Elastic tidal response of a laterally heterogeneous planet: a complete perturbation formulation
Elastic tidal response of a laterally heterogeneous planet: a complete perturbation formulation
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横向异质行星的弹性潮汐响应：完整的扰动公式
DOI：
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发表时间：
2016
期刊：
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通讯作者：
J. Wahr
中科院分区：
文献类型：
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作者：
C. Qin;S. Zhong;J. Wahr
S U M M A R Y约束行星内部的横向变化结构对于理解行星的组成和内部动力学都很重要。认识到地震成像技术目前只适用于研究地球的内部结构，可以由先进的空间大地测量技术支持的方法可能成为其他行星内部“成像”的替代方案。潮汐层析成像方法是一种可能性，它依赖于对行星对其体潮的响应的高精度测量。然而，它是必不可少的，以开发一个有效的分析工具，计算潮汐响应的依赖3-D内部结构。在本文中，我们提出了一个完整的制定这样一个分析工具，计算高精度的潮汐响应的类地行星的横向不均匀性，其弹性和密度结构。我们把横向非均匀性视为小扰动，并根据微扰理论推导出控制方程。在球谐表示中，每个扰动阶的方程在模式耦合允许的谐波处被简化为多个矩阵方程，并且总响应等于所有这些单谐响应的总和，这可以半解析地求解。我们测试我们的扰动方法，将其应用到月球的谐波度-1地幔结构的潮汐响应的扰动解进行比较，从一个完全的数值方法。这两种方法的结果之间的显着协议验证微扰方法。作为一个例子，我们然后使用摄动方法来评估月球地壳厚度变化对月球潮汐响应的影响。我们发现，月球地壳产生小得多的程度3潮汐响应比一个相对较弱的程度1在月球地幔深部的结构。我们的计算表明，3度潮汐响应测量可能持有关键的限制可能度1地幔结构的月球，从以前的模拟结果建议。
S U M M A R Y Constraining laterally varying structures in planetary interiors is important for understanding both the composition and the internal dynamics of a planet. Recognizing that seismic imaging technique is currently only viable for studying the Earth’s interior structures, methods that can be supported by advanced space geodetic techniques may become alternatives to ‘image’ the interiors of other planets. The method of tidal tomography is one possibility, and it relies on high precision measurement of the response of a planet to its body tide. However, it is essential to develop an efficient analytical tool that computes the dependence of tidal response to 3-D interior structures. In this paper, we present a complete formulation of such an analytical tool, which calculates to high accuracy the tidal response of a terrestrial planet with lateral heterogeneities in its elastic and density structures. We treat the lateral heterogeneities as small perturbations and derive the governing equations based on the perturbation theory. In a spherical harmonic representation, equations at each order of perturbation are reduced into multiple matrix equations at harmonics that are allowed by mode couplings, and the total response equals the sum of all those single-harmonic responses, which can be solved semi-analytically. We test our perturbation method by applying it to the Moon with a harmonic degree-1 mantle structure for which the perturbation solutions of the tidal response are compared with those from a fully numerical method. The remarkable agreement between results from these two methods validates the perturbation method. As an example, we then use the perturbation method to evaluate the impact of lunar crustal thickness variations on tidal response of the Moon. We find that lunar crust produces much smaller degree-3 tidal responses than a relatively weak degree-1 structure in the deep lunar mantle. Our calculations show that degree-3 tidal response measurements may hold key constraints on possible degree-1 mantle structure of the Moon, as suggested from previous modelling results.