基于小波变换的位场场源识别与异常分离方法研究
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摘要
重磁勘探是重要的物探方法，场源识别和位场分离是重磁数据处理中两个重要的问题。经典的频率域位场分离方法能有效分离不同深度、不同规模的异常，但由于傅立叶变换没有空间信息，存在分离不彻底和不能空间定位分离的缺点。小波变换具有多尺度分析、空间--尺度（频率）域定位分析等优点，有望解决上述位场分离和场源识别问题。
本文首先在阐述小波分析基本理论的基础上，开展基于小波变换的位场场源识别和位场分离方面的研究，主要成果如下：
1.在详细推导连续小波变换识别位场场源理论的基础上，设计各种类型场源模型，详细研究连续小波变换识别位场场源方法适用条件、母小波选择原则、噪声影响和尺度因子选取方法。
2.提出选择最佳母小波的定量指标稀疏指数和带空间-尺度定位的离散小波变换（DWT）位场异常分离方法。该方法对位场数据进行小波时频分析，确定出局部异常/区域异常对应的小波系数在空间-尺度域的范围，用特定范围内的小波系数重构出局部异常/区域异常，实现带空间-尺度域定位的位场异常分离。实验结果表明，先利用稀疏指数指标优选母小波，再采用带空间-尺度域定位的DWT位场异常分离方法，能提高位场异常分离的准确性，有效地从总异常中分离出区域异常和局部异常。
3.提出了基于格林等效层和维纳滤波的小波域优化位变滤波方法。该方法具有空间变化滤波能力，从而可解决局部频谱与全局频谱存在较大差异的位场异常分离问题。理论模型试验结果表明，在局部频谱与全局频谱差异较小的情况下，该方法的分离效果与Butterworth滤波法和优化滤波法相当；在局部频谱与全局频谱差异较大的情况下，该方法相对于Butterworth滤波法和优化滤波法具有一定优势。
4.对理论模型合成数据进行先位场分离再场源识别和直接场源识别进行对比实验，实验结果表明：采用带空间-尺度定位的DWT的分离方法，先分离出各个孤立局部异常再分别进行场源识别，能提高局部异常和区域异常场源识别的准确性。最后，通过实测资料处理检验上述结论的正确性。
The gravity and magnetic survey are the important geophysical methods. Theseparation and source identification of potential field are two key problems of gravityand magnetic field data processing. The classical separation method in frequencydomain can separate anomaly caused by sources of different depths and scaleseffectively. But they have some disadvantages, such as incomplete separation and cannot separate potential field with spatial localization, due to the lack of spatialinformation of Fourier transform. The wavelet transform, which has the ability ofmulti-resolution analysis and spatial localization, has been expected to solve theproblems presented above.
In this paper, after the basic theory of wavelet analysis has been introduced, thecausing sources identification and separation of potential field have been studied. Themain results are listed as follow:
1. The applicability of the identification of causing sources of potential field withContinuous Wavelet Transform(CWT) method, the principal of the choice of motherwavelet, the inference of noise and the choice of scaling factor have been studied,using several designed typical models, after the basic theory is re-derived in detail.
2. The quantitative indictor, Sparse Index(SI), for choosing the preferentialmother wavelet, and the potential field separation method based on Discrete WaveletTransform (DWT) with spatial-scale localization have been proposed. The range ofwavelet coefficients in the spatial-scale domain corresponding to the regional andlocal anomaly respectively is determined by means of wavelet time-frequencyanalysis to the potential field data. The regional and local anomaly can bereconstructed using the wavelet coefficients within the range determined aboverespectively, and then the potential field separation with spatial-scale localization isaccomplished. The numerical results show that the total field anomaly can beseparated into regional anomaly and several isolated local ones, and the accuracy ofthe separation result of potential field can be improved obviously by the method ofpotential field separation with spatial-scale localization with the preferable mother wavelet chosen by the indicator SI.
3. The preferable spatial-varying filtering method in wavelet domain has beenproposed based on the theories of the scale filtering in wavelet domain, Wienerfiltering and Green equivalent layer. The proposed method can solve the potentialfield separation problem whose local spectrum is different to global one obviouslybecause the spatial-varying filter parameter vary with position. The numerical resultsshow that the proposed method is as better as Butterworth filter and preferential filtermethod in the case of local spectrum is similar to global one, while the proposedmethod is better than the Butterworth filter and preferential filter method in the caseof local spectrum is much different to global one.
