Secular variation of the geomagnetic virtual dipole field during the last 2000 years as inferred from the spherical harmonic analysis of the available archeomagnetic data

Summary Recently excellent archeomagnetic data sequences have been bublished from several parts of the world. Using these sequences, an attempt is made to trace the secular variation of the virtual geomagnetic dipole field characterized by the three first order spherical harmonic coefficients . The archeomagnetic data (declination, inclination and total intensity) are transformed into the first order coefficients mentioned by a simple mathematical method. The secular variations of these coefficients, however, contain both dipole and non-dipole components. The separation of these is also attempted.Paper presented at the IAGA Symposium, Madrid, September 1969.     

Uncertainties in field-line tracing in the magnetosphere. Part I: the axisymmetric part of the internal geomagnetic field

The technique of tracing along magnetic field lines is widely used in magnetospheric physics to provide a magnetic frame of reference that facilitates both the planning of experiments and the interpretation of observations. The precision of any such magnetic frame of reference depends critically on the accurate representation of the various sources of magnetic field in the magnetosphere. In order to consider this important problem systematically, a study is initiated to estimate first the uncertainties in magnetic-field-line tracing in the magnetosphere that arise solely from the published (standard) errors in the specification of the geomagnetic field of internal origin. Because of the complexity in computing these uncertainties for the complete geomagnetic field of internal origin, attention is focused in this preliminary paper on the uncertainties in magnetic-field-line tracing that result from the standard errors in just the axisymmetric part of the internal geomagnetic field. An exact analytic equation exists for the magnetic field lines of an arbitrary linear combination of axisymmetric multipoles. This equation is used to derive numerical estimates of the uncertainties in magnetic-field-line tracing that are due to the published standard errors in the axisymmetric spherical harmonic coefficients (i.e. g_n⁰ ± g_n⁰). Numerical results determined from the analytic equation are compared with computational results based on stepwise numerical integration along magnetic field lines. Excellent agreement is obtained between the analytical and computational methods in the axisymmetric case, which provides great confidence in the accuracy of the computer program used for stepwise numerical integration along magnetic field lines. This computer program is then used in the following paper to estimate the uncertainties in magnetic-field-line tracing in the magnetosphere that arise from the published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) geomagnetic field of internal origin. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, calculated here for the axisymmetric part of the internal geomagnetic filed, should be regarded as first approximations in the sense that such estimates are only as accurate as the published standard errors in the set of axisymmetric spherical harmonic coefficients. However, all procedures developed in this preliminary paper can be applied to the derivation of more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.Also Visiting Reader in Physics, University of Sussex, Falmer, Brighton, BN1 9QH, UK     

Dayside isotropic precipitation of energetic protons

Recently it has been shown that isotropic precipitation of energetic protons on the nightside is caused by a non-adiabatic effect, namely pitch-angle scattering of protons in curved magnetic field lines of the tail current sheet. Here we address the origin of isotropic proton precipitation on the dayside. Computations of proton scattering regions in the magnetopheric models T87, T89 and T95 reveal two regions which contribute to the isotropic precipitation. The first is the region of weak magnetic field in the outer cusp which provides the 1–2° wide isotropic precipitation on closed field lines in a 2–3 hour wide MLT sector centered on noon. A second zone is formed by the scattering on the closed field lines which cross the nightside equatorial region near the magnetopause which provides isotropic precipitation starting 1.5–2 h MLT from noon and which joins smoothly the precipitation coming from the tail current sheet. We also analyzed the isotropic proton precipitation using observations of NOAA low altitude polar spacecraft. We find that isotropic precipitation of >30 to > 80 keV protons continues around noon forming the continuous oval-shaped region of isotropic precipitation. Part of this region lies on open field lines in the region of cusp-like or mantle precipitation, its equatorward part is observed on closed field lines. Near noon it extends 1–2° below the sharp boundary of solar electron fluxes (proxy of the open/closed field line boundary) and equatorward of the cusp-like auroral precipitation. The observed energy dispersion of its equatorward boundary (isotropic boundary) agrees with model predictions of expected particle scattering in the regions of weak and highly curved magnetic field. We also found some disagreement with model computations. We did not observe the predicted split of the isotropic precipitation region into separate nightside and dayside isotropic zones. Also, the oval-like shape of the isotropic boundary has a symmetry line in 10–12 MLT sector, which with increasing activity rotates toward dawn while the latitude of isotropic boundary is decreasing. Our conclusion is that for both dayside and nightside the isotropic boundary location is basically controlled by the magnetospheric magnetic field, and therefore the isotropic boundaries can be used as a tool to probe the magnetospheric configuration in different external conditions and at different activity levels.     

