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Evaluation Procedures for the Potential Harmonic Coefficients of a Generally Shaped Polyhedron 一般形状多面体势调和系数的评定方法
IF 4.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-08-16 DOI: 10.1007/s10712-023-09802-y
Georgia Gavriilidou, Dimitrios Tsoulis

Two computational strategies for the evaluation of the spherical harmonic coefficients of the gravitational potential due to a generally shaped homogeneous polyhedral source are examined in detail. The techniques are implemented numerically for the known asteroid shape models of Eros and Didymos. The aim of the investigation is to quantify specific numerical aspects of the two algorithms, such as the accuracy of the techniques compared to a closed analytical solution for varying distance between source and computation point, the band-limited spectral analysis of the obtained spherical harmonic models and the convergence behavior of the corresponding series expansion in the vicinity of the characteristic Brillouin sphere. From a computational point of view, the line integral approach demands approximately three times the CPU time of Werner’s method. The two sets of spherical harmonic coefficients are 100% correlated up to degree 45 for Eros and up to degree 49 for Didymos. Approaching degree 100, the correlation by degree decreases by 0.0004% for Eros and by 0.004% for Didymos, the corresponding values for the correlation by order being 0.0002% and 0.304%. Inside the Brillouin sphere and approaching its boundary, the numerical agreement of the gravitational potential between the line integral method and the analytical solution is at the 1E-4 level, while with Werner’s approach at the 1E-7 level. At a distance of 33.5 km outside the Brillouin sphere for Eros and 2.2 km for Didymos, both methods are identical, reaching an agreement level with the analytical solution of 1E-11 level for Eros and 1E-14 for Didymos. In terms of spherical harmonic representation, the series defined by the line integral approach converges faster to the analytical value for the gravitational potential by 4 degrees.

详细研究了评估一般形状的均质多面体源引起的引力势的球谐波系数的两种计算策略。这些技术是针对已知的厄洛斯和狄迪莫斯小行星形状模型进行数值计算的。研究的目的是对两种算法的具体数值方面进行量化,如在源和计算点之间的距离变化时,与封闭式分析解相比,两种技术的准确性;对所获球谐模型的带限频谱分析;以及在特征布里渊球附近相应序列展开的收敛行为。从计算角度来看,线积分方法所需的 CPU 时间大约是维尔纳方法的三倍。两组球谐波系数在厄洛斯(Eros)的 45 度以内和狄迪莫斯(Didymos)的 49 度以内是 100% 相关的。在接近 100 度时,Eros 和 Didymos 的度相关性分别降低了 0.0004%和 0.004%,阶相关性的相应值分别为 0.0002%和 0.304%。在布里渊球内部和接近其边界的地方,线积分法和解析解之间的引力势数值一致性达到了 1E-4 的水平,而维尔纳方法则达到了 1E-7 的水平。在布里渊球外 33.5 千米的距离(厄洛斯)和 2.2 千米的距离(狄狄莫斯),两种方法完全相同,厄洛斯与分析解的一致性达到了 1E-11 的水平,狄狄莫斯达到了 1E-14 的水平。就球面谐波表示法而言,线积分法定义的数列收敛速度比重力势能分析值快 4 度。
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引用次数: 0
PC Index as a Ground-Based Indicator of the Solar Wind Energy Incoming into the Magnetosphere: (2) Relation of PC Index to Magnetic Disturbances PC指数作为太阳风进入磁层的地面指标:(2)PC指数与磁扰动的关系
IF 4.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-08-02 DOI: 10.1007/s10712-023-09799-4
O. A. Troshichev

The paper summarizes the issues related to relationships between the PC index and magnetic disturbances: threshold level of the PC index required for the disturbances beginning, delay time in response of magnetic substorms and storms to the PC index growth, relation of PC index to magnetospheric field-aligned currents in course of substorm, different types of magnetic substorms (isolated, expanded, delayed, sawtooth) and magnetic storms (classic, pulsed and composite) and their relation to different regularities in the PC index alterations, linear dependence of the substorm and storm intensities on value of the preceding of PC index, special features of magnetic activity in the winter and summer polar caps, variations of PC index and magnetic disturbances in course of the 23/24 solar activity cycles. New aspects that have arisen due to the PC index application are concerned with the threshold-dependent mode of the substorm development and regular repeateness of sawtooth substorms occurring under conditions of steady powerful EKL field. The experimental results examined in the paper are indicative that the PC index serves as an indicator of the solar wind energy which comes in the magnetosphere and then realizes in the form of magnetosphere disturbances. This paper follows the review of Troshichev (Front Astron Space Sci 9:1069470, 2022), where the relationships between the solar wind electric field EKL and PC index have been examined.