4. The comparing experiments between identification the causing source afterseparation of potential field, and identification the causing source directly has beenmade. The conclusion can be drawn that separating the potential field into isolatedlocal anomaly before identifying using separation method based on DWT withspatial-scale localization can improve the accuracy of identification result of bothlocal and regional sources which interferes each other before separation. Theconclusion is verified by the field data processing result.
本文首先在阐述小波分析基本理论的基础上，开展基于小波变换的位场场源识别和位场分离方面的研究，主要成果如下：
1.在详细推导连续小波变换识别位场场源理论的基础上，设计各种类型场源模型，详细研究连续小波变换识别位场场源方法适用条件、母小波选择原则、噪声影响和尺度因子选取方法。
2.提出选择最佳母小波的定量指标稀疏指数和带空间-尺度定位的离散小波变换（DWT）位场异常分离方法。该方法对位场数据进行小波时频分析，确定出局部异常/区域异常对应的小波系数在空间-尺度域的范围，用特定范围内的小波系数重构出局部异常/区域异常，实现带空间-尺度域定位的位场异常分离。实验结果表明，先利用稀疏指数指标优选母小波，再采用带空间-尺度域定位的DWT位场异常分离方法，能提高位场异常分离的准确性，有效地从总异常中分离出区域异常和局部异常。
3.提出了基于格林等效层和维纳滤波的小波域优化位变滤波方法。该方法具有空间变化滤波能力，从而可解决局部频谱与全局频谱存在较大差异的位场异常分离问题。理论模型试验结果表明，在局部频谱与全局频谱差异较小的情况下，该方法的分离效果与Butterworth滤波法和优化滤波法相当；在局部频谱与全局频谱差异较大的情况下，该方法相对于Butterworth滤波法和优化滤波法具有一定优势。
4.对理论模型合成数据进行先位场分离再场源识别和直接场源识别进行对比实验，实验结果表明：采用带空间-尺度定位的DWT的分离方法，先分离出各个孤立局部异常再分别进行场源识别，能提高局部异常和区域异常场源识别的准确性。最后，通过实测资料处理检验上述结论的正确性。
The gravity and magnetic survey are the important geophysical methods. Theseparation and source identification of potential field are two key problems of gravityand magnetic field data processing. The classical separation method in frequencydomain can separate anomaly caused by sources of different depths and scaleseffectively. But they have some disadvantages, such as incomplete separation and cannot separate potential field with spatial localization, due to the lack of spatialinformation of Fourier transform. The wavelet transform, which has the ability ofmulti-resolution analysis and spatial localization, has been expected to solve theproblems presented above.
In this paper, after the basic theory of wavelet analysis has been introduced, thecausing sources identification and separation of potential field have been studied. Themain results are listed as follow:
1. The applicability of the identification of causing sources of potential field withContinuous Wavelet Transform(CWT) method, the principal of the choice of motherwavelet, the inference of noise and the choice of scaling factor have been studied,using several designed typical models, after the basic theory is re-derived in detail.
2. The quantitative indictor, Sparse Index(SI), for choosing the preferentialmother wavelet, and the potential field separation method based on Discrete WaveletTransform (DWT) with spatial-scale localization have been proposed. The range ofwavelet coefficients in the spatial-scale domain corresponding to the regional andlocal anomaly respectively is determined by means of wavelet time-frequencyanalysis to the potential field data. The regional and local anomaly can bereconstructed using the wavelet coefficients within the range determined aboverespectively, and then the potential field separation with spatial-scale localization isaccomplished. The numerical results show that the total field anomaly can beseparated into regional anomaly and several isolated local ones, and the accuracy ofthe separation result of potential field can be improved obviously by the method ofpotential field separation with spatial-scale localization with the preferable mother wavelet chosen by the indicator SI.
3. The preferable spatial-varying filtering method in wavelet domain has beenproposed based on the theories of the scale filtering in wavelet domain, Wienerfiltering and Green equivalent layer. The proposed method can solve the potentialfield separation problem whose local spectrum is different to global one obviouslybecause the spatial-varying filter parameter vary with position. The numerical resultsshow that the proposed method is as better as Butterworth filter and preferential filtermethod in the case of local spectrum is similar to global one, while the proposedmethod is better than the Butterworth filter and preferential filter method in the caseof local spectrum is much different to global one.
4. The comparing experiments between identification the causing source afterseparation of potential field, and identification the causing source directly has beenmade. The conclusion can be drawn that separating the potential field into isolatedlocal anomaly before identifying using separation method based on DWT withspatial-scale localization can improve the accuracy of identification result of bothlocal and regional sources which interferes each other before separation. Theconclusion is verified by the field data processing result.
引文
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