Meridian-scanning photometer, coherent HF radar, and magnetometer observations of the cusp: a case study

The dynamics of the cusp region and post-noon sector for an interval of predominantly IMF B_y, B_z < 0 nT are studied with the CUTLASS Finland coherent HF radar, a meridian-scanning photometer located at Ny Ålesund, Svalbard, and a meridional network of magnetometers. The scanning mode of the radar is such that one beam is sampled every 14 s, and a 30° azimuthal sweep is completed every 2 minutes, all at 15 km range resolution. Both the radar backscatter and red line (630 nm) optical observations are closely co-located, especially at their equatorward boundary. The optical and radar aurora reveal three different behaviours which can interchange on the scale of minutes, and which are believed to be related to the dynamic nature of energy and momentum transfer from the solar wind to the magnetosphere through transient dayside reconnection. Two interpretations of the observations are presented, based upon the assumed location of the open/closed field line boundary (OCFLB). In the first, the OCFLB is co-located with equatorward boundary of the optical and radar aurora, placing most of the observations on open field lines. In the second, the observed aurora are interpreted as the ionospheric footprint of the region 1 current system, and the OCFLB is placed near the poleward edge of the radar backscatter and visible aurora; in this interpretation, most of the observations are placed on closed field lines, though transient brightenings of the optical aurora occur on open field lines. The observations reveal several transient features, including poleward and equatorward steps in the observed boundaries, braiding of the backscatter power, and 2 minute quasi-periodic enhancements of the plasma drift and optical intensity, predominantly on closed field lines.     

Large-scale structure of the magnetic field in the outer heliosphere

Summary Magnetic field structures at great distances from the Sun have been analyzed qualitatively for a simple vacuum reconnection model of the interplanetary and interstellar magnetic field. In dependence on the mutual orientation of the main solar dipole _s and the local interstellar fieldB ₀ , either an open or closed configuration of the large-scale field is formed. For(_s B ₀ )>0, the field lines are represented by a system of magnetic lines open towards interstellar space. In the case of(_s B ₀ )<0 there exist two zero-points and a separating surface below the heliopause separating the open lines of the interstellar field from the closed lines of the interplanetary field. The magnetic field configuration is characterized by a certain asymmetry, which is considered for(_s B ₀ )=0.     

First- and higher-order dynamical controls on water exchanges between tidal basins and the open ocean. A case study for the East Frisian Wadden Sea

Observational data, high-resolution numerical modelling results and a simple analytical theory are combined in this paper to demonstrate the dependence of the volume transports through tidal inlets on topographical or morphological parameters of a Wadden Sea system. The area of interest covers the East Frisian Wadden Sea and consists of seven weakly connected tidal basins. The observations include time series of tidal gauge data and surface currents measured at a pile station in the backbarrier basin of the island Langeoog, as well as several ADCP transects in the Accumer Ee tidal inlet. The numerical simulations are based on the 3-D primitive equation General Estuarine Transport Model (GETM) with a horizontal resolution of 200 m and terrain following vertical coordinates. The model is forced at its open boundaries with sea-level data from an operational model for the German Bight (German Hydrographic Office). The simple theoretical concepts presented illustrate the effect of topography (hypsometry) in the tidal basins on the temporal variability of the exchange of water. This topographic control is effectuated through the bottom slope in the areas prone to drying and flooding. For our study area it takes about twice as long from slack water to maximum flood current than from slack water to maximum ebb current. The underlying physics of this signal modulation from a more or less harmonic forcing at the open-sea boundary and the quantification of the contributing physical processes are the major results of this paper. Estimates based simply on volume conservation are consistent with observations and results from numerical modelling, but they do not completely capture the actual non-linear tidal response. Our analysis shows that at least during part of the tidal cycle characteristic topographic parameters of the inlet/bay system have a major impact on the rate of exchange of waters between the Wadden Sea and the open ocean. This impact is especially strong during the transition between flood and ebb conditions. The possible morphodynamic responses are also addressed focusing on some common (universal) topographic features in seven tidal basins.Responsible Editor: Hans Burchard     

