基于离散余弦变换的磁位谱分析及磁异常导数计算方法

Magnetic potential spectrum analysis and calculating method of magnetic anomaly derivatives based on discrete cosine transform

针对提高磁异常导数的计算精度,提出磁位离散余弦变换谱的分析方法.根据重磁位场的泊松公式,利用余弦变换给出磁位与磁场分量间的余弦变换谱关系,推导出磁异常n阶导数的余弦变换谱公式.利用余弦变换法计算的无限长水平圆柱体磁异常水平和垂向一阶导数的最大误差分别为-0.28 nT/m、0.47 nT/m;水平一阶导数的误差一般在-3.57%-3.27%之间,垂向一阶导数的误差一般在-1.94%-1.88%之间;计算的磁异常一阶导数值与理论值大致重合,而且不受有效磁化倾角的影响.而Fourier变换法计算的水平和垂向一阶导数最大误差分别为-10.62 nT/m1、4.42 nT/m,计算曲线与理论曲线偏离大,受磁化倾角的影响也较大.这说明与Fourier变换法相比,余弦变换法计算的异常导数精度高,而且具有良好的稳定性.

A method of magnetic potential spectrum based on the cosine transform is proposed in order to improve the calculating accuracy of magnetic anomaly derivatives. According to the Poisson equation of gravitymagnetic potential, we derive the relation of cosine transform spectrum between magnetic potential and magnetic field constituent and deduce the cosine transform spectrum formula of n degree derivatives using the cosine transform. The horizontal and vertical first derivatives of magnetic anomalies of an infinite cylinder are calculated by the cosine transform method, in which the maximum errors are - 0.28 nT/m and 0.47nT/m, respectively and the percent errors are generally within - 3.57 % - 3.27 % and - 1.94 % - 1.88 %, respectively except several data of the boundary and part are bigger because of remains of Gibbus effect. The calculating curve and theoretical curve are approximately coincident, and there is no influence by effective magnetic dip angle in computing. But the errors with the Fourier transform method are - 10.62nT/m and 14.42nT/m, there is large departure between the calculating curve and theoretical curve and evident influence by effective magnetic dip angle in computing. It indicates that the calculating accuracy of magnetic anomaly derivatives calculated by cosine transform is higher than Fourier transform, and the computing stability is excellent.