Reto Stockmann, Chris Finlay and Andy Jackson

We present a method for imaging the global crustal magnetic field at Earth's surface that involves localised basis functions and a minimum norm model estimation philosophy. We adopt a spherical triangle tessellation (STT) parameterization of the vertical component of the crustal field at Earth's surface and a forward modelling scheme using the Greens functions for a potential field. The inversion procedure requires minimisation of an objective function consisting of a mean absolute deviation (L1) measure of misfit together with a norm measuring the model complexity. Both quadratic and entropy measures of complexity are investigated. We report results of synthetic tests performed on a geophysically-motivated scenario; these include a successful benchmark of the method and a comparison between the quadratic and entropy regularisation strategies. We find that the maximum entropy method allows construction of models with more realistic field amplitudes and higher correlations to the synthetic truth, but it also requires additional prior information concerning the default parameter in the entropy scheme. Applying our technique to real observations collected by the CHAMP, Oersted and SAC-C satellites we obtain robust images of the crustal field at Earth's surface that include sharp features with high amplitudes but which are nonetheless structurally simple. We present details of two such models STT-CRUST-Q and STT-CRUST-E which are regularized using quadratic and entropy norms respectively.

Ciaran Beggan

Secular variation (SV) on decadal time-scales is primarily driven by advection of the magnetic field by fluid flows in the outer core. By deriving core-flows from the inversion of SV data it may be possible to forecast the change of the present magnetic field (as measured) forwards in time for a short time period (e.g. less than five years) within an acceptable error budget. Using simple advection of steady or non-steady flows to forecast magnetic field change gives reasonably good fit to field models such as GRIMM, POMME or xCHAOS (< 100nT difference after five years).

The forecast of the magnetic field change can be improved by optimally assimilating measurements of the field into the forecast from flow models at discrete points in time (e.g. annually). To achieve this, an Ensemble Kalman Filter (EnKF) can be used to the capture non-linearity of the model and delineate the error bounds by means of a Monte Carlo representation of the field evolution over time. In the EnKF model, an ensemble of probable state vectors (Gauss coefficients) evolve over time, driven by SV derived from core flows. The SV is randomly perturbed at each step before addition to the state vectors. The mean of the ensemble is chosen as the most likely state (i.e. field model) and the error associated with the estimate can be gauged from the standard deviation from the mean.

I show an implementation of the EnKF for steady and non-steady flows generated from 'Virtual Observatory' field models, compared to the field models GRIMM and xCHAOS over the period 2002 – 2008. Using the EnKF, the maximum difference never exceeds 25nT over the period. This promising approach allows measurements to be included into model predictions to improve the forecast.

David Gubbins

The conventional way to calculate the crustal field from magnetisation is to sum the dipole contributions and do a spherical harmonic analysis for the geomagnetic coefficients. Changing the order of the two surface integrations allows one to be done analytically, saving considerable computer time, but the method still suffers considerable disadvantages: (1) Magnetisation estimates are needed on a sufficiently dense grid for the integration to be performed (2) There is no way to estimate the effect of errors in the magnetisation estimates (3) There is no way to assess the effect of inaccuracy in the numerical integration, in particular the leakage of internal potential fields and toroidal fields into the desired external field. To a first approximation the magnetisation estimate has uniform susceptibility we expect the internal field to dominate (Runcorn's theorem), so the leakage problem may be very serious.

The right way is to perform this "forward" problem as an inverse problem. Magnetisation estimates are essentially data, they are made painstakingly by studying geological maps, using crustal and lithospheric models, and rotating remanently magnetised oceanic lithosphere. These estimates should be restricted to those places where we have some confidence of the magnetisation and each should be assiged an error. The crustal field is a model in the form of geomagnetic coefficients that can be regularised in some way.

