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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.
In order to obtain high-precision total tensor magnetic gradient data, a fast frequency-domain calculation method based on discrete cosine transform is proposed. In order to solve the problem of boundary effect in the calculation of magnetic field derivatives by the commonly used fast Fourier transform method, / 2 two-dimensional cosine transform time domain differential theorem, combined with the field theory, derive the use of geomagnetic anomaly data to calculate the total tensor magnetic gradient uniform formula and give the algorithm to achieve process.Through an example to verify the cosine transform method in the numerical, Contour and other key features are in good agreement with the reference data, the average data center area error of 0.05nT / m below, while in the border area can reduce the Fourier transform method to bring the boundary error effect.