Hartley变换在位场(重、磁)异常导数计算中的应用

Hartley Transform in the Application of the Derivatives of Potential Field(Gravity and Magnetic)Data

导数计算是位场(重磁)数据处理中必不可少的技术手段,现今大多采用Fourier变换来进行。Hartley变换是在Fourier变换基础上定义的一种实数域运算,比Fourier变换更加对称,所需的运算量更少。笔者推导出基于Hartley变换的重磁异常导数计算公式,计算结果与理论值之间误差小于5%,通过理论模型证明Hartley变换可替代Fourier变换进行位场异常的导数计算,且受噪音干扰较小。将Hartley变换用于位场边界识别滤波器的计算,获得了清晰的断裂分布。

Derivative is an indispensable tool in the processing of potential field data . Now we usually use the Fourier transform to complete the computation ,but this method is sensitive to noise ,so cannot compute higher-order derivatives . Hartley transform （HT ） is a real-valued function that is defined on the basis of Fourier transform （FT ） ,however ,symmetry character of HT is better and computational complexity of HT is smaller compared with these properties of FT . We derive the derivative computation equations of gravity and magnetic anomaly based on the basic property of HT . We demonstrate the HT on theoretical anomalies ,and errors between the results computed by HT , which is insensitive to noise ,and the theoretical values are less than 5% ,so the HT can substitute the FT to compute the derivatives of potential field data .We also apply the HT to finish the computation of edge detection filters and obtain clearer distribution of faults .