Hydromagnetic dynamo model with spiral convection

Summary The present paper deals with a hydromagnetic dynamo model of the generation mechanism of the Earth's magnetic field. An attempt has been made at selecting a flow-velocity field in the Earth's core which would satisfy the condition 0 for regenerating the field according to [2], and which would yield a velocity field pattern on the core surface as given in the papers by Kahle et al. [9]. These conditions are satisfied by the velocityv=V ₁+U ₂ ^c –V ₂ ^c and, geometrically, this velocity field is represented in space by a spiral convective motion. On the core surface two downflows and two upflows with the corresponding rotating cells may then be found. Only the axisymmetric harmonic component regeneration of the magnetic field has been considered. Adequate regeneration equations have been obtained by means of Braginski's method of quantity estimates in order of magnitude.     

Uncertainties in field-line tracing in the magnetosphere. Part II: the complete internal geomagnetic field

The discussion in the preceding paper is restricted to the uncertainties in magnetic-field-iine tracing in the magnetosphere resulting from published standard errors in the spherical harmonic coefficients that define the axisymmetric part of the internal geomagnetic field (i.e. g_n⁰ ± g_n⁰). Numerical estimates of these uncertainties based on an analytic equation for axisymmetric field lines are in excellent agreement with independent computational estimates based on stepwise numerical integration along magnetic field lines. This comparison confirms the accuracy of the computer program used in the present paper to estimate the uncertainties in magnetic-field-line tracing that arise from published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) internal geomagnetic field (i.e. g_n^m ± g_n^m and h_n^m ± h_n^m). An algorithm is formulated that greatly reduces the computing time required to estimate these uncertainties in magnetic-field-line tracing. The validity of this algorithm is checked numerically for both the axisymmetric part of the internal geomagnetic field in the general case (1 n 10) and the complete internal geomagnetic field in a restrictive case (0 m n, 1 n 3). On this basis it is assumed that the algorithm can be used with confidence in those cases for which the computing time would otherwise be prohibitively long. For the complete internal geomagnetic field, the maximum characteristic uncertainty in the geocentric distance of a field line that crosses the geomagnetic equator at a nominal dipolar distance of 2 R_E is typically 100 km. The corresponding characteristic uncertainty for a field line that crosses the geomagnetic equator at a nominal dipolar distance of 6 R_E is typically 500 km. Histograms and scatter plots showing the characteristic uncertainties associated with magnetic-field-line tracing in the magnetosphere are presented for a range of illustrative examples. Finally, estimates are given for the maximum uncertainties in the locations of the conjugate points of selected geophysical observatories. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, including the associated uncertainties in thelocations of the conjugate points of geophysical observatories, should be regarded as first approximations in the sense that these estimates are only as accurate as the published standard errors in the full set of spherical harmomic coefficients. As in the preceding paper, howerver, all computational techniques developed in this paper can be used to derive more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.Also Visiting Reader in Physics, University of Sussex, Palmer, Brighton, BN1 9QH, UK     

Seasonal changes in diurnal variation of potential gradient at Fargo,North Dakota

