Chebyshev低通滤波器在位场数据波数域导数换算中的应用

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

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。

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 2 Dand 3 D 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.