位场梯度张量转换的频率域正则化迭代法
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摘要
常规位场异常向梯度张量转换的过程稳定性差。基于Tikhonov正则化原理及不同方向导数换算的内在关系,提出位场梯度张量转换的频率域正则化迭代法。根据L曲线基本原理,给出确定最佳迭代次数的曲率函数法。模型实验结果表明,位场梯度张量转换的频率域正则化迭代法具有较高的计算精度与稳定性,曲率函数法可以准确界定最佳迭代次数。实际资料处理结果验证了方法的有效性。该研究可为位场梯度张量反演提供高质量数据。
The paper proposes a regularization iterative method for potential field tensor conversion in frequency domain, based on Tikhonov regularization and the relationship of different direction derivatives so as to improve the stability of conversion and presents curvature function method for determining the optimal number of iterations based on the theory of the L-curve. The model tests show that this method features a higher computational accuracy and stability thanks to the curvature function method capable of an accurate definition of the optimal number of iterations. The actual data processing results prove that the method has a good application effect. The study could provide high-quality data for potential field tensor inversion.
The paper proposes a regularization iterative method for potential field tensor conversion in frequency domain, based on Tikhonov regularization and the relationship of different direction derivatives so as to improve the stability of conversion and presents curvature function method for determining the optimal number of iterations based on the theory of the L-curve. The model tests show that this method features a higher computational accuracy and stability thanks to the curvature function method capable of an accurate definition of the optimal number of iterations. The actual data processing results prove that the method has a good application effect. The study could provide high-quality data for potential field tensor inversion.
引文
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[18] 姚长利,李宏伟,郑元满,等.重磁位场转换计算中迭代法的综合分析与研究[J].地球物理学报,2012,55(6):2062-2078.
[2] Yin G,Zhang Y T,Fan H B,et al.Detection,localization and classification of multiple dipole-like magnetic sources using magnetic gradient tensor data[J].Journal of Applied Geophysics,2016,128:131-139.
[3] 舒晴,马国庆,刘财,等.全张量磁梯度数据解释的均衡边界识别及深度成像技术[J].地球物理学报,2018,61(4):1539-1548.
[4] 吴琼,滕云田,张兵,等.世界重力梯度仪的研究现状[J].物探与化探,2013,37(5):761-768.
[5] Luo Y,Wu M P,Wang P,et al.Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements:calculation and application[J].Applied Geophysics,2015,12(3):283-291.
[6] Kevin L M,Juan H H.The complete gravity gradient tensor derived from the vertical component of gravity:a Fourier transform technique[J].Journal of Applied Geophysics,2001,46(3):159-l74.
[7] 舒晴,朱晓颖,周坚鑫,等.重力梯度张量分量频率域转换处理方法[J].地球物理学进展,2016,31(6):289-296.
[8] Cooper G R J,Cowan D R.Edge enhancement of potential-field data using normalized statistics[J].Geophysics,2008,73(3):1-4.
[9] 徐世浙.用有限元法计算二维重力场垂直分量及重力位二阶导数[J].石油地球物理勘探,1984,19(5):468-476.
[10] 王宜昌,杨辉.重力异常四次导数的计算及应用[J].地球物理学报,1986,29(1):69-83.
[11] 汪炳柱.用样条函数法求重力异常二阶垂向导数和向上延拓计算[J].石油地球物理勘探,1996,31(3):415-422.
[12] Wang B Z,Krebes E S,Ravat D.High-precision potential-field and gradient-component transformations and derivative computations using cubic B-splines[J].Geophysics,2008,73(5):135-142.
[13] 蒋甫玉.位场数据处理中的滤波技术研究及其应用[D].长春:吉林大学,2008.
[14] 曾小牛,贾维敏,李夕海,等.位场各阶垂向导数换算的新正则化方法[J].地球物理学报,2015,58(4):1400-1410.
[15] 侯重初.补偿圆滑滤波方法[J].石油物探,1981(2):22-29.
[16] 王彦国,张瑾.位场高阶导数的波数域迭代法[J].物探与化探,2016,40(1):143-147.
[17] 邰振华.位场数据高精度处理方法的研究与应用[D].长春:吉林大学,2016.
[18] 姚长利,李宏伟,郑元满,等.重磁位场转换计算中迭代法的综合分析与研究[J].地球物理学报,2012,55(6):2062-2078.