Ciaran Beggan and Kathy Whaler

Over the past ten years, high-quality vector satellite measurements, in combination with data from ground-based observatories, have allowed very detailed models of the Earth’s magnetic field to be constructed. However, forecasting the detailed change of the main field still remains a challenge, primarily because the core processes controlling secular variation (SV) are highly non-linear. The strong agreement between current field models and the ‘true’ field noticeably declines over relatively short periods of time if global data coverage is not maintained. Indeed such a scenario could occur if satellite data became unavailable for a significant period of time (> 2 years). We examine whether an Ensemble Kalman Filter (EnKF) can efficiently combine disparate sources of information to produce an improved field model; in order to minimise the potential impact on model quality that a hiatus might impose. We use the filter to optimally assimilate field models derived from two sources (a) high resolution field models which have been projected forward in time using SV forecasts from a steady core flow model and (b) comparatively low resolution models based upon ground-based observatory measurements. By making certain error assumptions derived from the relative misfit of each type of field model to the ‘true’ field up to degree L = 13, we can combine the better parts of each model to form an improved estimate of the field. Our research suggests that errors in ground-based field models and the core flow model SV forecasts are sufficiently complementary to allow an improved model to be constructed. For example, without assimilation of ground-based observatory data, the predicted field model forecast from core flow SV alone has an RMS misfit of approximately 100nT after five years. We show that annual assimilation of ‘measured’ data into the EnKF can reduce the RMS misfit to less than 50nT, depending on the assumed error budget.

Robert Light

Remote referencing is used to correct for the daily variations of the magnetic field during an aero- or ship based magnetic survey. A permanent magnetic base station records the field and is then compared to and subtracted from the survey readings. This assumes that any observed variations are the same both at the reference base station and throughout the survey area. In recent years continued pressure for natural resources has meant that survey areas have become increasingly remote from any feasible survey base. This pressure forces the primary assumption into question as these daily fluctuations are rarely consistent over distances greater than 100km [1]. Accurate removal of these fluctuations is of key importance to the exploration industry as they can easily be of a magnitude with survey targets. This project aims to address this issue by applying insights from global geomagnetic modelling.

We introduce the remote referencing problem emphasising the effects of secondary induction on these daily fluctuations. The available data are presented, and potential solutions based on recent advances in global field modelling discussed. Particular emphasis is placed on Comprehensive Model – 4 (CM-4) [2], a model which predicts daily variations as a function of solar activity indices, and the Spherical Elementary Current System (SECS) technique[3] which allows an equivalent calculation of the current systems contributing to the daily magnetic fluctuations. Finally, the future development of these techniques will be discussed towards improving aeromagnetic remote referencing.

1. Reeves, C.,

2. Sabaka, T.J., N. Olsen, and M.E. Purucker, Extending comprehensive models of the Earth's magnetic field with Orsted and CHAMP data.

3. Pulkkinen, A., O. Amm, and A. Viljanen, Ionospheric equivalent current distributions determined with the method of spherical elementary current systems.

Gemma Kelly

A comparative study is presented between magnetic satellite data and geomagnetic field models. The availability of high-quality data during the past decade has allowed development of geomagnetic field models which correlate well with the observed magnetic field at low to mid latitudes. However, in the polar regions, due to the highly variable nature of field sources in the magnetosphere and ionosphere, significant differences (here referred to as residuals) are observed between the recorded data and the models.

The aim of this study is firstly to investigate the nature of these polar residuals, and then to find a method to improve the global models. We consider three models: CHAOS-2 [1], T01 [2] and CM4 [3], and data from two satellites: Ørsted and CHAMP.

On an orbit-by-orbit basis residuals from three models show very similar features in the residuals. We can identify current sources that are consistent in time, local time and co-latitude, even at very quiet times (Kp < 2o, night-side only). There is also some correlation between the size of the residuals and level of activity indicated by the PC and AE indices. When investigating two-day averaged residual plots, the auroral oval can be identified, and there are enhanced residuals over the polar caps, for both quiet and disturbed times. Motivated by these results we have begun work on identifying methods to improve the models, including improved data selection criteria and the removal of spherical elementary current systems (SECS) [4].

