基于小波多分辨探地雷达正演及偏移处理研究
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摘要
探地雷达是探测地下结构和特性的一种地球物理勘探方法。由于它具有高效、快速、无损、抗干扰能力强等优点，已广泛的应用在工程中的各个领域，成为浅层勘探的有力工具。但是，目前探地雷达技术尚存改进之处，如目前探地雷达的探测技术还滞留在二维阶段，雷达数据的解释技术也建立在凭经验对雷达图像的识别和手工圈定雷达异常体的基础上，明显存在很强的主观性，而深入了解电磁波传播规律，开展探地雷达二、三维正演及偏移技术的研究，会降低资料错误解释的概率，为三维探地雷达技术开展及雷达资料的准确解释提供依据。本论文主要研究两个方面的内容，即探地雷达的正演及探地雷达偏移处理研究。
在探地雷达正演模拟中，作者在研究小波变换的基本理论及Daubechies小波特性的基础上，选用伽辽金法着重对Maxwell的两个旋度方程进行离散化，并运用K．S．Yee的空间网格模型，导出了基于DB2小波基的MRTD算法，同时详细地推导该算法的探地雷达2D、3D差分公式、数值稳定性条件、色散关系等。然后，通过分析，得知MRTD算法与传统的FDTD算法相比具有较好的色散关系，它大大减少雷达模拟计算中的网格数目，节约内存空间，提高了探地雷达正演模拟效率。在此基础上，作者开发了探地雷达MRTD法正演模拟程序，对复杂二、三维雷达模型进行了数值模拟试验，突破了过去仅能对简单、规则雷达模型进行正演的局限，同时也验证了MRTD算法用于探地雷达正演计算的有效性。
在探地雷达偏移处理的研究中，作者首先分析了传统有限差分法偏移具有倾角限制、计算效率低，克希霍夫积分偏移法偏移噪声大、高频干扰严重，频率波数域偏移法不适应速度变化的缺点。为了更好地实现雷达偏移的目的，作者系统地总结小波多分辨与探地雷达偏移处理之间关系，利用小波多尺度压缩雷达波场外推矩阵，推导出探地雷达小波域二维波动方程逆时偏移算法，并以实例的形式，说明了小波域二维波动方程逆时偏移算法的具体优势：如偏移后雷达剖面中的噪声较Kirchhoff积分偏移法少、波形归位更准确、对速度模型适应性强、对雷达记录的信噪比要求低、无倾角限制等优点。在雷达波场多分辨分解过程设置阈值还可提高偏移计算速度，也可达到滤去部分高频噪声的特点。然后，从三维雷达波动方程出发，利用爆炸反射原理和浮动坐标变换，并通过应用方程分裂及小波多分辨理论，推导出探地雷达小波域三维差分法波动方程偏移算法。然后把该算法应用于三个球体空洞的3D正演结果中，通过对比偏移处理前后的雷达资料，得知该三维偏移算法能使3D正演剖面中的反射波归位、绕射波收敛，从而大大提高了雷达剖面的横向分辨率，更有利于探地雷达资料的地质解释，最后，作者在工程实践中，开展了探地雷达三维探测的野外工作方法、数据处理以及三维数据表达的研究工作，取得了较好的效果，为探地雷达的三维探测技术的开展打下了基础。
Ground penetrating radar is a geophysical exploration method whichdetects the underground structure and characteristics. Because of theadvantages such as high efficiency, quick speed, undamaged, highresolution, and strong anti-jamming features, it has been applied to everyaspect in engineering domain, and it has been a powerful tool of shallowlayer exploration. But nowadays, the technical of GPR also need to beimproved, because it exists apparently subjective, such as, the detectiontechnical of GPR is still detained in two-dimension moment, and theexplanation technical is also build on the experiences to identifyingradar image and blocking out radar anomalous body handful. Thoroughlyunderstanding electromagnetic wave propagation rules, and launching theresearch of GPR two or three-dimension forward simulation wouldreduce the probability of the wrong explanation to the data, and providethe reference to develop the three-dimensional GPR technical and theaccurate explanation to radar data. This paper could be divided into twoparts, whose first part introduces the GPR forward simulation, and secondpart introduces the GPR migration processing.
