Tuning of the mean-field geodynamo model

Parker’s two-dimensional (2D) dynamo model with an algebraic form of nonlinearity for the α-effect is considered. The model uses geostrophic distributions for the α-effect and differential rotation, which are derived from the three-dimensional (3D) convection models. The resulting configurations of the magnetic field in the liquid core are close to the solutions in Braginsky’s Z-model. The implications of the degree of geostrophy observed in the 3D dynamo models for the behavior of the mean magnetic field are explored. It is shown that the reduction in geostrophy leads to magnetic field reversals accompanied by the relative growth of the nondipole component of the field on the surface of the liquid core. The simulations with a random α-effect which causes turbulent pulsations are carried out. The approach is capable of producing realistic sequences of magnetic reversals.     

Annual variations of the amplitude characteristic of the noise magnetic field in the ELF frequency range based on the results of high-latitude observations

The annual variation of a number of amplitude characteristics of the noise electromagnetic field in the frequency range near the first Schumann resonance (and in particular the mean values of the modulus of horizontal magnetic components and parameters of the distribution function of noise pulses over amplitudes) was obtained and analyzed based on the results of three-year measurements performed at the high-latitude magnetic observatory Lovozero. The summer increase in mean and median values of the magnetic component of noises associated with electrical storms and the lack of annual variations of the exponent that empirically describes the distribution of amplitudes of noise signals were found. The relationship between the seasonal (winter/summer in the northern hemisphere) increase in the mean value of the modulus of the horizontal magnetic field component and seasonal increase in the global number of lightning discharges is shown by the correlation of the results of satellite observations and measurements of the magnetic component.     

Nonlinear and multifractal approaches of the geomagnetic field

Recent nonlinear dynamics techniques have been developed to analyse chaotic time series data. We first summarize the procedure which gives an appropriate reconstruction of the unknown dynamics from scalar measurements in a pseudophase space. It permits, firstly, the representation of the trajectories of the dynamical system—they define an attractor when the system is dissipative—by preserving its topological properties. We then present the invariant measures and ergodic quantities such as the multifractal spectrum and Lyapunov exponents which can be estimated on the reconstructed attractor. The multifractal analysis provides us with a characterization of the scaling energy of the process whereas the Lyapunov exponent gives another statistical measure of the stability of the dynamics. The estimation of these quantities was tested on synthetic data. The nonlinear and multifractal analyses were finally applied to the hourly mean values of the magnetic field recorded at the Eskdalemuir (ESK) observatory over 79 years (692,520 data measurements for each component). The estimations of a 5-dimensional pseudo-phase space and a positive Lyapunov exponent confirm the possibility of low-dimensional deterministic chaos in the magnetic field observations at ESK observatory. The correlation between the solar activity (the Wolf number), the unstable nature of the magnetic field, and the singularity spectrum points out the forcing of the solar cycles on the dynamics of the magnetic field at ESK observatory.     

Spatial and temporal spectra of the geomagnetic field and their scaling properties

Many natural phenomena show a relationship between their spatial and temporal Fourier spectra. This paper discusses such a connection for the geomagnetic field, when some assumptions are made about the (exponential or power-law) behaviour of the spatial power spectrum of the field itself and that of its time derivative (the spatial spectrum of the secular variation) as estimated from global geomagnetic field models. It is shown that, under either assumption, the temporal spectrum of the geomagnetic field computed at the core–mantle boundary (CMB) would have a power-law behaviour with a negative spectral exponent of about 0.5. At the Earth’s surface, although the temporal spectrum obtained from the power-law spatial model assumes a slightly more complicated form, it can be practically approximated with a power law with a negative exponent of about 3.6. Analysis of magnetic observatory data confirms these results and that the starting hypotheses are reasonable, especially in view of the possibly chaotic state of the dynamical processes underlying the generation and maintenance of the geomagnetic field.     