1. Olsen, N., et al., CHAOS-2 a geomagnetic field model derived from one decade of continuous satellite data.

2. Tsyganenko, N.A., A model of the near magnetosphere with a dawn-dusk asymmetry - 1. Mathematical structure.

3. Sabaka, T.J., N. Olsen, and M.E. Purucker, Extending comprehensive models of the Earth's magnetic field with Ørsted and CHAMP data.

4. Juusola, L., O. Amm, and A. Viljanen, One-dimensional spherical elementary current systems and their use for determining ionospheric currents from satellite measurements.

Richard Holme

New models of the geomagnetic field using data from recent low-Earth orbiting satellites (Ørsted, CHAMP and Sac-C) have led to substantially increased resolution in the field, particularly in terms of its temporal change, secular variation (SV). It should seem clear that such improved models should result in new insights into the behaviour of the field at the core-mantle boundary (CMB). Unfortunately, the spectrum of the secular variation there is “blue” – power increases with increasing harmonic degree, which means that mapping the SV at the CMB is a poorly-posed procedure, as the strength of the unknown short-wavelength component exceeds the observed SV. However, that something is impossible rarely prevents study in deep-Earth geophysics! Here, we consider the CHAOS-2 model of Olsen et al (2009), and its extension, the under-development CHAOS-4. Study of the spectrum suggests that this contains useful SV information up to spherical harmonic degree 13-14; plots at different truncation limits up to (and even beyond) this level show remarkable coherence, suggesting that although the power increases with degree, it is coherent with lower-degree structure. Maps truncated at this level (or equivalently tapered to give similar detail) show remarkable features – in particular, when plotted at the CMB, the low secular variation under the Pacific covers a much wider region (including the Antarctic), and indeed it might be more appropriate to describe limited regions of high secular variation under between the Atlantic hemisphere and Indonesia. This suggests that low SV is not (as has been suggested) directly correlated with the large low-shear wave velocity province under the pacific, and is more likely to result from processes of thermal core-mantle coupling than electromagnetic screening. Secular acceleration is even more divergent at the CMB; nonetheless, the maps suggest boundaries for the possible source of geomagnetic jerks at the CMB for the period 2000-2009. Comparison with the Comprehensive model (CM4) suggests similar features to the SV at earlier epochs.

Olsen, N., Mandea, M., Sabaka, T.J., Tøffner-Clausen, L., 2009. CHAOS-2 – a geomagnetic field model derived from one decade of continuous satellite data.

Richard Holme

It has been argued that Geomagnetic jerks – sharp changes in the observed geomagnetic secular variation - are caused by or associated with large-scale core flows, particularly torsional oscillations. Such motions should generate similar “jerks” in observed variation in Length of day. Holme and de Viron (2005) produced indirect evidence that this was indeed the case. More careful averaging and treatment of the length-of-day data allows direct indications of the times of such length-of-day jerks, but visual identification is hampered by the background secular change. However, two such signals have been identified in length-of-day contemporaneous with identified jerks in high-resolution satellite models of the geomagnetic field. If confirmed, this result would suggest zero lag between length-of-day and secular variation, which would place powerful lower limits on lower mantle electrical conductance. Objective determination of the position of the jerk is complicated by the presence of a previously identified 5.8-year oscillation in the data; we present a simple demonstration of this signal, and discuss whether it could be the sole generator of geomagnetic jerks.