The vector spherical harmonics (Y_l,l; Y_l,l-1; Y_l,l+1) of Condon & Shortley (see "Harmonics, Spherical" by DE Winch in Encyclopedia of Geomagnetism and Paleomagnetism, ed. Gubbins & Herrero-Bervera) provide an ideal basis for describing the magnetisation. They are a complete orthogonal set in which any vector may be expanded. The Y_l,l+1 describe that part of the magnetisation responsible for the desired external field, Y_l,l-1 the internal field, and Y_l,l the toroidal part associated with a vertical electric current. The conventional "dipole" integral may be converted to the single integral over the magnetisation that yields the coefficients of the internal harmonic Y_l,l+1, which are simply related to the geomagnetic coefficients.

The proposed inverse problem involves establishing a database of magnetisation estimates at suitable locations, which need not be equally spaced (although obviously good geographical coverage is desirable). The vector spherical harmonic expansion is used to write each magnetisation estimate as a sum of unknown coefficients. The magnetisations are then inverted for all 3 sets of coefficients; the usual procedures give estimates of resolution, error, and cross-contamination between the different types of magnetisation(external, internal, toroidal). While success is not guaranteed, we will at least have an idea of the validity of the result.

M. E. Purucker

Large and intermediate-scale tectonic features such as subduction zones, large igneous provinces, rifts, and diffuse plate boundary zones are often seen to have a magnetic signature visible from the perspective of near-Earth magnetic field satellites such as CHAMP and Orsted. Why do these tectonic features have a magnetic signature, while others don’t? A new model of the lithospheric field (MF-6, Maus et al., 2008) extending to spherical harmonic degree 120 (333 km wavelength) has been used to evaluate the magnetic state of the lithosphere under the assumption that the magnetization is either induced (with a seismic starting model), or remanent (with a minimum norm approach). Some of the features identified from these images include the Tethyan and NE Siberian diffuse plate boundary zones, the Red Sea rift, and Cretaceous rift basins developed on the West African shield. Almost without exception, subduction zones exhibit a magnetic signature, as do many large igneous provinces. In this talk we discuss some of the new insights this magnetic perspective provides, and speculate on the controls which determine whether tectonic features will be expressed magnetically.

Alan WP Thomson

A new data weighting scheme is introduced for satellite geomagnetic survey data. This scheme allows vector samples of the field to be used at all magnetic latitudes and results in an improved lithospheric model, particularly in the polar regions. Data weights for 20-second spaced satellite samples are derived from two noise estimators for the sample. Firstly the standard deviation along the 20 seconds of satellite track, centred on each sample, is computed as a measure of local magnetic activity. Secondly a larger-scale noise estimator is defined in terms of a 'local area vector activity' (Lava) index for the sample. This is derived from activity estimated from the geographically nearest magnetic observatories to the sample point. Weighting of satellite data by the inverse-sum-of-squares of these noise estimators leads to a robust model of the field (called MEME08) to about spherical harmonic degree 60. In particular we find that vector data may be used at all latitudes and that there is no need to use particularly complex model parameterizations, regularisation, or prior data correction to remove estimates of unmodelled source fields.

KL Turnbull

Substorms are known to cause Geomagnetically Induced Currents (GIC) in power transmission lines through variations in the ground magnetic field. An improved knowledge and understanding of how different phases of substorms affect the ground magnetic field will ultimately help to better understand how GIC arise. This study looks at 553 substorms during 2000 to 2003, in particular the link between onset and the differential of the horizontal magnetic field, dH/dt, also comparing onsets that occur in storm time conditions to those that occur in non-storm time. The results are compared with earliers studies.

Christian Lynch

There has been much recent speculation about the strength of the geomagnetic axial dipole in the days before Gauss invented a method of determining magnetic field intensity (Gubbins et al, 2006; Finlay, 2008). We have investigated the effect of fixing the axial dipole coefficient in the period prior to 1840 to its 1840 value in the gufm field model (Jackson et al., 2000) and inverting the perturbed field model for CMB flow. The flow is found to be relatively insensitive to the axial dipole value, for both steady flows and those on which no non-uniqueness reducing assumption has been imposed. Before 1600, the flow is rather different from present-day patterns, but around 1600 it settles into the familiar form.