Analysis of a 12-Hour Artifact in LF Oscillations of the Magnetic Field of Sunspots According to SDO/HMI Data

The properties of the 12-h artifact in the data of the SDO/HMI instrument (Helioseismic and Magnetic Imager) caused by the nonzero radial velocity of the station relative to the Sun are investigated. The study has been carried out with respect to long-period oscillations of the magnetic field of sunspots for different station positions in the Earth’s orbit by the alternative spectral method of singular decomposition of the signal CaterPillarSSA. Features of artifact filtering, both in special positions of the station (at the points of aphelion and perihelion) and at arbitrarily selected orbital points, are considered. It is shown that the 12-h artifact mode can be completely filtered from the time series of the observed variable, not only at these two orbital points (because of the symmetry of the station’s radial velocity with respect to the zero mean here) but also at any others. It is shown that only a 12-h mode is physically justified, while the 24-h harmonic appears only as an artifact in the Fourier decomposition of the amplitude-modulated signal. It is emphasized that the values of the magnetic field measured with SDO/HMI are sensitive only to the station’s radial velocity absolute values with respect to the Sun and do not depend on its direction. It has been noted that the periods of sunspot oscillation as a whole obtained from SDO/HMI data after orbital artifact filtration fit well into the dependence diagram of the period of sunspot oscillations on the value of its magnetic field strength constructed earlier by SOHO/MDIdata.     

Influence of a convective generator on the diurnal behavior of the electric field strength in the near-Earth atmosphere in Kamchatka

Diurnal variations in the electric field strength, electrical conductivity, and temperature in the near-Earth atmosphere under “fair-weather” conditions at the Paratunka observatory (Kamchatka) are considered. It is shown that the morning maximum in the electric field diurnal behavior is caused by air convection in the near-surface layer. The difference in the atmospheric temperatures near the Earth’s surface and at an altitude of 25 m is chosen as a measure of the convective air flow. A high correlation of the values of the temperature difference for these altitudes with the diurnal behavior of the electric field strength is obtained.     

Magnetic Rossby waves in a stably stratified layer near the surface of the Earth's outer core

Abstract

The stratification profile of the Earth's magnetofluid outer core is unknown, but there have been suggestions that its upper part may be stably stratified. Braginsky (1984) suggested that the magnetic analog of Rossby (planetary) waves in this stable layer (the ‘H’ layer) may be responsible for a portion of the short-period secular variation. In this study, we adopt a thin shell model to examine the dynamics of the H layer. The stable stratification justifies the thin-layer approximations, which greatly simplify the analysis. The governing equations are then the Laplace's tidal equations modified by the Lorentz force terms, and the magnetic induction equation. We linearize the Lorentz force in the Laplace's tidal equations and the advection term in the magnetic induction equation, assuming a zeroth order dipole field as representative of the magnetic field near the insulating core-mantle boundary. An analytical β-plane solution shows that a magnetic field can release the equatorial trapping that non-magnetic Rossby waves exhibit. A numerical solution to the full spherical equations confirms that a sufficiently strong magnetic field can break the equatorial waveguide. Both solutions are highly dissipative, which is a consequence of our necessary neglect of the induction term in comparison with the advection and diffusion terms in the magnetic induction equation in the thin-layer limit. However, were one to relax the thin-layer approximations and allow a radial dependence of the solutions, one would find magnetic Rossby waves less damped (through the inclusion of the induction term). For the magnetic field strength appropriate for the H layer, the real parts of the eigenfrequencies do not change appreciably from their non-magnetic values. We estimate a phase velocity of the lowest modes that is rather rapid compared with the core fluid speed typically presumed from the secular variation.     

Iterative Spherical Downward Continuation Applied to Magnetic and Gravitational Data from Satellite

In the last few decades, satellites have acquired various potential data sets hundreds of kilometers above the Earth’s surface. Conventionally, these global magnetic and gravitational data sets are approximated by using spherical harmonics that allow straightforward work with both fields outside the Earth’s mass. In this article, we present an alternative approach for working with potential data in mass-free space given over a regular coordinate grid on a spherical surface. The algorithm is based on an iterative scheme and the Poisson integral equation for the sphere. With help from the Fourier transform, global potential (magnetic or gravitational) data can efficiently be continued from a mean orbital sphere down to a reference surface without using the spherical harmonics. This is illustrated both with simulated magnetic field data and with real data from the satellite gradiometry mission GOCE. In the case of simulated magnetic data and the downward continuation for 450 km, we have achieved a root mean square at the level of 0.05 nT, while it was <1 E (eotvos) for real GOCE data continued for 250 km. The crucial point is to apply the algorithm twice as a large part of noise can be removed from the input data.     

