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 Magnetic Anomaly Detection (MAD) is an application in which airborne magnetometers are used to detect small magnetic variations against the Earth's background magnetic field. This technique is used in aeromagnetic surveys, to detect mineral deposits and in applications such as antisubmarine warfare. The magnetic signals of interest typically have periods of 1–100 s and amplitudes of 0.001–1 nT. In order to isolate and detect such signals, all other sources of magnetic noise in this frequency band must be modeled, or measured, and mitigated. Despite reduction of many error sources for MAD, a limiting factor remains: the small-amplitude variations caused by geomagnetic pulsations. In the frequency band of interest for MAD (0.01–1 Hz), Pc 3 pulsations represent a significant error source. These continuous pulsations are apparent as pulse trains in magnetic time series for intervals as long as several minutes. These pulsations arise from resonant oscillations in the dayside magnetosphere driven by the solar wind. Such fluctuations may be observed in GPS total electron content (TEC) observations. In this paper, analyses are conducted using 1 Hz data available from GPS reference stations and colocated magnetometers in Canada and Australia. Relative TEC variations are derived from the precise dual-frequency GPS carrier phase observations and band-pass-filtered. Dominant TEC variations at Pc 3 frequencies are then correlated with local magnetic time series from the ground reference. Results are analyzed as a function of solar wind parameters, and the potential for exploiting standalone GPS to derive Pc 3 pulsation indices is investigated.
 Pc 3 pulsations arise from resonant oscillations in the dayside magnetosphere driven by the solar wind [Le and Russell, 1994]. Figure 1 shows a schematic representation of the Earth's magnetosphere and the interplanetary magnetic field (IMF) of solar origin. This magnetic field is essentially “frozen-in” the solar wind plasma and convected earthward. As the sun rotates, these field lines bend at an angle with respect to the Sun-Earth line. This angle is referred to as the cone angle.
 A bow shock forms in the supersonic solar wind at the magnetopause boundary. Ions of solar wind origin are accelerated and reflected from the magnetopause back along IMF field lines in this bow shock region. In the morning to noon local time sector (where the IMF is generally perpendicular to the magnetopause), backstreaming ions travel upstream and are subsequently convected downstream in the solar wind toward the dawn magnetopause [Le and Russell, 1994]. An ion foreshock forms in the morning sector and ULF waves are generated in this region through resonant ion instabilities [Russell, 1994]. Associated pressure variations at the magnetopause launch magnetohydrodynamic (MHD) waves in the Earth's magnetosphere, which couple to the ionosphere electrojets and cause fluctuations in the horizontal component of ground-based magnetic field observations [Poole and Sutcliffe, 1987].
 If the MHD wave contains a compressional component, plasma density variations will occur. These effects would be observed as variations in total electron content measured by a GPS receiver. By forming a linear combination of the GPS L1 and L2 carrier phase observations for a given satellite, a time series of precise relative TEC observations can be derived:
where f is the carrier frequency, λ is the wavelength, and ϕ is the carrier phase in cycles. The subscripts 1 and 2 indicate the L1 and L2 frequencies, respectively. The carrier phase measurements are precise but include integer ambiguity biases. Equation (1) therefore provides a precise measure of relative TEC observations. In this paper, such observations are compared with ground-based magnetometer measurements to determine the correlation of TEC variations with geomagnetic pulsations.
2. Theory of Pc 3 Pulsations
 Properties of MHD waves can be derived by solving Maxwell's equations, combined with Ohms' law and the fluid equations (continuity equation and equation of motion). Such waves travel into the Earth's ionosphere, couple with the electrojet currents, and cause ground-based magnetic field perturbations. Solutions for MHD waves include three modes: slow, intermediate and fast. Phase velocity for the intermediate mode is given as follows [Park, 1991]:
where VA is the Alfvén velocity given by
θ is the angle between the wave vector and the ambient magnetic field (B0) and ρ0 is the background plasma density. Shear (intermediate) Alfvén waves travel along the Earth's magnetic field lines and do not have a compressional component. Alternatively, the fast (+) and slow (−) mode phase velocity is given as [Park, 1991]
where Cs is the speed of sound. These waves are compressive modes and change fluid/plasma properties as they travel, resulting in TEC variations which may be observed in GPS observations. Pc 3 pulsations are often associated with fast mode compressional waves [Anderson, 1994] and potential therefore exists to detect Pc 3 pulsations in GPS TEC measurements.