Qing-He Zhang

A large number of flux transfer events (FTEs) were simultaneously observed by Cluster/TC-1 Spacecraft and the EISCAT and SuperDARN radars between 11:48 and 13:00 UT on 1 April 2004, 09:00 and 12:00 UT on 11 February 2004, and 12:00 and 12:40 UT on 13 March 2004, during southward IMF (B

The motions of these FTEs are correspond well with the “poleward-moving radar auroral forms” (PMRAFs) (or “pulsed ionospheric flows” (PIFs)) observed by CUTLASS (or Stokkseyri) SuperDARN radar, and also correspond with the bursts of poleward flow and low-energy electron precipitation recorded by the EISCAT radars. Furthermore, the motion direction of the FTEs observed by Cluster/TC-1 and the expected flux tubes predicted by the Cooling model are temporally correlated with clear velocity enhancements in the ionospheric convection conjugate measured by SuperDARN radar in both hemispheres. The duration of these velocity enhancements implies that the evolution time of the FTEs is about 4-8 minutes from its origin on magnetopause to its addition into the polar cap. However, the ionospheric response time was different in each hemisphere. This suggests the reconnection site is located southward (or northward) of the subsolar region.

QingHe Zhang

Woodfield et al. (2007) have compared two years of magnetic field data from Cluster with the Tsyganenko 2001 (T01) model. The study has shown the residuals between the data and the model can reach ~20 nT near perigee and the deviations take two forms: a sharp, bipolar signature and well-defined trends over a larger spatial region. We are extending this analysis to compare eight years magnetic field data from Cluster with Tsyganenko 1989 (T89), 1996 (T96), and 2001 (T01) field models. The preliminary results are as follows. The deviations are much weaker during the later years, which might be because they are near the solar minimum year. Nevertheless, there are some differences in the comparisons of the data with the different models. For T89, the dB

Daniela Gerovska

The magnetic anomaly maps (

The magnitude magnetic transforms (MMTs) (Stavrev and Gerovska, 2000) produce anomalies that are closer to the magnetic-source’s true horizontal position and are simpler to interpret than the measured anomalous field itself. The MMTs are based on the total magnitude anomaly (TMA)

The MMTs require only first-order, horizontal derivatives for their calculation (Stavrev and Gerovska, 2000; Gerovska and Araúzo-Bravo, 2006) but at the same time they contain field derivatives of different order: the

Gemma Kelly

Previous consideration of the residual between field models and Oersted data had shown significant remaining signal which was coherent from orbit to orbit. This signal was particularly evident in the direction in which attitude error is maximum. We examine tracks from 10th-12th September 2004 to determine whether this is still the case. For these quiet-time orbits there is no longer an obvious signal in this direction, suggesting that recalibration of the star camera dealt with this problem. The largest remaining residual can be identified as inadequate modelling of the ring current. We also look at the high latitude signals for both Oersted and CHAMP data. In these regions there are large residuals which can be seen in all 3 components of the magnetic residual vector δB=(δB

Andy Jackson

Positioning errors are believed to be the largest error source of the magnetic intensity data of the POGO satellite series, which flew between 1965 and 1972. A position error of 100 m in the radial direction results in a maximum intensity error of 2.8 nT, while a similar positioning error in horizontal direction only gives about 0.5 nT field intensity error.

No advanced gravity field models were available at the time when the satellite positions were calculated several decades ago, and therefore a reprocessing of the POGO positions, using state-of-the-art gravity field models, may lead to better positions and thereby reduced magnetic residuals.

