吉林大学学报(地球科学版) ›› 2019, Vol. 49 ›› Issue (2): 559-568.doi: 10.13278/j.cnki.jjuese.20180091

• 地球探测与信息技术 • 上一篇    下一篇

Chebyshev低通滤波器在位场数据波数域导数换算中的应用

郝梦成, 张凤旭, 杜威, 李银飞, 任朗宁   

  1. 吉林大学地球探测科学与技术学院, 长春 130026
  • 收稿日期:2018-05-02 出版日期:2019-03-26 发布日期:2019-03-28
  • 通讯作者: 张凤旭(1969-),男,教授,博士生导师,主要从事重磁数据处理解释方面的研究,E-mail:zhangfx17@163.com E-mail:zhangfx17@163.com
  • 作者简介:郝梦成(1989-),男,博士研究生,主要从事重磁数据处理解释方面的研究,E-mail:haomc15@163.com
  • 基金资助:
    中国地质调查局项目（1212011120973-03）

Application of Chebyshev Low-Pass Filter in Calculating Derivative of Potential Field Data in Wavenumber Domain

Hao Mengcheng, Zhang Fengxu, Du Wei, Li Yinfei, Ren Langning   

  1. College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China
  • Received:2018-05-02 Online:2019-03-26 Published:2019-03-28
  • Supported by:
    Supported by Project of China Geological Survey (1212011120973-03)

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摘要： 导数换算作为常用的位场数据处理手段具有重要的物理意义。由于实际测量误差和噪声的影响，波数域导数换算存在计算过程不稳定、求导结果精度差的问题。为了降低噪声干扰，提高导数计算精度，提出了在波数域常规导数算子基础上附加Chebyshev低通滤波器的任意阶导数换算方法。通过分析该滤波器的滤波特性，并结合位场异常径向平均功率谱曲线特征，确定了Chebyshev低通滤波法的滤波参数，减少了人为因素对求导结果的干扰。二度体和三度体模型试验表明，与其他3种方法（常规FFT（fast Fourier transformation）法、向上延拓法和ISVD（integrated second vertical derivative）法）相比，该方法计算的导数与理论值的均方根误差最小，求导结果精度较高。在虎林盆地布格重力异常数据处理中，利用该方法计算的垂向二阶导数受噪声干扰小，结果可靠性较高，依此划分出的8条大断裂和11条小断裂在以往研究中均得到证实。

关键词: Chebyshev低通滤波器, 波数域, 导数换算, 径向平均功率谱

Abstract: Derivative conversion, as a commonly used data processing method of potential field, has important physical significance. Due to the measurement error and noise, the derivative conversion in wavenumber domain is unstable,and the accuracy of derivative results is poor. In order to reduce noise interference and to improve the accuracy of derivative calculation, an arbitrary-order derivative conversion combining Chebyshev low-pass filter with routine derivative operator in wavenumber domain is proposed. Through analyzing the filtering properties of the filter and the characteristics of the radially averaged power spectrum of potential field anomalies, the parameters of the Chebyshev low-pass filter method are determined, which can reduce the interference of human choice. The 2D and 3D model tests show that compared with the other three methods,routine FFT (fast Fourier transformation), upward continuation and ISVD (integrated second vertical derivative), the root mean square error (RMSE) of the derivative calculated by this method and the theoretical value is the smallest, and the accuracy of its derivation result is higher. In the data processing of Bouguer gravity anomaly in Hulin basin, the second vertical derivative calculated by the proposed method is less affected by noise, and has higher reliability. Eight large faults and eleven small faults recognized based on this result are confirmed by previous studies.

Key words: Chebyshev low-pass filter, wavenumber domain, derivative conversion, radially averaged power spectrum

中图分类号: 

