中文摘要：

首先分析调和函数的相关性质，验证Bm为准调和函数的结论。在精确计算各阶垂向导数基础上，提出利用改进泰勒级数实现磁场稳健向下延拓。为降低边界效应对向下延拓计算结果的影响，提出采用半余弦函数对磁场在4个方向上进行平滑扩边处理。通过船载实测磁场数据对提出的方法进行验证。结论表明，提出的技术方法可实现磁场稳健向下延拓，计算结果精度要优于现行的向下延拓方法。

英文摘要：

The properties of harmonic function are studied, and it is proved that Bm is a pseudo- harmonic function. Based on the use of stable vertical derivatives, a stable algorithm is presented to perform downward continuation applying improved Taylor series approximation. Furthermore, the problem of edge effects could be settled out using grid extension to the four directions with half a cosine function before the vertical derivative calculation. The effectiveness of the suggested algorithm has been illustrated by real magnetic data from an airborne and seaborne magnetic survey. The conclusion shows that the presented technique can be employed to perform stable downward continuation of total field magnetic data and provide better results than other techniques based on fast Fourier transformation （FFT） or on normal Talor＇s series or integral- iteration method when the data is noise-free, and almost the same as integral-iteration method if the data contains certain noise.