 It has been observed that a small cone angle is associated with excitation of Pc 3 pulsations [Engebretson et al., 1991]. Compressional waves generated in the foreshock are more easily coupled to the magnetosphere as the IMF becomes more closely aligned with the Earth-Sun line [Greenstadt and Olson, 1977]. A simple empirical relationship between the interplanetary magnetic field strength (BIMF) and the pulsation frequency has been derived [Hoppe and Russell, 1982]:
where BIMF is the interplanetary magnetic field in nT.
 Variations in TEC during intervals of Pc 3 pulsation activity have been observed using geostationary satellite ATS-6 signals. Relative variations of 4 parts in 104 were observed by Davies and Hartmann  and Okuzawa and Davies . In these studies there was evidence of some correlation with ground-based observations of geomagnetic pulsations with periods of 50 s.
 These findings suggest the potential of exploiting GPS observations to measure such TEC variations. Challenges exist in processing the GPS data, however. The GPS satellite-receiver line-of-sight moves horizontally through the ionosphere at speeds of up to 150 m/s, such that successive TEC measurements represent spatial as well as temporal variations in TEC. But given the large-scale generation of Pc 3 pulsations, it is expected that variations in TEC are spatially coherent across several degrees of longitude. The frequency of pulsation can also vary with latitude, due to a dependence of standing wave properties on magnetic field line length. In order to estimate the dominant ionosphere pulsation signature in the vicinity of a given GPS reference station, TEC observations are selected for high-elevation satellites with ionospheric pierce points within a few degrees latitude of the station.
3. Results and Analysis
 Results of recent studies [Skone and Nicholson, 2006] demonstrate that there may be limited periods, under ideal conditions, during which TEC variations detected using GPS are well correlated with variations in the horizontal magnetic field. In such cases the frequency of TEC variations correspond well with frequencies predicted from values of the interplanetary magnetic field using equation (5). Overall, however, the feasibility of using GPS to directly remove geomagnetic noise (using coherence processing) was determined to be limited, as the relative phase (and frequency) of the magnetic time series slowly shifts over time with respect to the TEC time series, making it nearly impossible to use the TEC information for direct mitigation of geomagnetic noise in MAD.
 It may be possible though to identify the local level of pulsation activity, in a statistical sense, from the GPS observations. The potential derivation of a Pc 3 index from GPS observations is investigated in this paper. Two studies are presented here: (1) analysis for two cases of ideal solar conditions (low solar activity and low cone angle) at Churchill during January 2006, and (2) general analysis of Pc 3 index derivation for a location near Canberra, Australia.
3.1. Churchill Canada Study
 A one-month period of the ACE satellite solar wind data has been analyzed to determine intervals of low cone angle, conditions conducive to the generation of compressional waves associated with Pc 3 pulsations. The cone angle is computed from the ACE data as cos−1(Bx/B) where Bx is the x component of the interplanetary magnetic field in GSM coordinates and B is the total magnetic field. Figure 2 shows the observed cone angle (angle of IMF with respect to Sun-Earth line) for January 2006. The periods 15–16 January and 21–22 January 2006 have been chosen for detailed analysis due to the low cone angles during these periods. It is expected that during these periods Pc 3 effects will be observed, with compressional waves causing corresponding variations in electron density (and TEC). GPS and magnetic data are obtained for Churchill, Canada (58.759°N, 94.089°W) at a 1 Hz observation rate. The TEC and magnetic time series are filtered in order to consider only frequencies in the range .01 to .20 Hz. This band is studied in order to investigate effects for the dominant period typically observed in the TEC oscillations for Pc 3 events. Filtering techniques are implemented using Matlab™ signal processing tools, in particular the built-in Butterworth filter function.