Tidal components of geomagnetic variations

The natural geomagnetic field is constantly disturbed. The total registered effect of geomagnetic variations depends on both planetary and local processes. Planetary sources and sources in the Earth’s core respond to tidal effects. In the accepted model, the complex MHD processes in the Earth’s outer core are approximated by the assumed ring current in the equatorial plain of the liquid core. The geomagnetic variation originating as a result of tidal deformations of ring currents are ～10^?4 and 0.10–1 nT in the liquid core and magnetosphere, respectively. The calculated values coincide in order of magnitude with the processed geomagnetic measurements at Paratunka observatory (Kamchatka region).     

基于有色噪声模型的GPS速度场精度与时间序列长度相关性研究

利用2010—2015年陆态网络GPS连续观测站的三维站坐标时序资料, 在采用最大似然估计MLE方法计算得到云南地区GPS基准站三维站坐标分量最优噪声模型的基础上, 进一步定量对比分析了有色噪声和白噪声模型下陆态网络GPS连续站速度场稳定性与时间序列长度的关系。 结果表明: 在闪烁噪声模型下, 中国大陆大部分地区GPS连续站1 a时段的速度不确定度大。 而随着时间的逐年累积, 闪烁噪声模型下的速度不确定度与同时段白噪声模型下的差异逐步减小, 闪烁噪声模型下3～4 a时段的速度不确定度与同时段白噪声模型的差异小于0.2 mm。 研究说明在有色噪声模型下要获得高精度的速度场需要3～4 a的观测数据, 白噪声模型下GPS速度场精度可靠可信的前提是采用不少于3～4 a的数据。     

Estimating external magnetic field differences at high geomagnetic latitudes from a single station

Providing an accurate estimate of the magnetic field on the Earth's surface at a location distant from an observatory has useful scientific and commercial applications, such as in repeat station data reduction, space weather nowcasting or aeromagnetic surveying. While the correlation of measurements between nearby magnetic observatories at low and mid‐latitudes is good, at high geomagnetic latitudes () the external field differences between observatories increase rapidly with distance, even during relatively low magnetic activity. Thus, it is of interest to describe how the differences (or errors) in external magnetic field extrapolation from a single observatory grow with distance from its location. These differences are modulated by local time, seasonal and solar cycle variations, as well as geomagnetic activity, giving a complex temporal and spatial relationship. A straightforward way to describe the differences are via confidence intervals for the extrapolated values with respect to distance. To compute the confidence intervals associated with extrapolation of the external field at varying distances from an observatory, we used 695 station‐years of overlapping minute‐mean data from 37 observatories and variometers at high latitudes from which we removed the main and crustal fields to isolate unmodelled signals. From this data set, the pairwise differences were analysed to quantify the variation during a range of time epochs and separation distances. We estimate the 68.3%, 95.4% and 99.7% confidence levels (equivalent to the 1σ, 2σ and 3σ Gaussian error bounds) from these differences for all components. We find that there is always a small non‐zero bias that we ascribe to instrumentation and local crustal field induction effects. The computed confidence intervals are typically twice as large in the north–south direction compared to the east‐west direction and smaller during the solstice months compared to the equinoxes.     

Modeling of deep magnetovariation soundings on the rotating earth

Induced magnetic fields in the Earth arise due to two phenomena: induction generated by the time-variable exciting field and the motional induction caused by movement of the conductive planet in the outer magnetic fields. The comparison of both approaches on the spherical Earth has been analyzed in the present work for two sources in the ionosphere and magnetosphere. For this aim, both sources with their natural sizes and positions have been modeled analytically to obtain the fields on the layered sphere at the middle latitudes. The conditions when the steady ring current field is not influenced by the Earth’s rotation have been established theoretically. The synthetic diurnal magnetograms were used for the deep sounding by the magnetovariation spatial gradient method and the result was compared with the one obtained on the nonrotating sphere. Sounding results using both approaches were found different above the 2D inhomogeneous mantle. The precessions of the magnetospheric belt current pole for daily sampling frequency were presented using several geomagnetic observatory data in the northern hemisphere.     

