An accurate and lightweight calculation for the high degree truncation coefficient via asymptotic expansion with applications to spectral gravity forward modeling

IF 3.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Journal of Geodesy Pub Date : 2024-10-10 DOI:10.1007/s00190-024-01895-6
Linshan Zhong, Hongqing Li, Qiong Wu
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Abstract

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.

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通过渐近展开计算高阶截断系数并将其应用于频谱引力前向建模的精确而轻便的方法
截断系数广泛应用于地球物理和大地测量的非全球覆盖计算中,并且始终与海拔高度有关。由于截断系数的两种常用计算方法,即频谱形式和递推公式,都存在高海拔导致精度下降的问题,导致前者收敛缓慢,后者数值不稳定递推。渐近展开在数学上随着度数的增加而收敛,可以精确地弥补这两种方法的不足。本研究引入渐近展开法,对频谱重力正演建模的截断系数进行高度精确计算。对整个高度和整个积分半径的评估表明,所提出的方法具有以下优点:(i) 计算精度随着度数的增加而增加,且与高度无关;(ii) 可通过双精度格式支持精确计算;(iii) 随着度数的增加,计算几乎无需额外的时间成本。一般情况下,使用渐近展开法计算高阶截断系数,而低阶截断系数可使用光谱形式或多精度格式的递推公式作为补充计算;附录中提供了渐近展开法的可用范围。
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来源期刊
Journal of Geodesy
Journal of Geodesy 地学-地球化学与地球物理
CiteScore
8.60
自引率
9.10%
发文量
85
审稿时长
9 months
期刊介绍: The Journal of Geodesy is an international journal concerned with the study of scientific problems of geodesy and related interdisciplinary sciences. Peer-reviewed papers are published on theoretical or modeling studies, and on results of experiments and interpretations. Besides original research papers, the journal includes commissioned review papers on topical subjects and special issues arising from chosen scientific symposia or workshops. The journal covers the whole range of geodetic science and reports on theoretical and applied studies in research areas such as: -Positioning -Reference frame -Geodetic networks -Modeling and quality control -Space geodesy -Remote sensing -Gravity fields -Geodynamics
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