In the GPR forward simulation, based on the basic wavelets theoriesand the characteristic of Daubechies wavelets, the author chooses theGalerkin method to discrete the two Maxwell rotation equations. And italso uses the K.S.Yee grid to deduce the MRTD algorithm based on theDB2 wavelets basis. At the same time, it deduces the GPR two orthree-dimension finite difference formula, numerical stability, dispersionrelation of this algorithm detailed. And then, through analysis, it isknown that compared to the normal FDTD algorithm, MRTD algorithmhas better dispersion relation which could reduce the grid number in radarsimulation calculation, save memory space, improve the efficiency ofGPR forward simulation. Based on this, the author explores MRTDforward simulation program of GPR, which could do the data simulationexperiment to the complex two or three radar models. This programbreaks the limitation which is only could forward simple and regulationradar model, at the same time, it conforms the validity of MRTD algorithm which is used to GPR forward simulation.
In the research of GPR migration processing, the author firstlyanalyzes the traditional finite difference method has some disadvantages,such as obliquity limitation, lowly calculation efficiency, big migrationnoise of Kirchhoff's method of integration migration, seriouslyinterference of high frequency, and the F-K migration inadaptable withthe changeable of velocity. For better to realize the radar migration, theauthor systematically summarizes the relationship between waveletsmulti-resolution and GPR migration processing, and uses the wavelet tomulti-scale compress extrapolate matrix of radar wave field. Then theauthor deduces inverse time migration algorithm of GPR two-dimensionwave equation in wavelets domain, and takes the real example to explainthe concrete advantages of inverse time migration algorithm of GPRtwo-dimension wave equation in wavelets domain, such as smaller noisecomparing to Kirchhoff's method of integration migration, more accuracyof waveform returning to original position, highly adaptation to velocitymodel, no obliquity limitation and lowly requirement for Signal-to-Noiseof radar data. It could improve the migration algorithm velocity if setdomain data during the decompose course of radar wave fieldmulti-resolution, and it could also filtrate some high frequency noise.Secondly, setting from the three-dimension radar wave equation, usingthe bursting reflection theory and floating coordinate transform, withequation splitting and multi-resolution of wavelets theory, the authordeduces the migration algorithm of GPR three-dimension FD waveequation in wavelets domain. Then the author puts this algorithm tothree-dimension forward result of three sphere cavern. Through comparethe radar data before and after the migration processing, it is known thisthree-dimension migration algorithm could make the reflection wavereturn to original position, and make the diffraction wave converge in thethree-dimension sections. The lateral resolution of radar sections could behighly enhanced, and it can instruct the geology expiation of GPRsections better. At last, the author does the research of GPRthree-dimension field working method, data processing andthree-dimension expression in the program practice, and gets the goodeffect, which sets the base for three-dimension technology of GPR.
在探地雷达正演模拟中，作者在研究小波变换的基本理论及Daubechies小波特性的基础上，选用伽辽金法着重对Maxwell的两个旋度方程进行离散化，并运用K．S．Yee的空间网格模型，导出了基于DB2小波基的MRTD算法，同时详细地推导该算法的探地雷达2D、3D差分公式、数值稳定性条件、色散关系等。然后，通过分析，得知MRTD算法与传统的FDTD算法相比具有较好的色散关系，它大大减少雷达模拟计算中的网格数目，节约内存空间，提高了探地雷达正演模拟效率。在此基础上，作者开发了探地雷达MRTD法正演模拟程序，对复杂二、三维雷达模型进行了数值模拟试验，突破了过去仅能对简单、规则雷达模型进行正演的局限，同时也验证了MRTD算法用于探地雷达正演计算的有效性。
在探地雷达偏移处理的研究中，作者首先分析了传统有限差分法偏移具有倾角限制、计算效率低，克希霍夫积分偏移法偏移噪声大、高频干扰严重，频率波数域偏移法不适应速度变化的缺点。为了更好地实现雷达偏移的目的，作者系统地总结小波多分辨与探地雷达偏移处理之间关系，利用小波多尺度压缩雷达波场外推矩阵，推导出探地雷达小波域二维波动方程逆时偏移算法，并以实例的形式，说明了小波域二维波动方程逆时偏移算法的具体优势：如偏移后雷达剖面中的噪声较Kirchhoff积分偏移法少、波形归位更准确、对速度模型适应性强、对雷达记录的信噪比要求低、无倾角限制等优点。在雷达波场多分辨分解过程设置阈值还可提高偏移计算速度，也可达到滤去部分高频噪声的特点。然后，从三维雷达波动方程出发，利用爆炸反射原理和浮动坐标变换，并通过应用方程分裂及小波多分辨理论，推导出探地雷达小波域三维差分法波动方程偏移算法。然后把该算法应用于三个球体空洞的3D正演结果中，通过对比偏移处理前后的雷达资料，得知该三维偏移算法能使3D正演剖面中的反射波归位、绕射波收敛，从而大大提高了雷达剖面的横向分辨率，更有利于探地雷达资料的地质解释，最后，作者在工程实践中，开展了探地雷达三维探测的野外工作方法、数据处理以及三维数据表达的研究工作，取得了较好的效果，为探地雷达的三维探测技术的开展打下了基础。