2013年吉林松原M5.8地震震前地磁异常分析

应用东北地区地磁观测台站地磁总场强度整点值观测数据,利用每日一值相关法和差值法;应用地磁垂直分量日变幅观测数据,利用加卸载响应比和逐日比方法,分析地磁总场强度F分量、垂直Z分量与吉林省松原M5.8地震应震关系,分析上述方法对提取地磁观测数据震前异常信息的有效性。     

Observing,Modeling, and Interpreting Magnetic Fields of the Solid Earth

Many Earth system processes generate magnetic fields, either primary magnetic fields or in response to other magnetic fields. The largest of these magnetic fields is due to the dynamo in the Earth’s core, and can be approximated by a geocentric axial dipole that has decayed by nearly 10% during the last 150 years. This is an order of magnitude faster than its natural decay time, a reflection of the growth of patches of reverse flux at the core–mantle boundary. The velocity of the North magnetic pole reached some 40 km/yr in 2001. This velocity is the highest recorded so far in the last two centuries. The second largest magnetic field in the solid Earth is caused by induced and remanent magnetization within the crust. Controlled in part by the thermo-mechanical properties of the crust, these fields contain signatures of tectonic processes currently active, and those active in the distant past. Recent work has included an estimate of the surface heat flux under the Antarctic ice cap. In order to understand the recent changes in the Earth’s magnetic field, new high-quality measurements are needed to continue those being made by Ørsted (launched in 1999), CHAMP and the Ørsted-2 experiment onboard SAC-C (both launched in 2000). The present paper is motivated by the advent of space surveys of the geomagnetic field, and illustrates how our way of observing, modeling, and interpreting the Earth’s magnetic field has changed in recent years due to the new magnetic satellite measurements.     

CM4模型数据与台站实测数据的对比研究

本文利用第四代地磁场综合模型(Comprehensive Model 4,CM4),计算了1982—2002年隆尧地磁台站的磁层源磁场及其感应场、电离层源磁场及其感应场的地磁北向分量X、东向分量Y、垂直分量Z,分析了各场源磁场随时间的变化特征。磁层源磁场及其感应场呈现出11年和27天的周期性变化,有些年的27天周期性变化显著,有些年则不太显著;电离层源磁场及其感应场具有明显的季节变化,不同年相同季节的变化形态一致但幅度不同;日变化分析显示,磁静日和磁扰日期间的模型数据与台站实测数据变化一致性较好,相关性较高。     

150 years of magnetic observatories: Recent researches on world data

A joint Discussion Meeting of the Royal Astronomical Society and the Royal Irish Academy, held on January 11th, 1991, commemorated the establishment of some early magnetic observatories, discussed recent research using global geomagnetic data and described the present status of magnetic observatories in the United Kingdom. The observatory and instruments at the Dublin magnetic observatory; the origins of the Greenwich magnetic observatory, and why it eventually had to be resited; and the history of the Munich magnetic observatory formed the historical part of the proceedings. Current research topics discussed were the geomagnetic secular variation and deep Earth structure and dynamics; fluid flow patterns near the top of the core; the origin of the annual variation of the geomagnetic field; results of an analysis of monthly means from some British observatories; a new theory of the geomagnetic daily variation; and the interactions between ionospheric science and geomagnetism. The present-day observatory scene was described in terms of the information that can be derived from the almost 40 year series of data from Hartland magnetic observatory; of the methods used to process data from the three UK magnetic observatories, which nowadays are operated automatically and remotely; and (a look into the future) of a new project, INTERMAGNET, which aims to make available, in near real time, data from the world-wide network of magnetic observatories.     

