Secular variation prediction of the Earth’s magnetic field using core surface flows

grants NER/O/S/2003/00674 and NER/O/S/2003/00677. NERC studentship award NER/S/J/2005/13496.The Earth’s magnetic field is generated by fluid motion of liquid iron in the outer core. Flows at the top of the outer core are believed to be responsible for the secular variation (SV) observed at the surface of the Earth. Modelling of this flow is open to considerable ambiguity, though methods adopting different physical assumptions do lead to similar flow velocity regimes. Some aspects of the ambiguities are investigated in this thesis. 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 groundbased observatories, which have continuous temporal coverage at a single point. I exploit these new data to model the secular variation (SV) globally and attempt to improve the core flow models that have been constructed to date. Using the approach developed by Mandea and Olsen (2006) I create a set of evenly distributed ‘Virtual Observatories’ (VO), at 400km above the Earth’s surface, encompassing satellite measurements from the CHAMP satellite over seven years (2001-2007), inverting 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 differences can be investigated in detail. Comparisons of residuals from flow models generated from a number of VO datasets provide evidence that they are consistent with internal and external field effects in the satellite data. I also show that the binning and processing of the VO data can induce artefacts, including sectorial banding, into the residuals. By employing the 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 (< 50nT root mean square 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

Space weather goes to schools

Ciarán D Beggan and Steve R Marple describe how they are using low-cost computers to develop a network of school magnetometers for measuring space-weather effects in the UK

Ensemble Kalman Filter Analysis of Magnetic Field Models During the CHAMP-Swarm gap

Between the de-orbiting of CHAMP in September 2010 and the launch of Swarm in November 2013, there was a lack of satellite vector magnetic field data to use for main field modelling. During this period the difference between field models derived at the time and retrospective analysis (using data both before and after the vector gap) rose to around 20 nT root-mean-square (RMS). We use Ensemble Kalman Filtering (EnKF) to combine models of steady flow at the outer core surface with magnetic field models derived from the period when no vector satellite data were available. Since we find that the field models produced during periods without vector satellite data are just as good as the annual predictions from a flow model, there appears, at present, to be no overall benefit to using EnKF to improve field forecasting. This will remain the case until flow modelling can better forecast secular variation

Developing a Raspberry Pi magnetometer for schools in the UK

We describe our efforts to build a magnetic field sensor to be deployed in schools across the United Kingdom, adding to the existing variometer network from AuroraWatch set up by the University of Lancaster (Figure 1). The aim is to encourage students from 14-18 years old to look at how sensors can be used to collect geophysical data and integrate it together to give a wider understanding of physical phenomena. A second aim is to provide useful data on the spatial variation of the magnetic field for analysis of geomagnetic storms, alongside data from the BGS observatory and SAMNET variometer network. The system uses a Raspberry Pi computer as a logging and data transfer device, connected to a set of miniature fluxgate magnetometers. The system has a nominal sensitivity of around 1 nT RMS (~1 part in 50,000) in each component and is relatively low-cost at about £250 per unit. We intend to build 10 systems initially. In this poster we show results from the build and testing of the sensor and examples of recorded horizontal field

Geolectric field measurement, modelling and validation during geomagnetic storms in the UK

Significant geoelectric fields are produced by the interaction of rapidly varying magnetic fields with the conductive Earth, particularly during intense geomagnetic activity. Though usually harmless, large or sustained geoelectric fields can damage grounded infrastructure such as high-voltage transformers and pipelines via geomagnetically induced currents (GICs). A key aspect of understanding the effects of space weather on grounded infrastructure is through the spatial and temporal variation of the geoelectric field. Globally, there are few long-term monitoring sites of the geoelectric field, so in 2012 measurements of the horizontal surface field were started at Lerwick, Eskdalemuir and Hartland observatories in the UK. Between 2012 and 2020, the maximum value of the geoelectric field observed was around 1 V/km in Lerwick, 0.5 V/km in Eskdalemuir and 0.1 V/km in Hartland during the March 2015 storm. These long-term observations also allow comparisons with models of the geoelectric field to be made. We use the measurements to compute magnetotelluric impedance transfer functions at each observatory for periods from 20 to 30,000 s. These are then used to predict the geoelectric field at the observatory sites during selected storm times that match the recorded fields very well (correlation around 0.9). We also compute geoelectric field values from a thin-sheet model of Britain, accounting for the diverse geological and bathymetric island setting. We find the thin-sheet model captures the peak and phase of the band-passed geoelectric field reasonably well, with linear correlation of around 0.4 in general. From these two modelling approaches, we generate geoelectric field values for historic storms (March 1989 and October 2003) and find the estimates of past peak geoelectric fields of up to 1.75 V/km in Eskdalemuir. However, evidence from high voltage transformer GIC measurements during these storms suggests these estimates are likely to represent an underestimate of the true value

