A Fractal Interpretation of the Topography of the Geomagnetic Scalar Potential at the Core-mantle Boundary

—The spatial power spectrum of the scalar potential (V) of the main geomagnetic field shows a power-law behaviour at the core-mantle boundary (CMB) and an almost uniform distribution of the corresponding phases. This is strong evidence for a fractal topography of V having a non-integer dimension of 2.2 (with an uncertainty of ± 0.1) which is, indeed, found from an analysis of the power spectra of 32 spherical harmonic models of V spanning the interval 1647 to 1990.     

Geomagnetic field mapping from a satellite: Spatial power spectra of the geomagnetic field at various satellite altitudes relative to natural noise sources and instrument noise

For a low-level geomagnetic satellite survey, for which the motion of the satellite converts spatial variation into temporal variation, the limit on accuracy may well be background temporal fluctuations. The sources of the temporal fluctuations are current systems external to the Earth and include currents induced in the Earth due to these sources. The internal sources consist primarily of two components, the main geomagnetic field with sources in the Earth's core and a crustal geomagnetic field.Power spectra of the vertical geomagnetic field internal component that would be observed by a spacecraft in circular orbit at various altitudes, due to satellite motion through the spatially varying geomagnetic field, are compared to power spectra of the natural temporal fluctuations of the geomagnetic field vertical component (natural noise) and to the power spectrum for typical fluxgate magnetometer instrument noise. The natural noise is shown to be greater than this typical instrument noise over the entire frequency range for which useful measurements of the geomagnetic field may be made, for all geomagnetic latitudes and all times. Thus there would be little benefit in reducing the instrument noise below the typical value of 10^?4 gamma² Hz^?1 plus a 1/f component of 10 milligamma rms decade^?1.For a given satellite altitude, there is a maximum frequency above which the natural noise is greater than the power spectrum of the crustal geomagnetic field vertical component. Below this maximum frequency, the situation is reversed. This maximum frequency depends on geomagnetic latitude (and to a lesser extent on time of day and season of year), being lower in the auroral zone than at lower latitudes. The maximum frequency is also lower at higher satellite altitudes. The maximum frequency determines the spatial resolution obtainable on a magnetic field map. The spatial resolution (for impulses) obtainable at low latitudes for a 100-km satellite altitude (possibly achievable by tethering a small satellite at this altitude to a space vehicle at a higher altitude) is 60 km, while at the auroral zone the obtainable spatial resolution is 100 km. At the higher satellite altitude of 300 km the obtainable spatial resolution is 230 km at low latitudes and 530 km at the auroral zone. At 500-km satellite altitude, the obtainable spatial resolution is 500 km at low latitudes, while maps cannot be made at all for the auroral zone unless the data are selected for “quiet” days.For the lower satellite altitudes, greater spatial resolution can be obtained than at higher altitudes. Furthermore since the crustal geomagnetic field power spectrum is larger at lower altitudes, the relative error due to the natural noise is less than for higher altitudes.     

利用大地电磁站间阻抗估算磁暴引起的大地电场

由磁暴引起的地下感应电场(geomagnetic induction electric field,GIE)会影响电网的安全稳定运行,GIE的大小取决于磁暴时磁场的变化率和周围地下介质的电性结构.本文利用在地表观测的磁场与电场数据,首先求得频率域实际地下三维大地电磁站间阻抗,再结合磁暴时段的磁场数据,计算GIE的频谱,最后通过傅里叶反变换,得到GIE时间序列.本文以日本地区三个长期观测的电磁电台站为例,讨论了站间阻抗的长期稳定性,并选取一次典型的磁暴事件,对本文方法进行了验证.结果表明,合成的GIE与实测数据基本一致,说明利用大地电磁站间阻抗,结合地磁台站数据,可以高精度合成GIE.本文方法有助于定量评价磁暴发生时产生的GIE对电网可能造成的破坏作用.     

地球主磁场空间功率谱的变化特征

根据第8代IGRF模型，计算分析了1900－2000年地球磁场和分量X，Y，Z的空间功率谱的变化特征。结果表明1900－2000年主磁场的空间功率谱呈减小趋势，由功率谱随谐波阶次n的变化关系得出的非偶极子场的等效磁源位于核幔边界附近，而且其位置随时间变化，用n=1,2两阶谐波的谱得到的等效磁源位于地球内核边缘，1900年以来离开地心一直向外增大。     