Holme R., and de Viron, O., 2005.Geomagnetic jerks and a high-resolution length-of day profile for core studies,

Kathy Whaler

Prior to instrumentation developed by Gauss in around 1840, the intensity of the geomagnetic field was unknown. This means that spherical harmonic models of field, based on measurements of inclination and declination, were non-unique. However, an additional assumption, such as the strength of the axial dipole, is sufficient to resolve the ambiguity. Barraclough (1974) noted that the axial dipole since 1840 decayed at a rate of about 15nT/yr; extrapolating back from its 1840 value, this rate of change was imposed on the axial dipole of temporally continuous models of the geomagnetic field in the ‘pre-Gauss era’ by Bloxham and Jackson (1992) and Jackson et al. (2000). However, recent studies (Gubbins et al., 2006; Finlay, 2008) have queried the decay rate deduced by Barraclough (1974). Finlay (2008) prefers a constant axial dipole strength. He cautions against attempting to infer the frozen-flux core-mantle boundary (CMB) flow explaining the secular variation (SV, rate of change of the field) in the pre-Gauss era because of the uncertainty in the axial dipole and its SV. Here, we modify the gufm model of Jackson et al. (2000) in the pre-Gauss era to have a constant axial dipole, in agreement with the preferred value of Finlay (2008), and modify the other main field and SV coefficients to predict the same declinations and inclinations (i.e. the pre-Gauss era data) as the original gufm coefficients. We find that inverting this revised model gives a steady core flow that is almost indistinguishably different from that deduced from the original gufm model. Imposing tangential geostrophy on the flow leads to slightly greater differences between the original and modified flows. This lack of sensitivity of the flow to axial dipole strength and SV is not confined to the pre-Gauss era when data were relatively few and inaccurate: making a similar change to early 20th century field models, when the axial dipole was rapidly varying (Jackson, 2000), leads to an almost identical steady flow from the original and modified coefficients. This is surprising, given that the axial dipole is the largest main field coefficient, and its rate of change amongst the largest SV coefficients. However, it means that CMB flows for the pre-Gauss era are likely to be as valid as those from later epochs.

Barraclough, D. R., 1974, Spherical harmonic analyses of geomagnetic field for 8 epochs between 1600 and 1910,

Bloxham J. and Jackson, A., 1992, Time-dependent mapping of the magnetic field at the core-mantle boundary,

Finlay, C. C., 2008, Historical variation of the geomagnetic axial dipole,

Gubbins, D., Jones, A. L. and Finlay, C. C., 2006,

Jackson, A., Jonkers, A. R. T. and Walker, M. R., 2000. Four centuries of geomagnetic secular variation from historical records,

Jackson, A., 2000. Comment on ‘Time evolution of the fluid flow at the top of the core. Geomagnetic jerks’ by M. Le Huy, M. Mandea, J.-L. Le Mouël and A. Pais,

V. Lesur

Section 2.3 Earth’s magnetic field,

Telegrafenberg

14473 Potsdam, Germany

Models of the lithospheric magnetic field of the Earth based on satellite data can be significantly improved because of the low flight altitude of the German CHAMP satellite and the remarkably quiet magnetic environment of these last three years. Despite tight data selection techniques, the models resolution is still limited to SH degree around 80. Above this degree, models are dominated by a noise made of short wavelength oscillations in the East--West directions. The usual approach to improve models consists in a pre-processing step known as the along track filtering. As an alternative, we investigate how the external magnetic field can leak in a lithospheric field model, and then derived a new regularization technique to minimize the associated noise in models. The technique has been tested on a data set made of 3 years of CHAMP data and proves to work well. Preliminary results will be shown.

Chris Finlay

High quality data provided by the Oersted, CHAMP and SAC-C satellites, together with complementary geomagnetic observatory measurements, are exploited to produced time-dependent models of the core surface field spanning the first decade of the 21st century. Only the core field is explicitly modelled; efforts are made to correct as far as possible for the influence of the magnetospheric and lithospheric fields. In order to produce parsimonious field models, the inversion procedure involves minimising an L1 norm measure of misfit together with norms measuring the spatial and temporal complexity of field at the core surface. Comparisons with observatory and satellite data and analysis of the spectral properties of the field models will be presented. Maps of field acceleration at the core surface will be presented and discussed. The relative merits of entropy versus quadratic regularization will be described. Finally, tests will be presented that probe the compatibility of the models with the quasi-geostrophic hypothesis of core dynamics.

