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中文摘要：
针对计算磁位高阶导数常用的频率域快速傅立叶变换方法在实际应用中存在边界效应的问题,提出了分别在x和y方向上移相π/2二维余弦变换定义及其时域微分定理,推导出了磁场矢量分量的导数计算公式,并将其应用于方向解析信号的磁异常边界识别方法。通过棱柱体源磁场理论数据对比分析,验证了基于余弦变换计算磁位高阶导数的方法在不需要扩边或滤波处理、未增加额外处理数据和算法复杂度的前提下,可避免或减小边界效应,算法稳定性更好,计算结果精度更高。
英文摘要：
The derivative of magnetic vector components plays an important role in the magnetic target interpretation process. A boundary effect problem is found in the computation of higher order derivatives of magnetic potential using the common methods such as the fast Fourier transform algorithm in actual applications. The paper presents a solution based on a π/2 phase-shifted cosine transform and its time-differentiation. Unified formulas for calculating the derivatives of magnetic vector components were deduced, and then applied to the directional analytic signals method. An analysis and comparison of magnetic field data between the rectangular prism source model and cosine transform method show that the influence of boundary effect can be avoided. The proposed method not only has higher precision and stability, but also doesnot require additional data and algorithm complexity for extending edge and filter processing.
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