  • P631.1
[1] Verduzco B,Fairhead J D,Green C M,et al.New Insights into Magnetic Derivatives for Structural Mapping[J].Leading Edge,2012,23(2):116-119.
[2] Guo C C,Xiong S Q,Xue D J,et al.Improved Euler Method for the Interpretation of Potential Data Based on the Ratio of the Vertical First Derivative to Analytic Signal[J].Applied Geophysics,2014,11(3):331-339.
[3] 张凤琴,张凤旭,刘财,等.利用DCT法计算重力归一化总梯度[J].吉林大学学报(地球科学版),2007,37(4):804-808. Zhang Fengqin,Zhang Fengxu,Liu Cai,et al.Using DCT to Calculate Normalized Full Gradient of Gravity Anomalies[J].Journal of Jilin University (Earth Science Edition),2007,37(4):804-808.
[4] 曾小牛,李夕海,贾维敏,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. Zeng Xiaoniu,Li Xihai,Jia Weimin,et al.A New Regularization Method for Calculating the Vertical Derivatives of the Potential Field[J].Chinese Journal of Geophysics,2015,58(4):1400-1410.
[5] Meskó,C A.Two-Dimensional Filtering and the Second Derivative Method[J].Geophysics,2012,31(3):606.
[6] Agarwal B N P,Lal T.Calculation of the Second Vertical Derivative of Gravity Field[J].Pure & Applied Geophysics,1969,76(1):5-16.
[7] 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. Xu Shizhe.Calculation of Vertical Component of 2D Gravitational Field and Second Derivative of Gravitational Potential by Finite[J].Oil Geophysical Prospecting,1984,19(5):468-476.
[8] 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. Wang Bingzhu.Computing the Vertical Second Derivative and Upward Continuation of Gravity Anomaly by Spline Function Method[J].Oil Geophysical Prospecting,1996,31(3):415-422.
[9] 侯重初.补偿圆滑滤波方法[J].石油物探,1981(2):27-34. Hou Zhongchu.Filtering of Smooth Compensation[J].Geophysical Prospecting for Petroleum,1981(2):27-34.
[10] 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. Wang Yanguo,Zhang Jin.The Iterative Method for Higher-Order Derivative Calculation of Potential Fields in Wave Number Domain[J].Geophysical & Geochemical Exploration,2016,40(1):143-147.
[11] 杜威,许家姝,吴燕冈,等.位场垂向高阶导数的Tikhonov正则化迭代法[J].吉林大学学报(地球科学版),2018,48(2):394-401. Du Wei,Xu Jiashu,Wu Yangang,et al.Tikhonov Regularization Iteration Method for High-Order Vertical Derivatives of Potential Field[J].Journal of Jilin University (Earth Science Edition),2018,48(2):394-401.
[12] 张凤旭,孟令顺,张凤琴,等.重力位谱分析及重力异常导数换算新方法:余弦变换[J].地球物理学报,2006,49(1):244-248. Zhang Fengxu,Meng Lingshun,Zhang Fengqin,et al.A New Method for Spectral Analysis of the Potential Field and Conversion of Derivatives of Gravity Anomalies:Cosine Transform[J].Chinese Journal of Geophysics,2006,49(1):244-248.
[13] 张凤旭,张凤琴,孟令顺,等.基于离散余弦变换的磁位谱分析及磁异常导数计算方法[J].地球物理学报, 2007,50(1):297-304. Zhang Fengxu,Zhang Fengqin,Meng Lingshun,et al.Magnetic Potential Spectrum Analysis and Calculating Method of Magnetic Anomaly Derivatives Based on Discrete Cosine Transform[J].Chinese Journal of Geophysics,2007,50(1):297-304.
[14] 马国庆,黄大年,杜晓娟,等.Hartley变换在位场(重、磁)异常导数计算中的应用[J].吉林大学学报(地球科学版),2014,44(1):328-335. Ma Guoqing,Huang Danian,Du Xiaojuan,et al.Hartley Transform in the Application of the Derivatives of Potential Field (Gravity and Magnetic) Data[J].Journal of Jilin University (Earth Science Edition),2014,44(1):328-335.
[15] Fedi M,Florio G.A Stable Downward Continuation by Using the ISVD Method[J].Geophysical Journal of the Royal Astronomical Society,2002,151(1):146-156.
[16] 蒋甫玉,孟令顺,张凤旭,等.Chebyshev逼近滤波器在位场分离中的应用[J].物探与化探,2008,32(3):311-315. Jiang Fuyu,Meng Lingshun,Zhang Fengxu, et al.The Application of Chebyshev Approximation Filter to Separating Potential Anomalies[J].Geophysical & Geochemical Exploration,2008,32(3):311-315.
[17] 张凤旭,张兴洲,张凤琴,等.黑龙江省虎林盆地单元结构的地质-地球物理研究[J].吉林大学学报(地球科学版),2010,40(5):1170-1176. Zhang Fengxu,Zhang Xingzhou,Zhang Fengqin,et al.Study on Geology and Geophysics on Structural Units of Hulin Basin in Heilongjiang Province[J].Journal of Jilin University (Earth Science Edition),2010,40(5):1170-1176.
[18] 刘志宏,梅梅,高军义,等.东北东部虎林盆地的构造特征、成盆机制及敦密断裂带北东段的形成时代[J].吉林大学学报(地球科学版),2014,44(2):480-489. Liu Zhihong,Mei Mei,Gao Junyi,et al.Structural Features Formation Mechanism of Hulin Basin and Deformation Time of Northeastern Segment of Dunhua-Mishan Fault Zone in Northeast China[J].Journal of Jilin University (Earth Science Edition),2014,44(2):480-489.
[19] 邰振华,张凤旭,刘国兴,等.基于差分求导的伪总梯度余弦值法的位场边界检测[J].石油地球物理勘探,2014,49(4),807-814. Tai Zhenhua,Zhang Fengxu,Liu Guoxing,et al.Potential Field Edge Detection Based on Difference Derivative with Cosine of Pseudo Total Gradient[J].Oil Geophysical Prospecting,2014,49(4):807-814.
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