Susan Macmillan

Observatory data holdings at the World Data Centre for Geomagnetism (Edinburgh) www.wdc.bgs.ac.uk include minute, hourly and annual mean values of the geomagnetic field from over 500 observatories since the early 19th century. We describe ongoing maintenance of this important data resource, data-checking procedures developed with global modelling in mind, and some recent additions and corrections.

Nils Olsen, Hermann Luehr, Terence J. Sabaka, Ingo Michaelis, Jan Rauberg, Lars Toeffner-Clausen

Data from the CHAMP satellite provide an excellent opportunity to model small-scale structures of the crustal field, due to the relatively low altitude of the satellite. Of special interest for this are data from the last months of the mission, when satellite altitude was below 300 km.

We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earths magnetic field with high spatial resolution (terms up to spherical degree n=80 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal resolution (allowing for investigations of sub-annual core field changes).

More than 11 years of data from the satellite Ørsted, CHAMP and SAC-C satellites, augmented with ground observatory monthly mean values have been used for this model. Maximum spherical harmonic degree of the static (crustal) field is n=100. The core field time changes are expressed by spherical harmonic expansion coefficients up to n=20, described by order 6 splines (with 6-month knot spacing) spanning the time interval 1997.0 to 2011.0. The third time derivative of the squared magnetic field intensity is regularized at the core-mantle boundary. No spatial regularization is applied for the core field, but the high-degree crustal field is regularized for n>80.

As part of the modelling effort we co-estimate a model of the large-scale magnetospheric field (with expansions in the GSM and SM coordinate system up to degree n = 2 and parameterization of the time dependence using the decomposition of Dst into external (Est) and induced (Ist) parts) and perform an in-flight alignment of the vector data (co-estimation of the Euler describing the rotation between the coordinate systems of the vector magnetometer and of the star sensor providing attitude information).

The final CHAOS-4 model is derived by merging two sub-models: its low-degree part has been derived using similar model parameterization and data sets as used for previous CHAOS models (but of course including newer satellite observations), while its high-degree crustal field part is solely determined from low-altitude CHAMP satellite observations after 2009.

Victoria Ridley

Planetary dynamos, resulting from fluid flow in electrically conductive parts of their interior, are thought to be highly time dependent. Currently, our understanding of time variation (secular variation) of these fields is limited because we only have observations for one example - the Earth. To overcome this, data acquired by 5 NASA space missions, from Pioneer 10 (1973) to Galileo (1995-2003), are being used to investigate possible time variation of Jupiter’s magnetic field.

The internal field of Jupiter is solved as a potential field expanded in spherical harmonics, using a regularised minimum norm approach. However, a highly charged plasma disk, encircling the planet, creates a strong external field contribution to the observations. Estimation of this magnetodisc field is performed for each flyby using the 6 parameter model of Connerney et al (1981) [1]; this highly simplified model aims to reduce the influence of the current disk on the measured magnetic field, allowing more robust determination of the internal planetary field.

The corrected data from all flybys are then used to determine a time-averaged model of the field; this model is of higher resolution than previous models restricted to only a few flybys because of the much better geographical coverage achieved by combining all of the data. Exploration of the parameter space allows further inferences to be made about the internal structure of Jupiter. This includes investigating the effect of the modelled depth to the dynamo source (between 0.7-0.9 Jovian radii) and inferring the drop-off in conductivity outside this region.

The procedure has been extended to consider linear time variation of the internal field. Through comparison of this model with the time-averaged model, secular variation would be indicated by a substantial improvement to the data fit or a decrease in model spatial complexity. As expected, there is an inclination for the models to preferentially fit the Pioneer 11 data, as this is only close approach and high latitude pass of the planet that has been made by a spacecraft. Results so far show dipole orientation consistent with previous studies of Jupiter’s magnetic field but a dipole magnetic moment of around 4.115 G, slightly less than that quoted by the majority of previous modelling attempts (e.g. 4.300 G, Connerney (1992) [2]).