Anisotropic turbulent thermal diffusion and thermal convection in a rapidly rotating fluid sphere

Estimates of the molecular values of magnetic, viscous and thermal diffusion suggest that the state of the Earth’s core is turbulent and that complete numerical simulation of the geodynamo is not realizable at present. Large eddy simulation of the geodynamo with modelling of the sub-grid scale turbulence must be used. Current geodynamo models effectively model the sub-grid scale turbulence with isotropic diffusivities larger than the molecular values appropriate for the core. In the Braginsky and Meytlis (1990) picture of core turbulence the thermal and viscous diffusivities are enhanced up to the molecular magnetic diffusivity in the directions of the rotation axis and mean magnetic field. We neglect the mean magnetic field herein to isolate the effects of anisotropic thermal diffusion, enhanced or diminished along the rotation axis, and explore the instability of a steady conductive basic state with zero mean flow in the Boussinesq approximation. This state is found to be more stable (less stable) as the thermal diffusion parallel to the rotation axis is increased (decreased), if the transverse thermal diffusion is fixed. To examine the effect of simultaneously varying the diffusion along and transverse to the rotation axis, the Frobenius norm is used to control for the total thermal diffusion. When the Frobenius norm of the thermal diffusion tensor is fixed, it is found that increasing the thermal diffusion parallel to the rotation axis is destabilising. This result suggests that, for a fixed total thermal diffusion, geodynamo codes with anisotropic thermal diffusion may operate at lower modified Rayleigh numbers.     

Determination of the Croatian geomagnetic observatory location

Ground survey within the Nature Park Lonjsko Polje, placed in the middle-northern Croatia was performed during the time interval 2007–2010 in order to find the best location for installing the geomagnetic observatory. The total magnetic field has been measured a few times using the Overhauser proton magnetometers. The horizontal and vertical gradients of the total field, and its temporal behaviour were investigated over the restricted region that we estimated as suitable for the observatory. The results obtained from thoroughly conducted measurements allowed us to find definitive positions for the instrument pillars. These results are in agreement with previously suggested location found based on combination of Comprehensive CM4 model prediction and measurements conducted from 2003 to 2005. This study contributes to the development of geomagnetism in Croatia and paves a way to install the first geomagnetic observatory in Croatia.     

An archeomagnetic analysis of burnt grain bin floors from ca. 1200 to 1250 AD Iron-Age South Africa

Recognition of the rapid decay of Earth’s magnetic field over the last 150 years, chronicled in magnetic observatory and satellite data, highlights the need for a higher resolution record of geomagnetic field behavior over the past millennium. Such a record would help us better understand the nature of the recent dramatic changes. A limitation of the existing database is undersampling of the Southern Hemisphere. Here we investigate the potential of obtaining archeomagnetic data from Iron-Age burnt grain bins from southern Africa. These structures preserve oriented material that can record both paleodirections and paleointensity information. Directional data collected from three sites (ca. 1200–1250 AD) fall 9–22° to the East of predictions. Thellier–Coe and Shaw paleointensity results differ from model values by ～15%. The consistency of results between the three sites suggests that further investigations of these materials with different ages could markedly improve the current spatial distribution of the archeomagnetic database.     

Interpretation of Magnetic Anomalies and Estimation of Depth of Magnetic Crust in Slovakia

The magnetic map of Slovakia used in the paper was compiled as part of a project titled Atlas of Geophysical maps and profiles in 2001. The residual magnetic data were analyzed to produce Curie point estimates. To remove distortion of magnetic anomalies caused by the Earth’s magnetic field, reduction to pole transformation was applied to the magnetic anomalies using the magnetization angle of the induced magnetization. Anomalies reduced to the pole tend to be better correlated with tectonic structures. We applied a 3-km upward continuation to the residually compiled magnetic anomalies in order to remove effects of topography. The depth of magnetic dipoles was calculated by an azimuthally averaged power spectrum method for the entire area. Such estimates can be indicative of temperatures in the crust, since magnetic minerals lose their spontaneous magnetization according to Curie temperature of the dominant magnetic minerals in the rocks. The computed Curie point depths in the Slovakia region vary between 15.2 km and 20.9 km. Heat flow higher than 100 mWm⁻² occurs at the central volcanics and eastern part of Slovakia, where the Curie point depths values are shallow. The correlation between Curie point depths, heat flow and crust depth was investigated for two E-W cross sections. Heat flow and Curie point depth values are correlated with each other however, these values could not be correlated with crust depth. The Curie point isotherm, which separates magnetic and non-magnetic parts of the crust, is represented in two cross sections.