The truncation coefficient is widely utilized in non-global coverage computations of geophysics and geodesy and is always altitude dependent. As the two commonly used calculation methods for truncation coefficients, i.e., the spectral form and the recursive formula, both suffer from decreasing precision caused by high-altitude, leading to slow convergence for the former and numerical instability recursion for the latter. The asymptotic expansion mathematically converges with increasing degree and can precisely compensate for the shortcomings of the two methods. This study introduces asymptotic expansion to accurately compute the truncation coefficient for the spectral gravity forward modeling to a high degree. The evaluation at the whole altitudes and whole integral radii indicates that the proposed method has the following advantages: (i) The calculation precision increases with increasing degree and is altitude independent; (ii) the accurate calculation can be supported by a double-precision format; and (iii) the calculation can be conducted nearly without extra time cost with increasing degree. Generally, asymptotic expansion is used to calculate the high degree truncation coefficients, while the truncation coefficients at low degrees can be calculated using spectral form or recursive formulas in multiprecision format as a supplement; and the available range of asymptotic expansion is provided in the appendix.

截断系数广泛用于地球物理学和大地测量学的非全球覆盖计算，并且始终与高度相关。由于截断系数的两种常用计算方法，即谱式和递归公式，都受到高空导致精度下降的问题，导致前者收敛缓慢，后者出现数值不稳定递归。渐近展开在数学上收敛程度越来越大，可以精确补偿两种方法的缺点。本研究引入了渐近展开，以准确计算谱重力正演建模的截断系数。在整个高度和整个积分半径处的评估表明，所提方法具有以下优点：（i） 计算精度随程度的增加而增加，并且与高度无关;（ii） 双精度格式可以支持准确的计算;（iii） 随着程度的增加，计算几乎可以在没有额外时间成本的情况下进行。通常，渐近展开用于计算高次截断系数，而低度的截断系数可以使用多精度格式的谱形式或递归公式作为补充来计算;附录中提供了可用的渐近展开范围。