基于离散余弦变换的全张量磁梯度计算方法

Full tensor magnetic gradient calculation method based on discrete cosine transform

为了获得高精度全张量磁梯度数据,提出了一种基于离散余弦变换的频域快速计算方法.针对常用的快速傅里叶变换方法在磁场导数计算中存在边界效应的问题,提出移相π/2二维余弦变换时域微分定理,结合位场理论,推导了利用地磁异常数据计算全张量磁梯度的统一公式,并给出算法实现过程.通过算例验证了余弦变换方法在数值、轮廓等关键特征方面均与参考数据符合较好,数据中心区域平均误差在0.05nT/m以下,同时在边界区域可减少傅里叶变换方法带来的边界误差效应.

To obtain accurate full tensor magnetic gradient data, a fast method based on discrete cosine transform was proposed. There was the edge effect in computing higher order derivatives of magnetic field using common method of fast Fourier transform（FFT）algorithm. Thus, a solution based on π/2 phase-shifted cosine transform time-differentiation was presented. Using the potential field theory, a unified formula was deduced in order to calculate the full tensor magnetic gradient from the pre-existing magnetic anomaly data, and the key algorithms in the computation was also introduced. Numerical analysis demonstrates that most value and characteristics of the estimated data by the novel method compare favorably with reference magnetic gradient data, and the average error is less than 0.05 nT/m precision in the central area. In addition, the influence of edge effect caused by the Fourier transform method can be reduced in the boundary area.