本文总结了与 PC 指数和磁扰动之间的关系有关的问题:扰动开始时所需的 PC 指数临界值、磁亚暴和磁风暴对 PC 指数增长的反应延迟时间、亚暴过程中 PC 指数与磁层场对齐电流的关系、不同类型的磁亚暴(孤立、扩展、延迟、锯齿)和磁风暴(典型、脉冲和复合)及其与 PC 指数变化的不同规律性的关系、亚暴和风暴强度的线性依赖性、脉冲和复合)及其与 PC 指数变化的不同规律性的关系、亚暴和磁暴强度与 PC 指数前值的线性关系、冬季和夏季极冠磁活动的特点、23/24 太阳活动周期中 PC 指数和磁扰动的变化。由于 PC 指数的应用而产生的新方面涉及亚暴发展的阈值依赖模式和在稳定的强大 EKL 场条件下发生的锯齿亚暴的规律重复性。本文研究的实验结果表明,PC 指数可作为太阳风能量的指标,这些能量进入磁层后以磁层扰动的形式实现。本文是继 Troshichev 的综述(Front Astron Space Sci 9:1069470, 2022 年)之后,对太阳风电场 EKL 和 PC 指数之间关系的研究。
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引用次数: 0
Closure of Earth’s Global Seasonal Cycle of Energy Storage 地球能量储存全球季节性循环的终结
IF 4.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-07-18 DOI: 10.1007/s10712-023-09797-6
Gregory C. Johnson, Felix W. Landerer, Norman G. Loeb, John M. Lyman, Michael Mayer, Abigail L. S. Swann, Jinlun Zhang

The global seasonal cycle of energy in Earth’s climate system is quantified using observations and reanalyses. After removing long-term trends, net energy entering and exiting the climate system at the top of the atmosphere (TOA) should agree with the sum of energy entering and exiting the ocean, atmosphere, land, and ice over the course of an average year. Achieving such a balanced budget with observations has been challenging. Disagreements have been attributed previously to sparse observations in the high-latitude oceans. However, limiting the local vertical integration of new global ocean heat content estimates to the depth to which seasonal heat energy is stored, rather than integrating to 2000 m everywhere as done previously, allows closure of the global seasonal energy budget within statistical uncertainties. The seasonal cycle of energy storage is largest in the ocean, peaking in April because ocean area is largest in the Southern Hemisphere and the ocean’s thermal inertia causes a lag with respect to the austral summer solstice. Seasonal cycles in energy storage in the atmosphere and land are smaller, but peak in July and September, respectively, because there is more land in the Northern Hemisphere, and the land has more thermal inertia than the atmosphere. Global seasonal energy storage by ice is small, so the atmosphere and land partially offset ocean energy storage in the global integral, with their sum matching time-integrated net global TOA energy fluxes over the seasonal cycle within uncertainties, and both peaking in April.

利用观测和再分析,对地球气候系统中能量的全球季节性循环进行了量化。在排除长期趋势后,进入和离开大气顶部气候系统的净能量(TOA)应与平均一年中进入和离开海洋、大气、陆地和冰的能量总和一致。通过观察实现这种平衡预算一直是一项挑战。先前的分歧被归因于高纬度海洋的稀疏观测。然而,将新的全球海洋热含量估计值的局部垂直整合限制在季节性热能储存的深度,而不是像以前那样在各地整合到2000米,可以在统计不确定性范围内关闭全球季节性能量收支。能量储存的季节周期在海洋中最大,在4月达到峰值,因为南半球海洋面积最大,海洋的热惯性导致了相对于南方夏至的滞后。大气和陆地能量储存的季节周期较小,但分别在7月和9月达到高峰,这是由于北半球陆地较多,陆地的热惯性比大气大。全球冰的季节性蓄能较小,因此大气和陆地在全球积分中部分抵消了海洋蓄能,它们的总和与季节周期内不确定因素的时间积分净全球TOA能量通量相匹配,并且都在4月份达到峰值。
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引用次数: 0
Electromagnetic Modeling Using Adaptive Grids – Error Estimation and Geometry Representation 使用自适应网格的电磁建模 - 误差估计和几何表示法
IF 4.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-06-22 DOI: 10.1007/s10712-023-09794-9
Klaus Spitzer

This review paper addresses the development of numerical modeling of electromagnetic fields in geophysics with a focus on recent finite element simulation. It discusses ways of estimating errors of our solutions for a perfectly matched modeling domain and the problems that arise from its insufficient representation. After a brief outline of early methods and modeling approaches, the paper mainly discusses the capabilities of the finite element method formulated on unstructured grids and the advantages of local h-refinement allowing for both a flexible and largely accurate representation of the geometries of the multi-scale geomaterial and an accurate evaluation of the underlying functions representing the physical fields. In summary, the accuracy of the solution depends on the geometric mapping, the choice of the mathematical model, and the spatial discretization. Although the available error estimators do not necessarily provide reliable error bounds for our complex geomodels, they are still useful to guide grid refinement. Therefore, an overview of the most common a posteriori error estimators is given. It will be shown that the sensitivity is the most important function in both guiding the geometric mapping and the local refinement.