[1] Connerney, J. E. P., Acuna, M. H., and Ness, N. F. (1981), Modelling the Jovian Current Sheet and Inner Magnetosphere,

[2] Connerney, J. E. P. (1992), Doing more with Jupiter’s magnetic field. In Rucker, H.O., Bauer, S.J. and Kaiser, M.L. (eds.),

E. E. Woodfield, J. A. Wild, A. J. Kavanagh, A. Senior, S. E. Milan

The size of the polar cap is very important for understanding the substorm process as well as reconnection rates in general. In this work we build on previous studies which use a combination of EISCAT (European Incoherent SCATter radar) electron temperature (Te ) measurements from two radars running simultaneously to track the motion of the Open-Closed Field Line Boundary (OCB). The second radar gives an estimate of the variation of Te with altitude which can then be subtracted from the radar beam being used to estimate the OCB location. We demonstrate that using the 12 International Reference Ionosphere model 2007 (IRI2007) can remove the second radar requirement and therefore increase the number of cases which could benefit from background Te subtraction. In this paper we focus our analysis on substorm intervals. We find that the IRI2007 method produces an OCB proxy location which on average is 0.25

Daniela Gerovska

Harmonic splines (HS) are global basis functions concentrated in localised regions that can be used to model geopotential data without loss of resolution. Shure et al. (1982) developed a minimum norm algorithm applicable to global datasets, which involves solving a data-by-data system of equations. Here, we apply HS modelling to produce two regional models of the Earth's lithospheric anomaly field from satellite data. We extract and use two subsets, one over Africa and one over North America, from the dataset of Stockman et al. (2009). This is the xCHAOS_03p_08 data set selected and used by Olsen and Mandea (2008) to derive their xCHAOS model but with subtracted xCHAOS model predictions for the external field and for the core field and its secular variation up to spherical harmonic degree 14. We were able to fit the data with very smooth solutions which guarantees that the method will not put a structure that is not in the data. As expected, on regional scale our solutions visually are smoother than that of Stockmann et al. (2009) because theirs is regularised by a maximum entropy norm. Independently treating the CHAMP and Ørsted vector data, we find a similar pattern but difference in the anomaly intensities in the produced regional lithospheric models. Therefore, we should introduce a weighting factor between the CHAMP and Ørsted vector data if used together. We observe no edge effects when working locally and that is contrary to the depleted basis method (Whaler, 1994).We apply the HS modelling method on MF4 lithospheric model data at altitude of 300 km over the same areas in Africa and North America in order to validate the use of the HS modelling method when used regionally. Thus, we compare directly the results at satellite altitudes and on the Earth’s surface. We model the MF4 data with zero-misfit and absolutely no edge effects, and obtain very similar field patterns as those obtained with the HS modelling at 300 km altitude. The differences are more distinct when the fields are continued downward to the Earth’s surface. The MF4 field shows short-wavelength features looking like noise and the HS field is smooth.

Olsen, N. and M. Mandea .2008. Rapidly changing flows in the Earth’s core.

Shure, L., R.L. Parker, and G.E. Backus. 1982. Harmonic splines for geomagnetic modelling

Stockmann, R., C.C. Finley, and A. Jackson. 2009. Imaging Earth’s crustal magnetic field with satellite data: a regularizes spherical triangle tesselation approach.

Whaler, K.A. 1994. Downward continuation of Magsat lithospheric anomalies to the Earth’s surface.