Ground penetrating radar is a geophysical exploration method whichdetects the underground structure and characteristics. Because of theadvantages such as high efficiency, quick speed, undamaged, highresolution, and strong anti-jamming features, it has been applied to everyaspect in engineering domain, and it has been a powerful tool of shallowlayer exploration. But nowadays, the technical of GPR also need to beimproved, because it exists apparently subjective, such as, the detectiontechnical of GPR is still detained in two-dimension moment, and theexplanation technical is also build on the experiences to identifyingradar image and blocking out radar anomalous body handful. Thoroughlyunderstanding electromagnetic wave propagation rules, and launching theresearch of GPR two or three-dimension forward simulation wouldreduce the probability of the wrong explanation to the data, and providethe reference to develop the three-dimensional GPR technical and theaccurate explanation to radar data. This paper could be divided into twoparts, whose first part introduces the GPR forward simulation, and secondpart introduces the GPR migration processing.
In the GPR forward simulation, based on the basic wavelets theoriesand the characteristic of Daubechies wavelets, the author chooses theGalerkin method to discrete the two Maxwell rotation equations. And italso uses the K.S.Yee grid to deduce the MRTD algorithm based on theDB2 wavelets basis. At the same time, it deduces the GPR two orthree-dimension finite difference formula, numerical stability, dispersionrelation of this algorithm detailed. And then, through analysis, it isknown that compared to the normal FDTD algorithm, MRTD algorithmhas better dispersion relation which could reduce the grid number in radarsimulation calculation, save memory space, improve the efficiency ofGPR forward simulation. Based on this, the author explores MRTDforward simulation program of GPR, which could do the data simulationexperiment to the complex two or three radar models. This programbreaks the limitation which is only could forward simple and regulationradar model, at the same time, it conforms the validity of MRTD algorithm which is used to GPR forward simulation.
In the research of GPR migration processing, the author firstlyanalyzes the traditional finite difference method has some disadvantages,such as obliquity limitation, lowly calculation efficiency, big migrationnoise of Kirchhoff's method of integration migration, seriouslyinterference of high frequency, and the F-K migration inadaptable withthe changeable of velocity. For better to realize the radar migration, theauthor systematically summarizes the relationship between waveletsmulti-resolution and GPR migration processing, and uses the wavelet tomulti-scale compress extrapolate matrix of radar wave field. Then theauthor deduces inverse time migration algorithm of GPR two-dimensionwave equation in wavelets domain, and takes the real example to explainthe concrete advantages of inverse time migration algorithm of GPRtwo-dimension wave equation in wavelets domain, such as smaller noisecomparing to Kirchhoff's method of integration migration, more accuracyof waveform returning to original position, highly adaptation to velocitymodel, no obliquity limitation and lowly requirement for Signal-to-Noiseof radar data. It could improve the migration algorithm velocity if setdomain data during the decompose course of radar wave fieldmulti-resolution, and it could also filtrate some high frequency noise.Secondly, setting from the three-dimension radar wave equation, usingthe bursting reflection theory and floating coordinate transform, withequation splitting and multi-resolution of wavelets theory, the authordeduces the migration algorithm of GPR three-dimension FD waveequation in wavelets domain. Then the author puts this algorithm tothree-dimension forward result of three sphere cavern. Through comparethe radar data before and after the migration processing, it is known thisthree-dimension migration algorithm could make the reflection wavereturn to original position, and make the diffraction wave converge in thethree-dimension sections. The lateral resolution of radar sections could behighly enhanced, and it can instruct the geology expiation of GPRsections better. At last, the author does the research of GPRthree-dimension field working method, data processing andthree-dimension expression in the program practice, and gets the goodeffect, which sets the base for three-dimension technology of GPR.
引文
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