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地球表面磁场、引力场的实测资料延拓出球外的场值，对地球物理资料的解释是很有意义的。现已导出了水平面上三维场向上延拓的精确解、任意曲线上二维场向上延拓的模拟解。至于球面上三维场的向上延拓，现采用球谐级数的近似解，但级数收敛较慢，计算精度较低。本文介绍一种球面上磁场、引力场垂直分量向上延拓的精确解析解，公式十分简单。
The measurement of the magnetic field and gravitational field on the surface of the Earth extends the field values beyond the field of view. It is very meaningful to explain the geophysical data. An exact solution to the continuation of the three-dimensional field in the horizontal plane and an extended analog solution to the two-dimensional field on an arbitrary curve have now been derived. As for the upward extension of the three-dimensional field on the spherical surface, the approximate solution of spherical harmonic series is adopted, but the series convergence is slow and the calculation accuracy is low. In this paper, we introduce an exact analytic solution of the upward extension of the magnetic field and the vertical component of the gravitational field on a spherical surface. The formula is very simple.