Induction of auroral zone electric currents within the Alaska pipeline

The Alaskar pipeline is a highly conducting anomaly extending 800 miles (1300 km) from about 62° to 69° geomagnetic latitude beneath the most active regions of the ionospheric electrojet current. The spectral behavior of the magnetic field from this current was analyzed using data from standard geomagnetic observatories to establish the predictable patterns of temporal and spatial changes for field pulsation periods between 5 min and 4 hr. Such behavior is presented in a series of tables, graphs and formulae. Using 2- and 3-layer models of the conducting earth, the induced electric fields associated with the geomagnetic changes were established. From the direct relationship of the current to the geomagnetic field variation patterns one can infer counterpart temporal and spatial characteristics of the pipeline current. The relationship of the field amplitudes to geomagnetic activity indices,A _p, and the established occurrence of various levels ofA _p over several solar cycles were employed to show that about half of the time the induced currents in the pipe would be under 1 A for the maximum response oscillatory periods near 1 hr. Such currents should be of minimal consequence in corrosion effects for even a section of the pipeline unprotected by sacrificial electrodes. Of greater interest was the result that the extreme surges of current should reach over one-hundred amperes in the pipeline during high activity.     

磁线圈对地磁场的物理模拟及对地磁导航研究的意义

利用磁线圈对地球基本磁场开展动态模拟,将地磁场随空间的变化转化为在实验室中随时间的变化,能够为地磁导航系统的匹配试验提供物理仿真的地磁场环境。本项研究依照虚拟仪器技术思路,对磁线圈、恒流电源、磁通门磁力仪(或Overhauser磁力仪)和工控机进行数字化连接,并采用LabVIEW编程进行驱动控制,通过自动调节线圈绕组中的电流大小来实现对磁场的物理模拟并进行实时监测,尝试组建了地磁场动态模拟系统,并分别开展了对地磁场总强度和三分量信号的动态模拟实验。模拟系统可以实现天然地磁场和人工编制两种动态信号的输出模拟,且拟合效果良好。地磁场动态模拟系统的初步建立为今后地磁匹配试验等研究提供了仿真磁场环境。     

北京及邻区地磁总场频谱的分析研究

应用北京及邻区2min采样的地磁总场观测资料，分析了北京台与各临时台地磁总场的频谱特性与频谱幅比的时空变化。结果显示，该地区地磁总场的频谱幅度随周期增大呈下降趋势；各临时台与北京台的频谱幅比具有一定的时空变化，可能与该地区地下电磁结构、地震及构造活动有关。     

Wiener optimal filtering of GRACE data

We present a spatial averaging method for Gravity Recovery and Climate Experiment (GRACE) gravity-field solutions based on the Wiener optimal filtering. The optimal filter is designed from the least-square minimization of the difference between the desired and filtered signals. It requires information about the power spectra of the desired gravitational signal and the contaminating noise, which is inferred from the average GRACE degree-power spectrum. We show that the signal decreases with increasing spherical harmonic degree j with approximately j^−b, where b = 1.5 for GRACE data investigations. This is termed the Second Kaula rule of thumb for temporal variations of the Earth’s gravity field. The degree power of the noise increases, in the logarithmic scale, linearly with increasing j. The Wiener optimal filter obtained for the signal model with b = 1.5 closely corresponds to a Gaussian filter with a spatial half width of 4° (∼440 km). We find that the filtered GRACE gravity signal is relatively insensitive to the exponent b of the signal model, which indicates the robustness of Wiener optimal filtering. This is demonstrated using the GFZ-GRACE gravity-field solution for April 2004.     

Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

We investigate the temporal behaviour of the axial component of the electromagnetic core-mantle coupling torque that is associated with the poloidal part of the geomagnetic field observable at the Earth surface. For its computation, we use different models of the geomagnetic field, expanded into spherical harmonics (Wardinski and Holme, 2006; Sabaka et al., 2004), and the mantle conductivity. The geomagnetic field, which we have to know at the core-mantle boundary for the associated computations, will be inferred from the field at the Earth surface by the non-harmonic field continuation through a conducting mantle shell. The aims of this investigation are (i) to check how sensitive is the computation of the torque with respect to the different geomagnetic field models, (ii) to check its dependence on the spherical harmonic degree n, and (iii) to determine the difference between the mechanical torque derived from the observed length-of-day variations (atmospheric influence subtracted) and the poloidal electromagnetic torque in dependence on the assumed conductivity. To use the non-harmonic field continuation for the torque calculation and to obtain an insight into the influence of the different geomagnetic field models on the EM torques are the major aspects of this paper. grm@gfz-potsdam.de     

Analysis of the time-scaling behaviour in the sequence of the aftershocks of the Bovec (Slovenia) April 12, 1998 earthquake

