is obtained by using Fourier transform. But now, time frequency spectrum isobtained by using time-frequency analysis. The Q value is estimated by using the ratio oftime frequency spectrum.
The algorithm of estimating Q value by using frequency shift method is furtherdeveloped in this paper. this algorithm is validated by taking advantage of layered constant Q-model.
The wavelet is confirmed by modulation frequency, Energy attenuation factor of wavelet,the amplitude and phase of wavelet in seismic theory. Drawing lessons from this theory inthis paper, the Q value in each layer is set as a constant in horizontally layered medium (Qvalue is independent of frequency). And firstly the frequency-domain equation of the singlepass propagation theory of plane wave is solved. Through definition envelope peakinstantaneous frequency and discussing algorithm, it shows that Q value is confirmed by thechanges of envelope peak instantaneous frequency, travel time and the wavelet energyattenuation factor. So the method to estimate Q value using envelope peak instantaneousfrequency of ground penetrating radar VRP data direct wave is obtained. At last, theeffectiveness and accuracy of the algorithm is verified using synthetic VRP data andsynthesis experimental data applying FDTD theory and practical data.
Drawing lessons from inverse Q filtering algorithm in the seismic theory, the theory ofwavefield downward continuation is combined with generalized S transform and the jointtheory is applied to the data processing of inverse Q filtering of ground penetrating radarsignal horizontally layered medium. The underground Q model is assumed to layeredconstant Q structure and for each constant Q layer, the earth’s surface wavefield records isdirectly prolonged the top of current layer; the wave domain prolonged is done generalized Stransform in time frequency domain in constant Q layer and the signal is done inverse Qfiltering; the filtering result is done generalized S inverse transform and the time domainsignal after being inverse Q filtering is obtained. Finally, the complex layered groundpenetrating radar attenuation records based on the theory of wavefield downwardcontinuation and the two layer ground penetrating radar attenuation records obtained fromFDTD theory are done amplitude and phase compensation. It verifies the effectiveness andaccuracy of the algorithm in ground penetrating radar inverse Q filtering.
Inverse Q filtering method in ground penetrating radar absorption dispersion mediumand the inverse scattering theory of medium are combined in this paper. The problem ofinverse Q filtering of layered medium in ground penetrating radar is transformed into theproblem of inverse scattering of medium according to scattering domain theory and greenfunction knowledge. The distortion of amplitude and phase generated in communicationprocess of electromagnetic waves in the underground is compensated by solving inversescattering problem.
The traditional ground penetrating radar convolution model is discussed in this paper. Itproposes to use linear time-varying systems to describe the radar return signal. Namely, theradar return signal is described to linear integral form between wavelet and formation. For validating the correctness of this model, the model is used in the process of extracting groundpenetrating radar wavelet in this paper. In this process, the underground medium used aretraditional layered medium and random medium possessing local small scale inhomogeneouscharacter. The final result shows that this kind of linear time-varying systems can be better todescribe the ground penetrating radar return signal than the convolution form of thetraditional linear time invariant system.
Fractional Fourier transform theory is applied to ground penetrating radar waveletextraction algorithm in the process of ground penetrating radar wavelet extraction in thispaper. It assumes that ground penetrating radar signal meets the prior knowledge of fractionalFourier transform optimal filtering in the process of wavelet extraction. The problem ofwavelet extraction can be transformed the problem of optimal filtering in fractional Fouriertransform domain since fractional Fourier transform is a unitary transform and has normconserving. The optimal solution is found in fractional Fourier transform domain and finallythe time domain signal of wavelet estimation is obtained after fractional Fourier transforminverse transform. In addition, when the single optimal filter is not ideal and the signal isaffected by noise, single optimal filter can not meet the needs. Thus a concept of multilevelfilter in the fractional Fourier transform domain is proposed. The shape and characteristics ofwavelet have no special requirements in the wavelet extraction algorithm in this paper. So,the algorithm described in this article is more universal.
Ground penetrating radar deconvolution technology based on formation spectrumcompensation factor and linear time varying formation system response model is proposed inthis paper. A formation spectrum correction factor in the fractional Fourier transform domainis solved using fractional Fourier transform optimal filtering algorithm to verify the originalrecords of the spectrum and improve resolution. The algorithm proposed in this paper iscompared with ground penetrating radar deconvolution algorithm built on the traditionalconvolution model and based on formation spectrum correction factor. The result verifies theproposed algorithm is more reasonable and effective than the traditional methods.
引文
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