Scaling of the geomagnetic secular variation time scale

IF 2.8 3区 地球科学 Q2 GEOCHEMISTRY & GEOPHYSICS Geophysical Journal International Pub Date : 2024-07-06 DOI:10.1093/gji/ggae234
Yue-Kin Tsang, Chris A Jones
{"title":"Scaling of the geomagnetic secular variation time scale","authors":"Yue-Kin Tsang, Chris A Jones","doi":"10.1093/gji/ggae234","DOIUrl":null,"url":null,"abstract":"Summary The ratio of the magnetic power spectrum and the secular variation spectrum measured at the Earth’s surface provides a time scale τsv(l) as a function of spherical harmonic degree l. τsv is often assumed to be representative of time scales related to the dynamo inside the outer core and its scaling with l is debated. To assess the validity of this surmise and to study the time variation of the geomagnetic field $\\dot{B}$ inside the outer core, we introduce a magnetic time-scale spectrum τ(l, r) that is valid for all radius r above the inner core and reduces to the usual τsv at and above the core–mantle boundary (CMB). We study τ in a numerical geodynamo model. At the CMB, we find that τ ∼ l−1 is valid at both the large and small scales, in agreement with previous numerical studies on τsv. Just below the CMB, the scaling undergo a sharp transition at small l. Consequently, in the interior of the outer core, τ exhibits different scaling at the large and small scales, specifically, the scaling of τ becomes shallower than l−1 at small l. We find that this transition at the large scales stems from the fact that the horizontal components of the magnetic field evolve faster than the radial component in the interior. In contrast, the magnetic field at the CMB must match onto a potential field, hence the dynamics of the radial and horizontal magnetic fields are tied together. The upshot is τsv becomes unreliable in estimating time scales inside the outer core. Another question concerning τ is whether an argument based on the frozen-flux hypothesis can be used to explain its scaling. To investigate this, we analyse the induction equation in the spectral space. We find that away from both boundaries, the magnetic diffusion term is negligible in the power spectrum of $\\dot{B}$. However, $\\dot{B}$ is controlled by the radial derivative in the induction term, thus invalidating the frozen-flux argument. Near the CMB, magnetic diffusion starts to affect $\\dot{B}$ rendering the frozen-flux hypothesis inapplicable. We also examine the effects of different velocity boundary conditions and find that the above results apply for both no-slip and stress-free conditions at the CMB.","PeriodicalId":12519,"journal":{"name":"Geophysical Journal International","volume":null,"pages":null},"PeriodicalIF":2.8000,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geophysical Journal International","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1093/gji/ggae234","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0

Abstract

Summary The ratio of the magnetic power spectrum and the secular variation spectrum measured at the Earth’s surface provides a time scale τsv(l) as a function of spherical harmonic degree l. τsv is often assumed to be representative of time scales related to the dynamo inside the outer core and its scaling with l is debated. To assess the validity of this surmise and to study the time variation of the geomagnetic field $\dot{B}$ inside the outer core, we introduce a magnetic time-scale spectrum τ(l, r) that is valid for all radius r above the inner core and reduces to the usual τsv at and above the core–mantle boundary (CMB). We study τ in a numerical geodynamo model. At the CMB, we find that τ ∼ l−1 is valid at both the large and small scales, in agreement with previous numerical studies on τsv. Just below the CMB, the scaling undergo a sharp transition at small l. Consequently, in the interior of the outer core, τ exhibits different scaling at the large and small scales, specifically, the scaling of τ becomes shallower than l−1 at small l. We find that this transition at the large scales stems from the fact that the horizontal components of the magnetic field evolve faster than the radial component in the interior. In contrast, the magnetic field at the CMB must match onto a potential field, hence the dynamics of the radial and horizontal magnetic fields are tied together. The upshot is τsv becomes unreliable in estimating time scales inside the outer core. Another question concerning τ is whether an argument based on the frozen-flux hypothesis can be used to explain its scaling. To investigate this, we analyse the induction equation in the spectral space. We find that away from both boundaries, the magnetic diffusion term is negligible in the power spectrum of $\dot{B}$. However, $\dot{B}$ is controlled by the radial derivative in the induction term, thus invalidating the frozen-flux argument. Near the CMB, magnetic diffusion starts to affect $\dot{B}$ rendering the frozen-flux hypothesis inapplicable. We also examine the effects of different velocity boundary conditions and find that the above results apply for both no-slip and stress-free conditions at the CMB.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
地磁世俗变化时间尺度的缩放
摘要 在地球表面测量到的磁功率谱和世俗变化谱的比值提供了一个时间尺度τsv(l),它是球谐波度l的函数。τsv通常被假定为代表与外核内部动力相关的时间尺度,它与l的比例关系还存在争议。为了评估这一推测的正确性,并研究外核内部地磁场 $\dot{B}$ 的时间变化,我们引入了一个磁时间尺度谱 τ(l,r),它对内核上方所有半径 r 都有效,并在核幔边界(CMB)及以上还原为通常的 τsv。我们在数值地球动力模型中研究了 τ。我们发现,在 CMB 上,τ∼ l-1 在大尺度和小尺度上都是有效的,这与之前对 τsv 的数值研究一致。因此,在外核内部,τ 在大、小尺度上表现出不同的缩放比例,具体来说,τ 的缩放比例在小 l 时变得比 l-1 浅。相反,CMB 的磁场必须与势场相匹配,因此径向磁场和水平磁场的动态是联系在一起的。结果是,τsv 在估算外核内部的时间尺度时变得不可靠。有关 τ 的另一个问题是,基于冻结流假说的论证是否可以用来解释它的缩放。为了研究这个问题,我们分析了频谱空间中的感应方程。我们发现,在远离两个边界的地方,磁扩散项在 $\dot{B}$ 的功率谱中可以忽略不计。然而,$\dot{B}$ 是由感应项的径向导数控制的,从而使冻结流论证失效。在CMB附近,磁扩散开始影响$\dot{B}$,从而使冻结通量假说失效。我们还研究了不同速度边界条件的影响,发现上述结果适用于 CMB 处的无滑动和无应力条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Geophysical Journal International
Geophysical Journal International 地学-地球化学与地球物理
CiteScore
5.40
自引率
10.70%
发文量
436
审稿时长
3.3 months
期刊介绍: Geophysical Journal International publishes top quality research papers, express letters, invited review papers and book reviews on all aspects of theoretical, computational, applied and observational geophysics.
期刊最新文献
A rapid analysis of aftershock processes after a moderate magnitude earthquake with ML-methods Influence of upwelling mantle magmas on cratonic crust implied from Vp/Vs beneath South America platform Observations from the Seafloor: Ultra-low-frequency ambient ocean-bottom nodal seismology at the amendment field Upscaling from Mineral Microstructures to Tectonic Macrostructures Towards a new standard for seismic moment tensor inversion containing 3D Earth structure uncertainty
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1