Analysis of the temporal fluctuations, described by a power spectral density S(f) decaying as 1/f with exponent >0, in the sequence of aftershocks of the Bovec (Slovenia) earthquake of April 12, 1998 has been performed, using the Allan Factor (AF) method. The sequence of the occurrence times of the events with threshold magnitude M_th≥2.0 is characterised by a scale-invariant behaviour from the time scale τ2·10⁴ s with a scaling coefficient 0.9, evaluated by a least-square method. By gradually increasing the threshold magnitude up to M_th=2.9, the AF curves, associated, respectively with the processes of selected events with magnitude M≥M_th, indicate a monotonic decrease of the value of the scaling exponent , in the range of time scales stretching from 10² to 5·10⁵ s. For all the thresholds considered, the AF curves increase monotonically with the counting time and are well fitted by an increasing power-law function for counting times greater than approximately 2·10⁴ s. This monotonic power-law increase indicates the presence of fluctuations on many time scales and therefore of fractal clustering.     

短周期地磁扰动的时空分布特征研究

本文对2008—2010年隆尧地磁台站的地磁水平分量H和磁偏角D的秒数据进行了短时快速傅里叶变换,按连续型地磁脉动Pc2—Pc6所对应的频率范围对频谱进行了频段划分,在此基础上研究了各频段频谱总幅值即短周期地磁扰动的时空分布特征.在时间变化上,同一年中不同频段的幅值具有相似的变化规律,每年的幅变特性与该年对应的Vr指数的时间分布也具有一致的变化形态,仅仅在变化的幅度上存在差异.磁偏角D的幅值和VrD均呈现出显著的季节变化特征,而水平分量H的幅值和VrH却不显著.在空间变化上,各频段幅值均随地磁纬度的增加而增大,随地方时变化呈现出双峰双谷的特征.     

多台站地磁观测资料综合处理的一种方法

通过利用空间线性度方法，分析处理地磁场前兆观测资料，并从“场”的角度综合计算多台站的地磁场观测资料，确立地磁基本场的统一信息量－空间线性度ａ。分析处理华北地区多个台站１９７５￣１９９４年的地磁场前兆观测资料。结果表明，中强地震之前约１ａ左右的时间内，空间线性度ａ可能出现明显的下降异常，有些在临震前回升，因此地磁场空间线性度ａ有可能作为中强地震前兆预报的指标。     

Crustal geomagnetic field: two-dimensional intermediate-wavelength spatial power spectra

Two-dimensional Fourier spatial power spectra of equivalent magnetization values are presented for a region that includes a large portion of the western United States. The magnetization values were determined by inversion of POGO satellite data, assuming a magnetic crust 40 km thick, and were located on an 11 × 10 array with 300 km grid spacing. The spectra appear to be in good agreement with values of the crustal geomagnetic field spatial power spectra given by McLeod and Coleman (1980) and with the crustal field model given by Serson and Hannaford (1957). The spectra show evidence of noise at low frequencies in the direction along the satellite orbital track (N-S), indicating that for this particular data set additional filtering would probably be desirable. These findings illustrate the value of two-dimensional spatial power spectra both for describing the geomagnetic field statistically and as a guide for diagnosing possible noise sources.     

全球电离层VLF电场功率谱特征

分析2006年3月至2009年2月DEMETER卫星VLF电场功率谱数据发现,卫星高度上全球电离层电场功率谱有以下特征:高纬度区域电场辐射强度平均高于低纬度区域,几个地磁场异常区相应的电场辐射增强;全球电场功率谱,向阳侧强于夜侧,大陆强于海洋,夏季强于分点季,冬季最弱;不同频段的电场功率谱特征有显著差异,某些频段的功率...     

大震前地磁场时空间线性度变化的初步研究

把用来分析地震波波形的时间线性度和空间线性度两种方法，应用到地磁资料分析当中，具体分析处理了１９７６年７月２８日唐山Ｍｓ７．８地震和１９８９年１０月１９日大同Ｍｓ６．１地震前后地磁场资料，并对这两次地震前后地磁时空线性度变化情况进行了研究。所得结果表明：①较大地震前地磁场的时空线性度均可能呈现出较明显的下降异常变化，有些在震前回升，②各分量的时空线性度呈现异常的时间基本上同步，并与波速异常发展趋势基本相符。     