Summary The atmospheric electric potential gradient was recorded continuously by a field mill at Fargo, North Dakota, for the period August, 1972–March, 1973. Hourly averages were taken by the equal areas technique to eliminate short period variations. The diurnal variation of monthly averages is shown for the fair weather periods and all weather. In addition, the diurnal variation is shown for all positive values of the potential gradient, which excludes periods of major local space charge generators, but includes periods when the potential gradient might be influenced by regional conditions not otherwise present during fair weather. For a given month the diurnal variation curves are generally similar, with the fair weather curve giving the highest values, and all weather curve giving the lowest values. The months September–November have similar curves with the lowest values and least deviation from the average. The months December–February have similar curves with the highest values.Harmonic analysis is used to compute the times of maxima and contributions to variance of the first four harmonics for each diurnal variation curve. The fair weather first harmonic accounts for the majority of variance and has a maximum near 19.5 h GMT. It is attributed to the global diurnal variation of potential gradient due to thunderstorm activity in the tropics. The second harmonic has one maximum occurring from 9–12 h local time and is attributed to the austausch effect of convection, where ions affect the conductivity of the air locally.The differences in these monthly diurnal variation curves emphasize that the season of year, weather conditions, and length of time over which data is averaged must be specified in atmospheric electricity studies if meaningful conclusions are to be drawn.     

Problem of the Rotating Magnetoconvection in Variously Stratified Fluid Layer Revisited

The linear magnetoconvection in the rotating uniformly as well as non-uniformly stratified horizontal layer with azimuthal magnetic field is investigated for the various mechanical and electrical boundary conditions and especially, for various values of Roberts number. The developed diffusive perturbations (modes) are strongly influenced not only by the mentioned properties of boundaries but also by complicated coupling of viscous, thermal and magnetic diffusive processes. The mean electromotive force produced by developed hydromagnetic instabilities is also investigated to determine the hydromagnetic processes which are appropriate for -effect. The presented paper is an unification of hitherto published results of the authors and gives a short survey of many developments of corresponding model by Soward (1979).     

Waves in an elastic plate with an irregular boundary

Summary Green's function corresponding to the displacements for anSH-line source inside a wedge shaped medium finite or infinite in which the density and the elastic parameter are not constant throughout but some class of function ofr, the radial distance (i.e. and satisfy some differential equation) has been obtained. The paths of propagation of the cylindrical waves, their reflections on different boundaries and their continuous refractions within the medium has been clearly established. The scattered field from the different parts of the body have been pointed out with prescribed distribution of and in this inhomogeneous wedge. It is shown that for some distribution of and the rays are curved and the reflections at the two plane boundaries occur in such a way that no ray will go to infinity by reflection, rather they are coming back towards the apex after suitable number of reflections with variable intensity. Also there are some distributions of and in the same class as mentioned earlier, such that the behaviour of the waves is similar to that in a homogeneous wedge, i.e. these waves will go to infinity by a suitable number of reflections and ultimately die out. The first case is quite unlike the usual homogeneous medium with non parallel boundaries and so care must be taken in computing the field within the nonhomogeneous medium within the non-parallel boundaries.     

Reflected and refracted waves from a linear transition layer — A periodic source

Summary The problem of a transiton layer lying between two homogeneous liquid media has been discussed in a previous paper. There, some of the terms in the integrands in the expressions for the displacement potentials due to a periodic point source, lying in the upper layer, have been evaluated along the Sommerfeld loops. Both first order and second order discontinuities in density and bulk modulus at the boundaries of the transition layer have been considered. In the present paper, the integrals for the displacement potentials have been evaluated by the method of stationary phase and the results obtained are compared with those obtained previously. Also the first order discontinuities in density and velocity at the two ends of the transition layer are removed and the work is extended to an explosion type pulse. It is found that for a pulse source, the decrease with distance is the same as for a periodic point source. Also the frequency dependence for the refraction arrivals, when frequency is extremely high, is ^1/3 as compared to ^–1 in the case when there are discontinuities at the boundaries of the transition layer.     