Unfortunately, the original tracking data are not readily available for the POGO satellites. One therefore has to rely on the processed positions, which we use as input to the BERNESE orbit determination software. This program adjusts the positions by minimizing the difference between the actual "observed positions" (which in our case are the preprocessed orbits) and predicted positions by introducing small corrections. Application to one month of OGO-4 data results in position changes of a few hundred meters.

Fitting a magnetic field model to the magnetic field observations using the reprocessed orbits gives slightly reduced magnetic field residuals. We will report on plans for future activities.

Sheona Masterton

The passive upwelling of upper mantle material between diverging plates at mid-ocean ridges suggests that spreading rate determines how quickly material is sequestered from the mantle. If the absolute velocity of plate motion on either side of a ridge axis is not exactly equal and opposite, the ridge will migrate over time with respect to an absolute reference frame. A slow spreading, fast migrating ridge system sequesters a smaller volume of upper mantle material from a finite source region than a fast spreading, slowly migrating ridge system. The duration of time that a ridge spends over a region from which mantle material is sourced, is expected to impact on the chemical and physical characteristics of asthenosphere and overlying lithosphere in that region. The present work aims to identify absolute palaeo-positions of MORs and their migration rates, and investigate any correlations they have with mantle depletion due to partial melting, seamount distributions, seafloor roughness and depth to basement.

Mid-ocean ridge positions have been reconstructed at 1 My intervals for the past 140 Ma, using the plate reconstruction model and present-day global isochron data of Muller et al. (2008). The absolute rate at which these mid-ocean ridges migrate across the Earth's surface over time is characterised by first binning the ages of palaeo-MORs into equal area cells, and computing the standard deviation of the mean age within each cell. Areas of fast and slow migrating ridges are indicated by low and high standard deviations from the mean age, respectively. Standard deviations are then interpolated onto a regular grid to produce a global map; this map is analogous to the duration of time that palaeo-ridges have occupied areas on the Earth’s surface above mantle which has been subject to sequestration of material. Comparisons are then made with physical and chemical properties of the lithosphere and upper mantle.

Nils Olsen

Time series of annual differences of Observatory Monthly Means contain signatures that change within a few months. Present core field models are only partly able to describe these rapid changes. I'll present recent efforts to improve the temporal (and spatial) resolution of the xCHAOS field model.

Brian Hamilton

We present on-going work towards building a global model of the quiet-time geomagnetic daily variation using observatory data. We select hourly mean data spanning the last solar cycle. We fit Fourier series in time, with a fundamental period of 24 hours, to the 5 quietest days of data within each month and at each observatory. We then use spherical harmonic expansions to produce a global model of the daily variation for each month, as characterised by the Fourier coefficients in time. Annual, semi-annual and 11-year harmonics are derived from the spherical harmonic coefficients to give a model that estimates the daily variation field values for a given location, date, and time. The model is assessed by comparison with the input data, and two other daily variation models: WDCA/SQ1 (using observatory data), and CM4 (observatory and satellite).

Derek Fairhead

NOAA's National Geophysical Data Center (NGDC) has extensive holdings of airborne and marine magnetic data. Such data have been collected for more than half a century, providing global coverage of the Earth. Due to the changing main field from the Earth's core, and due to differences in quality and coverage, combining these data to a consistent global magnetic anomaly grid is challenging. A key ingredient is the long wavelength magnetic field observed by the low-orbiting CHAMP satellite. To produce a homogeneous grid, the marine and aeromagnetic trackline data are first line-leveled and then merged with the existing grids of continental-scale compilations by Least Squares Collocation. In the final processing step the short-to- intermediate wavelengths of the near-surface grid are merged with the latest CHAMP satellite magnetic anomaly model MF6 (http://geomag.org/models/MF6.html). In analogy to NGDC's 2-arc-minute resolution ETOPO2 grid, we call our magnetic anomaly grid EMAG2. The grid will be updated regularly. It is available in digital form and as plug-ins for NASA World Wind and Google Earth.