Qinghe Zhang and Malcolm Dunlop

Extending previous studies, a full-circle investigation of the ring current has been made using Cluster 4-spacecraft observations near perigee, at times when the Cluster array had relatively small separations and nearly regular tetrahedral configurations, and when the Dst index was greater than -30 nT (non-storm conditions). The ring current flows westward and average current density is asymmetric, ranging from 5 to 30 nAm-2. The current density is enhanced between about 05 and 11 magnetic local time (MLT) and is reduced between at 12-14 MLT. This suggests that region-2 field aligned-currents (FACs) flow upward into the ring current around 09 MLT and downward out of the ring current around 14 MLT. We also find evidence of localized reduction to the ring current around local midnight which might be part of the DP-1 substorm current wedge.

Rob Shore

We seek to build an improved model of the magnetic field generated in the Earth’s liquid iron core to aid studies of Earth phenomena. To make effective use of the abundance of high-precision satellite magnetic data from the last decade, we follow the approach developed by Mandea and Olsen (2006), constructing a set of ‘Virtual Observatories’ (VO) to reduce the huge data sets to a series of values averaged over small regions of the globe. Each VO acts as a data bin for satellite magnetic measurements for a single month. From these data the mean magnetic field at the centre of the bin is calculated using robust least squares inversion, assuming a potential field; the output magnetic field values are used to produce a global internal field model via spherical harmonic analysis. We investigate in more detail the result of Beggan et al. (2009) that the VO method output is prone to contamination from external sources. The authors found temporally and spatially varying biases and patterns in the vector components of the residuals to the global model. These biases cannot be accounted for by uncertainty descriptions which assume zero mean, Gaussian distribution of errors; we therefore look to remove these external field errors. The aim of this research is to minimise the external field contamination within internal field models created with the VO method, by use of data processing and selection methods. Particular emphasis is given to the processing benefits available from the improved spatial and temporal resolution of the external fields provided by the forthcoming ESA SWARM magnetic satellite constellation mission. We report on the effectiveness of combining the SWARM constellation data in deriving VO solutions, and focus on a more complete description of the contamination arising from use of a single satellite. In these analyses we make use of the E2Eplus simulator (Olsen et al, 2007) synthetic SWARM data, allowing the description of the relative effect of each isolated external field source on the VO solutions. Severe small-scale spatial biases in the global distribution of VO solutions are found to have a minimal effect on the subsequent global internal field model. The composition of the contamination signal is found to be more complex than initially assumed, motivating further study into the impacts of these spatially and temporally varying signals on the global inversion.

Beggan, C.D., Whaler, K.A. & Macmillan, S., 2009. Biased residuals of core flow models from satellite-derived 'virtual observatories',

Mandea, M. & Olsen, N., 2006. A new approach to directly determine the secular variation from magnetic satellite observations,

Olsen, N., Sabaka, T.J., Gaya-Pique, L.R., Kuvshinov, A. & Tøffner-Clausen, L., 2007. Study of an Improved Comprehensive Magnetic Field Inversion Analysis for Swarm: Final Report.

Virginie Penquerc’h, Arnaud Chulliat

Equipe de Géomagnétisme

Institut de Physique du Globe de Paris

The quiet-time daily geomagnetic variation observed at mid-to low latitudes is generated by electrical currents flowing in the lower ionosphere, around 110 km altitude. These currents result from the displacement of the conducting ionosphere in the main magnetic field of internal origin. An important parameter of the Sq field amplitude is the electrical conductivity of the ionospheric E-layer, which varies daily, seasonally, and with solar activity. The latter variations are usually parameterized by a linear dependence upon the solar radiation flux index F10.7 in spherical harmonics models of the Sq field. Yet it has been pointed out by some studies that (a) the proportionality factor between the Sq amplitude and the F10.7 index is not the same at all seasons, (b) the relationship becomes non-linear during intense solar activity (F10.7 > 200). Here we will present the results of a new study of this problem, based upon the method proposed by Hibberd (1984) for obtaining the Sq currents intensity from magnetic data recorded at a pair of ground magnetic stations. The purpose of this work is to refine the empirical relationship between the Sq field and the solar flux used in spherical harmonics models.