曲面磁场的有效建模及其应用研究地球曲率对正演计算的影响

IF 1.9 4区 地球科学 Q2 GEOCHEMISTRY & GEOPHYSICS
Changqing Yuan, Jinsong Du, Jiangsong Gui, Liang Yin, Chao Chen
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引用次数: 0

摘要

随着CHAMP、Swarm、ses -1、MSS-1等先进卫星对岩石圈磁场测量的不断积累和全球模型的逐渐可靠,对考虑地球曲率的磁场(即磁势及其导数)的真实正模拟方法提出了要求,同时也提出了挑战。利用一组初等曲面的空间离散化方法,利用叠加原理在球面域近似复杂磁化源,使源体无“孔洞”饱和。由于曲面的磁场没有解析解(除了位于极轴上的特殊点),数值解是有效的方法,其中通常采用高斯-勒让德正交(GLQ)。然而,当曲面的几何尺寸非常大或曲面与观测点的距离非常近,即距离-尺寸比(DSR)很小时,所需的计算就会变得非常耗时。此外,在实际应用中,dsr随震源位置和观测点之间的相对距离而变化,因此往往不均匀。因此,为了在减少计算时间的同时保持每个观测点的期望精度(即相对百分比误差),采用了一种高效的正演建模方案。该方案的关键是采用了一种新的简单高效的自适应细分方法。它是一种基于最长边长的等距细分方法,而不是递归或堆叠。通过对细分曲面的个数进行比较,该方法采用了一种新的先验终止条件进行细分,而不是传统的后验方法,因此可以避免过度细分,并且比递归方法计算效率更高。通过数值模拟得到所需的dsr,误差分别为0.1%和0.01%。同时,对该方案进行了打包,并发布了用c++编程编写的开源正演计算软件。然后,利用Runcorn定理对全局齐次球壳的解析解进行了验证。作为实际应用,研究了地球曲率对磁场正演模拟的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficiently Modelling Magnetic Fields of the Tesseroid and its Application to Investigate Impacts of Earth’s Curvature on Forward Calculation

With the continually accumulated magnetic measurements and the gradually reliable global models of the lithospheric magnetic field by several advanced satellites (such as CHAMP, Swarm, CSES-1 and MSS-1), now present a requirement and also a challenge to develop realistic forward modelling methods for magnetic fields (i.e., the magnetic potential and its derivatives) that take the curvature of the Earth into account. The spatial discretization by a set of elementary tesseroids is generally utilized to approximate the complex magnetized source in spherical domain by the principle of superposition and saturate the source volume without “holes”. Since there is no analytic solution for magnetic fields of the tesseroid (except for the special points located on the polar axis), the numerical solution is the efficient way, where the Gauss–Legendre quadrature (GLQ) is usually employed. However, the required computation becomes notably time-consuming when the geometric sizes of the tesseroids are very large or the distances between the tesseroids and the observation points are very close, that is, the distance-to-size ratio (DSR) is quite small. Moreover, in an actual application, the DSRs vary with relative distances between source locations and observation points and hence are often non-uniform. Therefore, in order to reduce the computational time while maintaining a desired accuracy (i.e., relative percentage error) of each observation point, an efficient forward modelling scheme is employed. The key point of this scheme is the adoption of a new simple and efficient adaptive subdivision method. It is an equidistant subdivision method based on the longest side length, rather than recursion or stacking. By comparing the number of subdivided tesseroids, this method demonstrates its ability to avoid over-subdivision and perform more efficient calculations compared to the recursive method, because it adopts a new priori termination condition for subdivision rather than the traditional posteriori way. We obtain the required DSRs with errors of 0.1% and 0.01% through numerical simulation. At the same time, we package this scheme and release the open-source forward calculation software written by the C++ programming. Then, the analytical solution of the global homogeneous spherical shell using Runcorn’s theorem is utilized to test our newly proposed method. As a practical application, the impacts of Earth’s curvature on forward modelling of the magnetic fields are investigated.

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来源期刊
pure and applied geophysics
pure and applied geophysics 地学-地球化学与地球物理
CiteScore
4.20
自引率
5.00%
发文量
240
审稿时长
9.8 months
期刊介绍: pure and applied geophysics (pageoph), a continuation of the journal "Geofisica pura e applicata", publishes original scientific contributions in the fields of solid Earth, atmospheric and oceanic sciences. Regular and special issues feature thought-provoking reports on active areas of current research and state-of-the-art surveys. Long running journal, founded in 1939 as Geofisica pura e applicata Publishes peer-reviewed original scientific contributions and state-of-the-art surveys in solid earth and atmospheric sciences Features thought-provoking reports on active areas of current research and is a major source for publications on tsunami research Coverage extends to research topics in oceanic sciences See Instructions for Authors on the right hand side.
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