Upper-truncated Power Laws in Natural Systems

—?When a cumulative number-size distribution of data follows a power law, the data set is often considered fractal since both power laws and fractals are scale invariant. Cumulative number-size distributions for data sets of many natural phenomena exhibit a “fall-off?” from a power law as the measured object size increases. We demonstrate that this fall-off is expected when a cumulative data set is truncated at large object size. We provide a generalized equation, herein called the General Fitting Function (GFF), that describes an upper-truncated cumulative number-size distribution based on a power law. Fitting the GFF to a cumulative number-size distribution yields the coefficient and exponent of the underlying power law and a parameter that characterizes the upper truncation. Possible causes of upper truncation include data sampling limitations (spatial or temporal) and changes in the physics controlling the object sizes. We use the GFF method to analyze four natural systems that have been studied by other approaches: forest fire area in the Australian Capital Territory; fault offsets in the Vernejoul coal field; hydrocarbon volumes in the Frio Strand Plain exploration play; and fault lengths on Venus. We demonstrate that a traditional approach of fitting a power law directly to the cumulative number-size distribution estimates too negative an exponent for the power law and overestimates the fractal dimension of the data set. The four systems we consider are well fit by the GFF method, suggesting they have properties characterized by upper-truncated power laws.     

地磁活动指数Vr的时空分布特征分析

本文使用2008-2010年三年内的国内41个地磁台站和国外4个地磁台站的地磁水平分量H和磁偏角D的分钟值数据,研究了H和D的Vr指数(以下简称VrH和VrD)与Kp指数的关系及其时空分布特征,发现在时间变化上,VrH和VrD均具有27天太阳自转周变化;VrD呈现出显著的季节变化,而VrH却无,但与太阳风速度(SWS, Solar Wind Speed)变化密切相关,其三年的相关系数分别是0.97、0.70、0.88;去除季节变化后的VrD也表现出与SWS的相关,相关系数分别是0.96、0.77、0.5(2010年相关系数低主要受3月份Vr指数不明原因异常变化影响).在空间变化上,在我国大陆范围内,VrH和VrD均随纬度的增高而增大,并且具有地方时效应和显著的晨-昏不对称性,这种地方时效应和晨昏不对称性可能与部分环电流和场向电流有关系.研究认为Vr指数可以反映地磁场的快速变化,并可以间接反映SWS、部分环电流和场向电流对地磁场变化的影响和控制作用.     

主磁场谐波成分的空间相对强度分析

利用IGRF国际参考地磁场模型, 计算并分析了7~13阶球谐成分对主磁场的贡献。 结果表明, 地磁场要素F、 H和I的空间梯度具有显著的空间不均匀性, 有些区域梯度变化平缓, 有些地区梯度呈涡状结构, 进而由地磁场的空间梯度估算得到卫星高度的空间相对变化强度, 以及卫星上安装磁强计的伸杆震颤可能引起的观测误差。 此外, 主磁场梯度的长期变化非常缓慢, 在大约150年间其最大变化强度约为6 nT。 对于中国电磁卫星5年的设计寿命而言, 梯度变化幅度可能约为0.04 nT, 该梯度变化量对于主磁场的空间相对强度不会产生显著影响。     

2011年日本东北大地震特低频地磁信号的分形标度特征研究

本文选择2011年3月11日M9.0日本东北大地震震中附近三个地磁台站16个月(2010/01/01—2011/04/30)的特低频地磁观测资料,采用去倾扰动分析方法,得到了这三个台站地磁记录的非均匀标度特征随时间的变化,提出了一种能反映地磁三分量非均匀标度特征同步变化的指标,并据此探讨了特低频地磁信号分形标度特征变化与日本东北大地震之间的可能关联性,初步结果表明,这三个台站的特低频地磁信号分形标度特征指标在日本东北大地震前25~50天左右呈现出同步的异常增加,基于磁静日观测资料的随机合成地磁数据的统计检验结果可知前述异常并非随机异常,而是一种具有统计显著性的异常,可能反映了日本东北大地震对周边地磁信号内在的非线性系统特征产生了有统计意义的影响.     

基于陆态网络GNSS数据的2013年和2015年磁暴期间中国地区电离层特性研究

2013年3月和2015年3月爆发了2次相似的地磁暴,引起了全球不同地区电离层的变化。本文利用中国大陆构造环境监测网络260余个基准站在中国地区的GNSS电离层TEC观测数据,结合电离层测高仪和电离层甚高频相干散射雷达观测,对2次磁暴期间中国地区的电离层变化特性进行了对比分析。结果显示,2013年3月磁暴期间,中国不同地区电离层变化较弱或不明显,而2015年3月磁暴期间中国地区电离层变化整体表现为大范围的强负相暴,中国地区不同程度的电离层响应主要受到不同的磁暴强度和磁暴期间不同的能量输入影响。2次磁暴期间电离层F层不均匀体的发生受到不同程度的影响,可能由不同种类的暴时电场导致。陆态网络数据空间覆盖范围广、时间分辨率高,在研究中国地区磁暴期间的电离层变化特性方面具有优势。