Chris Finlay, Nicolas Gillet and Andrew Jackson |
Maximum Entropy core field models from 21st century satellite data |
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James Hawe and Richard Holme |
Tidal Magnetic Models: A New Field Modelling Approach |
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Emma Woodfield, Anasuya Aruliah, Richard Holme and George Millward |
Storm-enhanced neutral wind dynamo effects on the Earth’s magnetic field. |
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Derek Fairhead |
TILT-DEPTH METHOD: A SIMPLE DEPTH ESTIMATION METHOD USING FIRST ORDER
MAGNETIC DERIVATIVES |
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Ciaran Beggan, Kathy Whaler, Susan Macmillan |
Core Flow Modelling from Satellite-Derived ‘Virtual Observatories’ |
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Sheona Masterton |
Intermediate wavelength anomalies over the Atlantic ocean |
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Nicolas Gillet, Andy Jackson and Chris Finlay |
Meso-scale core flow reconstruction from satellite geomagnetic
field models |
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Nils Olsen |
On external field contributions and the regularisation of core field models |
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Brian Hamilton and Susan Macmillan |
Global modelling of quiet-time daily geomagnetic variations using
ground-based observatories |
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Chris C. Finlay

High precision magnetic measurements from the Oersted, CHAMP and SAC-C satellites are now available that span the past 8 years. This poses a challenge for those interested in understanding the origin and evolution of the main field generated in Earth's core: How should such data be modelled to extract the maximum information concerning core field structure, its evolution and the underlying magnetohydrodynamic processes?

In this poster, we present 3 new core field models. All are constructed from the CHAOS data set (Olsen et al., 2006), with 1st order corrections applied for the large scale magnetospheric field and the crustal field (from the GRIMM model of Lesur et al., 2008). Account is taken of anisotropic errors due to the satellite measurement setup, and an attempt is made to take account of addition correlations due to fluctuations in ring and auroral oval currents (Holme et al, 2003, Fujii and Schultz, 2002). An L1 measure of misfit, without data rejection, is also employed to downweight the influence of outliers. The 3 models are also regularized in space and time at the core mantle boundary so are suitable for future use in core flow studies. One model has quadratic regularization in both space and time, another has quadratic regularisation in time but maximum entropy regularization in space, while the remaining has maximum entropy regularization in both space and time. The method of Gillet et al. (2007) is used to carry out the maximum entropy regularization. The properties of these models and their limitations will be discussed.

For many years it has been recognised that the passive flow of the circulating oceans through the Earth’s magnetic field generates a secondary field through the process of motional induction. However, while this phenomena is known to exist, little work has been carried out to characterise these secondary fields. Global flows such as tides have received some attention, but have not been the subject of an intensive magnetic field modelling process. Here we present a new, multi-mode spherical harmonic field model derived to represent the induced magnetic field associated with global tides. By integrating data from all three of the major orbiting satellites, CHAMP, SAC-C and Oersted, in both scalar and vector forms, we are able to derive a tidal model that in preliminary testing has been found to be consistent with early work by others. We are also able to extend the latitude range of the model from mid latitudes into the previously problematic, high latitude region. This model also has the potential to be expanded to include any number of previously unstudied tidal modes, thus giving the opportunity to greatly increase our understanding of global tidal behaviour on a whole range of timescales.

The neutral wind dynamo driven currents in the E-region of the ionosphere are one of many sources contributing to the Earth’s overall magnetic field. Characterisation of the various sources is a vital step in understanding the Earth’s whole magnetic environment from the core to the magnetosphere. Storm activity increases the kinetic energy in the neutral atmosphere and the enhanced motion decays gradually. This has a knock-on effect on the magnetic field at the ground at low to mid-latitudes. We have used the Coupled Thermosphere Ionosphere Plasmasphere model (CTIP) to assess the impact of the neutral particle inertia on the magnetic field. Our motivation is to quantify the magnitude of this effect such that it can be accounted for in geomagnetic field modelling. Our initial results using an artificial storm indicated a small (of the order of 10 nT) and long-lived (a few days) elevation in the magnetic field originating from this source.

MAGNETIC DERIVATIVES

Derek Fairhead

Mapping the magnetic tilt angle, derived from first order derivatives, has the advantage of enhancing weak magnetic anomalies compared to stronger magnetic anomalies due to the effective automatic gain control(AGC) imposed by the arctan operator that restricts the tilt angle to within the range -90 deg to +90 deg, irrespective of the amplitude or wavelength of the magnetic field. We have found that it is possible to simply use the contours of the tilt angle to estimate the location and depth of the magnetic sources. The zero contours (shown as a dashed line in figures) indicate the location of source edges and the half distance between the -45 deg and +45 deg contours provides an estimate of their depth. In a synthetic example and a field example, we demonstrate that when the region between the -45 deg and the +45 deg contours is high-lighted (in grey), the resulting map provides an intuitive means of identifying the location and depth of the magnetic sources. For this contribution we assume that the sources are simple vertical contacts; that there is no remanent magnetization; and the inducing field has either vertical inclination or has been reduced to the pole (RTP). Advantages of the method, called here the 'Tilt-Depth'method, are discussed with respect to existing methods using second and third order derivatives.