Multiple scattering ofSH waves in 2-D media with many cavities

The full waveform synthetic seismogram of multiple scatteredSH waves by many cylindrical cavities in two-dimensional homogeneous elastic media is computed. We used the so-called single-layer potential integral representation of the scattered field and a discretization scheme with line source distribution for each cavity. The total field is the sum of the incident wave plus the field radiated from all sources, each multiplied by an unknown complex constant representing its strength. These constants are determined by imposing the appropriate boundary conditions in the least-squares sense. Here we solve scattering problems involving one, two, four, twelve and fifty cavities regularly distributed in a half-space. The seismograms computed along the free-surface show regions where the incident wave is strongly attenuated, as well as the arrivals of all multiple scattered phases. The accuray of the method is estimated from the degree of agreement of our solution for one cavity with the corresponding analytical solution, and also from the magnitude of the residual tractions along the boundaries of two cavities separated at various distances. Finally we apply the method to compute the case of fifty cylindrical cavities, each of radiusa, randomly distributed in a region 80a wide by 30a deep in a half-space. The value of scattering loss is obtained from the amplitude decay of the primary wave with distance for wavelengths in the range from 1.7a to 13.3a, using the synthetic seismogram calculated for the same distribution of 50 cavities as above, but in full-space.     

NOUVELLES APPLICATIONS DE LA THEORIE DES MILIEUX ALPHA HARMONIQUES A LA PROSPEGTION ELECTRIQUE EN COURANT CONTINU*

The equation which determines the distribution of the stationary potential ? in isotropic heterogeneous conductive media with continuously varying local conductivity σ, takes the symmetrical form if we choose as new variables For certain grounds (half-spaces) in which α is a harmonic function (Δα=ΔΨ= 0), it is possible to obtain by means of simple calculations the lines of equal apparent resistivity and the geoelectrical apparent cross-sections for the usual devices of d.c. prospecting methods. Graphical examples are also given.     

A Grid-Spectral Method of the Solution of the 3D Kinematic Geodynamo with the Inner Core

A 3D kinematic geodynamo model in a sphere with the conductive solid inner core is considered. The 3D magnetic field and velocity field are resolved in the physical space for r- and -coordinates, whereas the sin- and cos-decomposition is applied to the -coordinate. The additional boundary conditions for the case of non-zero velocity field on the boundaries of the liquid spherical shell and for different magnetic diffusivities of the inner and outer core are applied. The computer code was tested by free decay mode solutions and comparisons were made also with results reported by other authors. This work is a part of a project to study 3D inviscid geodynamo models.     

A simplified method for simulation of strong ground motion using finite rupture model of the earthquake source

We present a simplified method to simulate strong ground motion for a realistic representation of a finite earthquake source burried in a layered earth. This method is based on the stochastic simulation method of Boore (Boore, D. M., 1983, Bull. Seism. Soc. Am. 73, 1865–1894) and the Empirical Greens Function (EFG) method of Irikura (Irikura, K., 1986, Proceedings of the 7th Japan Earthquake symposium, pp. 151–156). The rupture responsible for an earthquake is represented by several subfaults. The geometry of subfaults and their number is decided by the similarity relationships. For simulation of ground motion using the stochastic simulation technique we used the shapping window based on the kinetic source model of the rupture plane. The shaping window deepens on the geometry of the earthquake source and the propagation characteristics of the energy released by various subfaults. The division of large fault into small subfaults and the method for accounting their contribution at the surface is identical to the EGF. The shapping window has been modified to take into account the effect of the transmission of energy released form the finite fault at various boundaries of the layered earth model above the source. In the present method we have applied the correction factor to adjust slip time function of small and large earthquakes. The correction factor is used to simulate strong motion records having basic spectral shape of ² source model in broad frequency range. To test this method we have used the strong motion data of the Geiyo earthquake of 24th March 2001, Japan recorded by KiK network. The source of this earthquake is modelled by a simple rectangular rupture of size 24 × 15 km, burried at a depth of 31 km in a multilayered earth model. This rupture plane is divided into 16 rectangular subfaults of size 6.0 × 3.75 km each. Strong motion records at eight selected near-field stations were simulated and compared with the observed records in terms of the acceleration and velocity records and their response spectrum. The comparison confirms the suitability of proposed rupture model responsible for this earthquake and the efficacy of the approach in predicting the strong motion scenario of earthquakes in the subduction zone. Using the same rupture model of the Geiyo earthquake, we compared the simulated records from our and the EGF techniques at one near-field station. The comparison shows that this technique gives records which matches in a wide frequency range and that too from simple and easily accessible parameters of burried rupture.     