这篇综述论文探讨了地球物理学电磁场数值建模的发展,重点是最近的有限元模拟。论文讨论了如何估算完全匹配建模域的解的误差,以及由于其表示不充分而产生的问题。在简要概述了早期的方法和建模方法之后,论文主要讨论了在非结构网格上制定的有限元方法的能力,以及局部 h- 精化的优势,这种方法既能灵活、基本准确地表示多尺度地球材料的几何形状,又能准确评估表示物理场的基本函数。总之,求解的准确性取决于几何映射、数学模型的选择和空间离散化。虽然现有的误差估计值并不一定能为复杂的地质模型提供可靠的误差范围,但仍可用于指导网格细化。因此,本文概述了最常见的后验误差估算器。结果将表明,灵敏度是指导几何映射和局部细化的最重要函数。
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引用次数: 0
Mass Balances of the Antarctic and Greenland Ice Sheets Monitored from Space 从太空监测南极和格陵兰冰盖的物质平衡
IF 4.6 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-06-15 DOI: 10.1007/s10712-023-09795-8
Inès N. Otosaka, M. Horwath, R. Mottram, S. Nowicki
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引用次数: 3
Correction: Hydrometeorological Extreme Events in West Africa: Droughts 修正:西非水文气象极端事件:干旱
IF 4.6 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-06-12 DOI: 10.1007/s10712-023-09796-7
Pauline A. Dibi-Anoh, Moussa Koné, Helena Gerdener, Jürgen Kusche, Christophe K. N’Da
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引用次数: 0
Theories of Growth and Propagation of Parallel Whistler-Mode Chorus Emissions: A Review 平行哨声模式合唱辐射的生长和传播理论综述
IF 4.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-06-01 DOI: 10.1007/s10712-023-09792-x
Miroslav Hanzelka, Ondřej Santolík

The significant role of nonlinear wave–particle interactions in the macrodynamics and microdynamics of the Earth’s outer radiation belt has long been recognised. Electron dropouts during magnetic storms, microbursts in atmospheric electron precipitation, and pulsating auroras are all associated with the rapid scattering of energetic electrons by the whistler-mode chorus, a structured electromagnetic emission known to reach amplitudes of about (1%) of the ambient magnetic field. Despite the decades of experimental and theoretical investigations of chorus and the recent progress achieved through numerical simulations, there is no definitive theory of the chorus formation mechanism, not even in the simple case of parallel (one-dimensional) propagation. Here we follow the evolution of these theories from their beginnings in the 1960s to the current state, including newly emerging self-consistent excitation models. A critical review of the unique features of each approach is provided, taking into account the most recent spacecraft observations of the fine structure of chorus. Conflicting interpretations of the role of resonant electron current and magnetic field inhomogeneity are discussed. We also discuss the interplay between nonlinear growth and microscale propagation effects and identify future theoretical and observational challenges stemming from the two-dimensional aspects of chorus propagation.

非线性波粒相互作用在地球外辐射带的宏观动力学和微观动力学中的重要作用早已得到公认。磁暴中的电子骤降、大气电子沉淀中的微暴以及脉动极光都与高能电子被啸叫模式合唱快速散射有关,众所周知,这种结构化的电磁辐射的振幅可以达到环境磁场的(1%)左右。尽管对合唱进行了数十年的实验和理论研究,最近又通过数值模拟取得了进展,但关于合唱的形成机制,即使是在平行(一维)传播的简单情况下,也没有确定的理论。在此,我们将跟踪这些理论从 20 世纪 60 年代开始到现在的演变过程,包括新出现的自洽激发模型。考虑到最新的航天器对合唱精细结构的观测,我们对每种方法的独特之处进行了批判性的评论。讨论了对共振电子电流和磁场不均匀性作用的相互矛盾的解释。我们还讨论了非线性增长和微尺度传播效应之间的相互作用,并确定了未来在合唱传播的二维方面所面临的理论和观测挑战。
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引用次数: 0
The Magma Emplacement of a Composite Volcanic-Intrusive System and Its Mineralization 火山—侵入复合体系岩浆侵位及其成矿作用
IF 4.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-05-19 DOI: 10.1007/s10712-023-09793-w
Yihao Wu, Jiangtao Han, Guoqing Ma, Yunhe Liu, Fuxing Han, Lijia Liu, Lei Guo, Ye Guan, Yinghui Zhang