The last decade has seen a significant improvement in the capability to observe the global field at high spatial resolution. Several satellite missions have been launched, providing a rich new set of scalar and vector magnetic measurements from which to model the global field in detail. These data complement the existing record of ground-based observatories, which have continuous temporal coverage at a single point. We wish to exploit these new data to model the secular variation (SV) globally and improve the flow models that have been constructed to date.

Using the approach developed by Mandea and Olsen (2006) we create a set of 648 evenly distributed `Virtual Observatories' (VO), at 400km above the Earth's surface, encompassing satellite measurements from the CHAMP satellite over five years (2001-2005). We invert the SV calculated at each VO to infer flow along the core-mantle boundary. Direct comparison of the SV generated by the flow model to the SV at individual VO can be made. Thus, the residual errors can be investigated in detail.

We show comparisons of flow models from generated from a number of VO datasets. We also show evidence, in the residual distributions of the field and SV models derived from the VO, of signals that are consistent with unmodelled external field effects in the satellite data. We show that using only the internal field (derived from the VO data using spherical harmonics) to generate the flow models produces the best fit of the model to the data. However, these may still include contamination from noise internal to the satellite orbit.

A GIS-based forward modelling technique has been adopted to predict intermediate wavelength magnetic anomalies over the Atlantic Ocean and allow separate assessment of the contribution of both induced and remanent magnetisation to the potential field.

Magnetic anomalies due to remanent magnetisation are computed from vertically integrated magnetisation (VIM) and palaeofield unit vectors, both of which are age-dependent and implement the latest digital isochron age map provided by the Earthbyte group at Sydney University. VIM assumes a simple three-layer crustal thickness model, exponential decay of thermo-remanence and acquisition of chemical remanence. Calculation of palaeofield unit vectors requires spreading centre palaeopositions for the ocean floor; these are obtained by performing finite rotations within a moving hotspot reference frame. Palaeofield direction is then obtained using an axial geomagnetic dipole approximation.

Magnetic anomalies due to induced magnetisation are computed from vertically integrated susceptibility (VIS); this assumes a three-layer crustal thickness model and associated standard susceptibilities.

Comparisons were made between magnetic anomalies predicted by the present work, by Hemant and Maus (2005) and with observations (MF5) at satellite altitude; these suggest that the correct application of finite rotations and the use of an updated palaeo-reconstruction model has improved model accuracy for Atlantic regions.

The next stage in the present work is to use heat flow modelling to constrain Curie temperature depth, and thus magnetic crustal thickness in the Atlantic. Palaeofield unit vectors will also be computed for all other oceanic regions in the digital age map, allowing the eventual prediction of global oceanic magnetic anomalies.

Nicolas Gillet

We address the question of retrieving meso-scale core flow patterns from satellite geomagnetic field secular variation (SV) models. We specifically developed for this purpose a SV model from the CHAOS dataset (period 1999--2006, see the poster by Finlay et al). Core flow models result from the inversion of the induction equation in the frozen flux approximation. Eymin and Hulot [2005] have shown that the interaction between small scales of both the flow and the magnetic field generate SV at large scales which cannot be modelled. The integration of such "modelling" errors (Pais and Jault [2008]) is crucial to consistently extract the information from the data.

Our problem is ill-posed and require the addition of (i) an extra constraint about the flow morphology to reduce the parameter space (we use in this study the tangentially geostrophic approximation) and (ii) a regularisation to reduce the unconstrained effect of the small scales. Usual quadratic regularisations add unnecessary a priori information, lead to underestimate the power at large wave numbers and thus to a loss of contrast in the reconstructed picture. Recently introduced to invert for magnetic field models (Jackson [2003], Gillet et al [2007]) the maximum entropy method is known to provide sharper pictures containing a minimum of a priori about their structure. We adapt here this technique to image the core flow at the core-mantle boundary.

We show that the maximum entropy method and the use of modelling errors allow to isolate robust meso-scale flow patterns. Perspectives and implications for the Earth's core dynamics are discussed.

The quality of the time-dependence of models of the recent core field depends on our ability to account for external field contributions, either by data selection or by data correction (or external field co-estimation).

When looking at the time evolution of core models that are derived on a monthly basis (for instance from the CHAMP virtual observatory data set) it turns out that coefficients with low

The time dependence of spline models of the core field is typically damped by applying a regularization that depends on spherical harmonic

As an appetizer for a discussion on external field contributions and model regularization I'll present some of the problems that I encountered when deriving the xCHAOS field model.

Global modelling of quiet-time daily geomagnetic variations using ground-based observatories

Brian Hamilton

The quiet-time daily variations in the geomagnetic field are known to show strong dependence on latitude, local time, season and solar cycle. In this poster we present preliminary results from surface-harmonic models of these variations derived from ground-based observatories. The data input to the models are hourly means from the five geomagnetically quietest days in June and December 2004 from 98 observatories. These data from each observatory are linearly de-trended and Fourier coefficients are fit to them with a fundamental period of 24 hours and minimum period of 6 hours. Surface harmonics up to degree 4 are then fit to the distribution of each Fourier coefficient, separately. The accuracy of the Fourier and spherical harmonic models with respect to the input data is discussed. We also comment on the geographical and seasonal variations in the model.