基于最小二乘QR算法的质心频率下移法应用研究
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摘要
时间域振幅比法层析成像利用直达波的振幅变化来反演介质的衰减系数,具有简易快速等优点,在单一地质构造勘察中极具优势,但该方法易受几何扩散、仪器响应、天线耦合以及辐射模式等因素的干扰,导致成像结果失真,难以适应复杂地质构造的高精度成像.为解决该问题,提出质心频率下移法,从频率域分析振幅谱与衰减系数的关系,在此基础上实现衰减层析成像,此外,采用正则化least-squares QR (LSQR)分解算法求解层析成像方程组,提高计算速度和数值稳定性.数值模型算例和实测算例的结果表明,电磁波通过衰减介质时质心频率向主频方向减小,质心频率下移法具有较高成像精度.
Time domain amplitude tomography using the difference of first wave amplitude to invert the attenuation coefficient, which has the advantages of simple and quick in the single geological survey. However. the method is susceptible to the geometric diffusion, instrument response, antenna coupling, radiation patterns and other factors, which resulting in a distortion of the imaging results. Hence, the amplitude method is difficult to adapt to the complex geological structures of high-precision imaging. In order to improve the accuracy of attenuation tomography, we propose a centroid frequency down-shift method regarding the frequency domain, which based on the relationship between the amplitude spectrum and the attenuation coefficient, and then implements the tomography. In addition, the regularized least-squares QR(LSQR) algorithm is employed to solve the tomographic equations, which improves the calculation speed and numerical stability. The numerical results and in-situ example show that the centroid frequency decreases as the electromagnetic wave passes through the decaying medium, and verify that the centroid frequency downshift method is feasible with high stability and accuracy.
Time domain amplitude tomography using the difference of first wave amplitude to invert the attenuation coefficient, which has the advantages of simple and quick in the single geological survey. However. the method is susceptible to the geometric diffusion, instrument response, antenna coupling, radiation patterns and other factors, which resulting in a distortion of the imaging results. Hence, the amplitude method is difficult to adapt to the complex geological structures of high-precision imaging. In order to improve the accuracy of attenuation tomography, we propose a centroid frequency down-shift method regarding the frequency domain, which based on the relationship between the amplitude spectrum and the attenuation coefficient, and then implements the tomography. In addition, the regularized least-squares QR(LSQR) algorithm is employed to solve the tomographic equations, which improves the calculation speed and numerical stability. The numerical results and in-situ example show that the centroid frequency decreases as the electromagnetic wave passes through the decaying medium, and verify that the centroid frequency downshift method is feasible with high stability and accuracy.
引文
[1]程久龙,邱伟.工作面电磁波高精度层析成像及其应用[J].煤田地质与勘探,1999, 27(4):62-64.
[2]谭捍华,HUANG Jia-hui,黄家会等.甚高频电磁波多参数层析成像技术及其应用研究[J].岩土力学,2008, 29(10):3307-3310.
[3]陈昌彦,沈小克,苏兆锋,等.电磁波层析成像技术在复杂地质边坡工程勘察中的应用研究[J].地球物理学进展,2012, 27(2):0796-0803.
[4]杨文采.应用地震层析成像[M].地质出版社,1993.
[5]刘鑫明,刘树才,易洪春,杨光,刘英.复杂断层构造电磁波衰减系数层析成像模拟研究[J].地球科学进展,2013(03):391-397.
[6]Holliger K, Musil M, Maurer H R. Ray-based amplitude tomography for crosshole georadar data:A numerical assessment[J]. Journal of Applied Geophysics, 2001, 47(3):285-298.
[7]王飞.跨孔雷达走时层析成像反演方法的研究[D].吉林大学,2014.
[8]王宗俊,范廷恩,马淑芳等.地震波质心频率变化规律[J].石油地球物理勘探,2015, 50(4):861-872.
[9]Quan Y, Harris J M. Seismic attenuation tomography using the frequency shift method. Geophysics,1997, 62(3):895-905.
[10]Liu L, Lane J W, Quan Y. Radar attenuation tomography using the centroid frequency downshift method[J]. Journal of Applied Geophysics, 1998, 40(1):105-116.
[11]刘广亮,于师建.基于质心频移的无线电波透视层析成像[J].地球物理学进展,2008, 23(2):583-587.
[12]张文权,翁爱华.地面核磁共振正则化反演方法研究[J].吉林大学学报(地球科学版),2007, 37(4):809-813.
[13]王宝龙,李青元,贾会玲等.正则化薄板样条函数拟合地层界面[J].煤田地质与勘探,2017, 45(4):23-27.
[14]Paige C C, Saunders M A. LSQR:An Algorithm for Sparse Linear Equations and Sparse Least Squares[J]. Acm Transactions on Mathematical Software, 1982, 8(1):43-71.
[15]林芳鹏,戴前伟,雷轶,等.基于光滑约束正则化的电磁波层析反演[J].物探化探计算技术,2018, 40(2):212-217.
[16]冯德山,王珣.大地电磁双二次插值FEM正演及最小二乘正则化联合反演[J].中国有色金属学报,2013(8):2524-2531.
[2]谭捍华,HUANG Jia-hui,黄家会等.甚高频电磁波多参数层析成像技术及其应用研究[J].岩土力学,2008, 29(10):3307-3310.
[3]陈昌彦,沈小克,苏兆锋,等.电磁波层析成像技术在复杂地质边坡工程勘察中的应用研究[J].地球物理学进展,2012, 27(2):0796-0803.
[4]杨文采.应用地震层析成像[M].地质出版社,1993.
[5]刘鑫明,刘树才,易洪春,杨光,刘英.复杂断层构造电磁波衰减系数层析成像模拟研究[J].地球科学进展,2013(03):391-397.
[6]Holliger K, Musil M, Maurer H R. Ray-based amplitude tomography for crosshole georadar data:A numerical assessment[J]. Journal of Applied Geophysics, 2001, 47(3):285-298.
[7]王飞.跨孔雷达走时层析成像反演方法的研究[D].吉林大学,2014.
[8]王宗俊,范廷恩,马淑芳等.地震波质心频率变化规律[J].石油地球物理勘探,2015, 50(4):861-872.
[9]Quan Y, Harris J M. Seismic attenuation tomography using the frequency shift method. Geophysics,1997, 62(3):895-905.
[10]Liu L, Lane J W, Quan Y. Radar attenuation tomography using the centroid frequency downshift method[J]. Journal of Applied Geophysics, 1998, 40(1):105-116.
[11]刘广亮,于师建.基于质心频移的无线电波透视层析成像[J].地球物理学进展,2008, 23(2):583-587.
[12]张文权,翁爱华.地面核磁共振正则化反演方法研究[J].吉林大学学报(地球科学版),2007, 37(4):809-813.
[13]王宝龙,李青元,贾会玲等.正则化薄板样条函数拟合地层界面[J].煤田地质与勘探,2017, 45(4):23-27.
[14]Paige C C, Saunders M A. LSQR:An Algorithm for Sparse Linear Equations and Sparse Least Squares[J]. Acm Transactions on Mathematical Software, 1982, 8(1):43-71.
[15]林芳鹏,戴前伟,雷轶,等.基于光滑约束正则化的电磁波层析反演[J].物探化探计算技术,2018, 40(2):212-217.
[16]冯德山,王珣.大地电磁双二次插值FEM正演及最小二乘正则化联合反演[J].中国有色金属学报,2013(8):2524-2531.
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