Magma emplacement can restrict the nature and distribution of an ore deposit, and is an important topic for the study of mineralization mechanisms. Previous studies of magma emplacement have focused mainly on the superimposed mineralization of multi-stage magma in time, whereas the superimposed characteristics and mineralization of different magma emplacement in space are unclear. We estimate a 3-D multiple geophysical model in the Shuangjianzishan Ag–Pb–Zn district, northeastern China, using gravity, magnetic, magnetotelluric and seismic data. The model describes the distribution of buried magmatic rocks related to mineralization in the ore district and highlights the detailed structure and connection of volcanism and intrusion. The volcanism is characterized by a tree-like structure consisting of a near-conical channel and an annular fault system; the intrusion appears as a dome-shaped structure, and its lateral distribution is controlled by faults. The geophysical results reveal a deep fault system connecting volcanism and intrusion. Combining the results with regional geology, petrophysical properties and borehole information, we propose a composite metallogenic model for the ore district, which is that the volcanism caused the ore-bearing magma to migrate to the present-day location of the base of the ore deposit through the deep fault system, and formed an intrusive complex with the ore-bearing magma emplaced in a dome below the present-day location of the deposit. This resulted in the formation of complex and fault-controlled ore bodies. Reviewing the global metallogenic characteristics related to magmatism, our results demonstrate the magma emplacement pattern of a composite volcanic-intrusive system may be an important factor for the formation of super-large deposits.

岩浆的赋存可以制约矿床的性质和分布,是成矿机制研究的重要课题。以往对岩浆赋存的研究主要集中在多期岩浆在时间上的叠加成矿作用,而对不同岩浆赋存在空间上的叠加特征和成矿作用尚不清楚。我们利用重力、磁力、磁电和地震数据估算了中国东北双剑子山银铅锌矿区的三维多重地球物理模型。该模型描述了矿区内与矿化有关的埋藏岩浆岩的分布,并突出了火山活动和侵入活动的详细结构和联系。火山活动的特征是由一个近锥形通道和一个环形断层系统组成的树状结构;侵入体呈圆顶形结构,其横向分布受断层控制。地球物理结果显示,一个深层断层系统连接着火山活动和侵入体。结合区域地质、岩石物理特性和钻孔资料,我们提出了矿区的复合成矿模式,即火山作用使含矿岩浆通过深部断层系统迁移到今天的矿床底部位置,并形成了一个侵入复合体,含矿岩浆赋存在今天矿床位置下方的穹窿中。这就形成了复杂的、受断层控制的矿体。回顾与岩浆活动有关的全球成矿特征,我们的研究结果表明,火山-侵入复合系统的岩浆赋存模式可能是形成超大型矿床的一个重要因素。
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引用次数: 0
Towards Millimeter-Level Accuracy in GNSS-Based Space Geodesy: A Review of Error Budget for GNSS Precise Point Positioning 面向毫米级精度的GNSS空间大地测量:GNSS精确点定位误差预算综述
IF 4.6 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-05-13 DOI: 10.1007/s10712-023-09785-w
Xianjie Li, Jean-Pierre Barriot, Yidong Lou, Weixing Zhang, Pengbo Li, Chuang Shi

The aim of the new generation of Global Geodetic Observing System is a millimeter-level accuracy in positioning, with a crucial role to be played by Global Navigation Satellites Systems (GNSS) in the Precise Point Positioning (PPP) mode. This is of course because GNSS constellations and receivers provide an efficient stand-alone technique with a homogeneous performance over large areas (positions, navigation and meteorology) when used in conjunction with the PPP mode, with also an ever-increasing data flow and different satellite line-of-sights. The requirement of accuracies reaching the millimeter or sub-millimeter implies a knowledge at this level of each line in the GNSS-PPP error budget, including, but not restricted to: clock biases, troposphere and ionosphere delays, multipath and ground deformations. In this review study, we consider this millimeter-/submillimeter level GNSS-PPP error budget, and possible mitigations and improvements in the frame of the existing global constellations: GPS, Galileo, GLONASS and BDS, in view of augmented constellations and/or Low Earth Orbit constellations, which will be available in the near future. We also pay a special attention to systematic biases that can/could exist between constellations.