Modelling the earth’s geomagnetic environment on Cray machines using PETSc and SLEPc

The British Geological Survey's global geomagnetic model, Model of the Earth's Magnetic Environment (MEME), is an important tool for calculating the strength and direction of the Earth's magnetic field, which is continually in flux. While the ability to collect data from ground‐based observation sites and satellites has grown rapidly, the memory bound nature of the original code has proved a significant limitation on the size of the modelling problem required. In this paper, we describe work done replacing the bespoke, sequential, eigensolver with that of the PETSc/SLEPc package for solving the system of normal equations. Adopting PETSc/SLEPc also required fundamental changes in how we built and distributed the data structures, and as such, we describe an approach for building symmetric matrices that provides good load balance and avoids the need for close coordination between the processes or replication of work. We also study the memory bound nature of the code from an irregular memory accesses perspective and combine detailed profiling with software cache prefetching to significantly optimise this. Performance and scaling characteristics are explored on ARCHER, a Cray XC30, where we achieved a speed up for the solver of 294 times by replacing the model's bespoke approach with SLEPc

Decadal period external magnetic field variations determined via eigenanalysis

We perform a reanalysis of hourly mean magnetic data from ground-based observatories spanning 1997-2009 inclusive, in order to isolate (after removal of core and crustal field estimates) the spatiotemporal morphology of the external fields important to mantle induction, on (long) periods of months to a full solar cycle. Our analysis focuses on geomagnetically quiet days, and mid- to low-latitudes. We use the climatological eigenanalysis technique called Empirical Orthogonal Functions (EOFs), which allows us to identify discrete spatiotemporal patterns with no a priori specification of their geometry – the form of the decomposition is controlled by the data. We apply a spherical harmonic analysis (SHA) to the EOF outputs in a joint inversion for internal and external coefficients. The results justify our assumption that the EOF procedure responds primarily to the long-period external inducing field contributions. Though we cannot determine uniquely the contributory source regions of these inducing fields, we find that they have distinct temporal characteristics which enable some inference of sources. An identified annual-period pattern appears to stem from a north-south seasonal motion of the background mean external field distribution. Separate patterns of semi-annual and solar-cycle-length periods appear to stem from the amplitude modulations of spatially fixed background fields

Automatic detection of Ionospheric Alfvén Resonances in magnetic spectrograms using U-net

Ionospheric Alfven Resonances (IARs) are weak discrete non-stationary Alfven waves along magnetic field lines, at periods of ~0.5-20 Hz, that occur during local night-time, particularly during low geomagnetic activity. They are detectable through time-frequency analysis (spectrograms) of measurements made by sensitive search coil magnetometers. The IARs are generated by the interaction of electromagnetic energy partially trapped in the Earth-ionosphere cavity with the main geomagnetic field and their behavior provides proxy information about atmospheric ion density between 100-1000 km altitude. Limited methods exist to automatically detect and analyse their properties and behavior as they are difficult to extract using standard image and signal processing techniques. We present a new method for the detection of IARs based on the fully convolutional neural network U-net. U-net was chosen as it is able to perform accurate image segmentation and it can be trained in a supervised fashion on a relatively small labeled dataset utilizing data augmentation. We show that the resulting predictive model generated by training the U-net is able to detect IAR signals while mislabelling considerably less noise than other data analysis methods. We achieved our best results by using a training set of 178 hand-digitized examples from high-quality spectrograms measured at the Eskdalemuir Geophysical Observatory (UK). We find that the network converges in ten iterations with a final intersection over union (IoU) metric of 0.9 and a training loss of below 0.2. We use the trained network to extract IARs from over 2300 images, covering six years of search coil magnetometer data measured at the Eskdalemuir Observatory. U-net can also automatically handle missing data or days without IARs, giving a null result as expected. This constitutes the first use of a neural network for pattern recognition of unstructured image data such as spectrograms containing IAR signals, though the method is applicable to other types of resonances or geophysical features in the time-frequency domain