The ionospheric response to flux transfer events: the first few minutes

We utilise high-time resolution measurements from the PACE HF radar at Halley, Antarctica to explore the evolution of the ionospheric response during the first few minutes after enhanced reconnection occurs at the magnetopause. We show that the plasma velocity increases associated with flux transfer events (FTEs) occur first 100–200 km equatorward of the region to which magnetosheath (cusp) precipitation maps to the ionosphere. We suggest that these velocity variations start near the ionospheric footprint of the boundary between open and closed magnetic field lines. We show that these velocity variations have rise times 100 s and fall times of 10 s. When these velocity transients reach the latitude of the cusp precipitation, sometimes the equatorward boundary of the precipitation begins to move equatorward, the expected and previously reported ionospheric signature of enhanced reconnection. A hypothesis is proposed to explain the velocity variations. It involves the rapid outflow of magnetospheric electrons into the magnetosheath along the most recently reconnected field lines. Several predictions are made arising from the proposed explanation which could be tested with ground-based and space-based observations.     

Complex image method for calculating electric and magnetic fields produced by an auroral electrojet of finite length

The electromagnetic field due to ionospheric currents has to be known when evaluating space weather effects at the earths surface. Forecasting methods of these effects, which include geomagnetically induced currents in technological systems, are being developed. Such applications are time-critical, so the calculation techniques of the electromagnetic field have to be fast but still accurate. The contribution of secondary sources induced within the earth leads to complicated integral formulas for the field at the earths surface with a time-consuming computation. An approximate method of calculation based on replacing the earth contribution by an image source having mathematically a complex location results in closed-form expressions and in a much faster computation. In this paper we extend the complex image method (CIM) to the case of a more realistic electrojet system consisting of a horizontal line current filament with vertical currents at its ends above a layered earth. To be able to utilize previous CIM results, we prove that the current system can be replaced by a purely horizontal current distribution which is equivalent regarding the total (= primary + induced) magnetic field and the total horizontal electric field at the earths surface. The latter result is new. Numerical calculations demonstrate that CIM is very accurate and several magnitudes faster than the exact conventional approach.     

A study of atmospheric gravity waves and travelling ionospheric disturbances at equatorial latitudes

A global coupled thermosphere-ionosphere-plasmasphere model is used to simulate a family of large-scale imperfectly ducted atmospheric gravity waves (AGWs) and associated travelling ionospheric disturbances (TIDs) originating at conjugate magnetic latitudes in the north and south auroral zones and subsequently propagating meridionally to equatorial latitudes. A fast dominant mode and two slower modes are identified. We find that, at the magnetic equator, all the clearly identified modes of AGW interfere constructively and pass through to the opposite hemisphere with unchanged velocity. At F-region altitudes the fast AGW has the largest amplitude, and when northward propagating and southward propagating modes interfere at the equator, the TID (as parameterised by the fractional change in the electron density at the F2 peak) increases in magnitude at the equator. The amplitude of the TID at the magnetic equator is increased compared to mid-latitudes in both upper and lower F-regions with a larger increase in the upper F-region. The ionospheric disturbance at the equator persists in the upper F-region for about 1 hour and in the lower F-region for 2.5 hours after the AGWs first interfere, and it is suggested that this is due to enhancements of the TID by slower AGW modes arriving later at the magnetic equator. The complex effects of the interplays of the TIDs generated in the equatorial plasmasphere are analysed by examining neutral and ion winds predicted by the model, and are demonstrated to be consequences of the forcing of the plasmasphere along the magnetic field lines by the neutral air pressure wave.