新一代全球大地观测系统的目标是达到毫米级的定位精度,全球导航卫星系统(GNSS)将在精确点定位(PPP)模式中发挥关键作用。当然,这是因为GNSS星座和接收器在与PPP模式结合使用时,提供了一种高效的独立技术,在大范围内(定位、导航和气象)具有均匀的性能,同时还具有不断增加的数据流和不同的卫星视距。对达到毫米或亚毫米精度的要求意味着对GNSS-PPP误差预算中每条线的这一级别的了解,包括但不限于:时钟偏差、对流层和电离层延迟、多径和地面变形。在本综述研究中,我们考虑了这种毫米/亚毫米级别的GNSS-PPP误差预算,以及在现有全球星座框架下可能的缓解和改进:GPS、伽利略、GLONASS和BDS,考虑到增强星座和/或近地轨道星座,将在不久的将来可用。我们还特别关注星座之间可能存在的系统性偏差。
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引用次数: 2
On Gravimetric Detection of Thin Elongated Sources Using the Growth Inversion Approach 利用生长反演方法对细长源进行重力探测
IF 4.6 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS Pub Date : 2023-04-29 DOI: 10.1007/s10712-023-09790-z
Jozef Bódi, Peter Vajda, Antonio G. Camacho, Juraj Papčo, José Fernández

Thin elongated sources, such as dykes, sills, chimneys, inclined sheets, etc., often encountered in volcano gravimetric studies, pose great challenges to gravity inversion methods based on model exploration and growing sources bodies. The Growth inversion approach tested here is based on partitioning the subsurface into right-rectangular cells and populating the cells with differential densities in an iterative weighted mixed adjustment process, in which the minimization of the data misfit is balanced by forcing the growing subsurface density distribution into compact source bodies. How the Growth inversion can cope with thin elongated sources is the subject of our study. We use synthetic spatiotemporal gravity changes caused by simulated sources placed in three real volcanic settings. Our case studies demonstrate the benefits and limitations of the Growth inversion as applied to sparse and noisy gravity change data generated by thin elongated sources. Such sources cannot be reproduced by Growth accurately. They are imaged with smaller density contrasts, as much thicker, with exaggerated volume. Despite this drawback, the Growth inversion can provide useful information on several source parameters even for thin elongated sources, such as the position (including depth), the orientation, the length, and the mass, which is a key factor in volcano gravimetry. Since the density contrast of a source is not determined by the inversion, but preset by the user to run the inversion process, it cannot be used to specify the nature of the source process. The interpretation must be assisted by external constraints such as structural or tectonic controls, or volcanological context. Synthetic modeling and Growth inversions, such as those presented here, can serve also for optimizing the volcano monitoring gravimetric network design. We conclude that the Growth inversion methodology may, in principle, prove useful even for the detection of thin elongated sources of high density contrast by providing useful information on their position, shape (except for thickness) and mass, despite the strong ambiguity in determining their differential density and volume. However, this yielded information may be severely compromised in reality by the sparsity and noise of the interpreted gravity data.

火山重力研究中经常遇到的细细长源,如岩脉、岩台、烟囱、斜板等,对基于模型勘探和源体生长的重力反演方法提出了很大的挑战。这里测试的Growth反演方法是基于将地下划分为右矩形单元,并在迭代加权混合调整过程中以不同密度填充单元,其中通过将不断增长的地下密度分布强制到紧凑的源体中来平衡数据不拟合的最小化。生长反转如何处理细长源是我们研究的主题。我们使用在三个真实火山环境中模拟源引起的合成时空重力变化。我们的案例研究证明了Growth反演应用于由细长源产生的稀疏和噪声重力变化数据的优点和局限性。Growth无法准确地复制这些来源。它们的成像密度对比较小,同样厚,体积夸张。尽管有这样的缺点,Growth反演可以提供一些有用的源参数信息,甚至对于细长的源,如位置(包括深度)、方向、长度和质量,这是火山重力测量的一个关键因素。由于源的密度对比不是由反演决定的,而是由用户在运行反演过程时预先设定的,因此不能用于指定源进程的性质。解释必须借助于外部约束,如构造或构造控制,或火山背景。综合建模和生长反演,如这里所提出的,也可以用于优化火山监测重力网络的设计。我们得出的结论是,增长型反演方法在原则上可能被证明是有用的,即使对高密度对比的细长源的检测也有用,因为它提供了关于它们的位置、形状(厚度除外)和质量的有用信息,尽管在确定它们的差密度和体积方面存在很强的模糊性。然而,这种所得的信息在现实中可能会受到解释重力数据的稀疏性和噪声的严重影响。
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引用次数: 0
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Surveys in Geophysics
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