 Raw data were obtained from a ground-based magnetometer (part of the Carisma array operated by University of Alberta) and the horizontal magnetic field observations were computed. The 1 Hz GPS observations were also obtained from NRCan GPS reference station Churchill. TEC series were computed from this data using TECMODEL software [Skone, 2006] and TEC values were limited to elevation angles greater than 40 degrees and with pierce points within two degrees latitude of the Churchill site. This was done to limit observations to reflect local conditions, and to represent pulsations along magnetic field lines (and the associated pulsation frequencies) at the same latitude as the magnetometer. Both the magnetic and TEC times series were filtered in the range 0.01 to 0.20 Hz.
Figure 3 shows the filtered magnetic and TEC time series at Churchill for 15–16 January 2006. Note that different colors in the TEC plot represent observations from different satellites. There is some consistency in terms of the presence of larger-amplitude TEC variations during periods where larger amplitude magnetic variations occur.
 Similarly Figure 4 shows the filtered magnetic and TEC time series at Churchill for 21–22 January 2006. Again it is observed that there is a general positive correlation, in terms of larger-amplitude magnetic and TEC variations being observed simultaneously. In order to better examine the correlation in amplitudes of magnetic and TEC variations, further analysis is conducted. Average amplitudes are computed for 5-min windows for both the magnetic and TEC time series. In the case of the GPS TEC series, these averages may include TEC values from multiple satellites at the same epoch, if more than one satellite meets the selection criteria at the given epoch.
 Results are shown in Figure 5 for the two selected January 2006 intervals. For both periods there is general consistency between the magnetic and GPS 5-min Pc 3 indices. There are periods, however, during which there is poor correlation between the magnetic and TEC indices. For example, early on 15 January (prior to 0500 UT) there is a high TEC index but no significant magnetic variations. Later in the day on 16 January (after 1430 UT) there is very poor correlation between the magnetic and TEC indices. The TEC index fails to reflect the high level of pulsation activity observed in the magnetometer data. From the results shown here, however, it can be inferred that such GPS TEC indices do have potential application in detecting the presence of Pc 3 pulsation effects in magnetic data.
3.2. Canberra Australia Study
 The Australian government operates an ionospheric predictions and monitoring service for various types of ionospheric phenomena (http://www.ips.gov.au). Owing to a need within the Australian aeromagnetic survey community, this service includes Pc 3 pulsation indices. High-frequency magnetometer data are processed for five locations in Australia and one in Tasmania to compute 20-min RMS values for the horizontal magnetic field variations. Observations are first band-pass-filtered to exclude all periods outside the range 10–45 s. The Australian Space Agency notes that these indices are well correlated with rejection of high-resolution aeromagnetic survey flight data and therefore are a reliable indicator of local pulsation effects. The frequencies included in the Australian processing (0.022 to 0.1 Hz) are close to the dominant frequency observed in GPS TEC variations associated with Pc 3 activity (0.02 Hz from Skone and Nicholson ). It is therefore expected that variations in GPS TEC time series from Australian sites would be positively correlated with the Pc 3 indices.
 In this investigation GPS data from Tidbinbilla (TIDB) and Pc 3 indices for Canberra are analyzed. Canberra is located in the southeast part of Australia. Publicly available high-rate GPS data are available via the International GNSS Service (IGS) for station TIDB (35.398°S, 148.979°E). This station is located approximately 43 km southwest of Canberra. For the purposes of this investigation, it is assumed that TIDB will observe dominant ionospheric effects in the vicinity of Canberra.
 The GPS data are processed to derive TEC series for the frequency range 0.02 to 0.1 Hz. Similar to the previous section, only observations above 40 degrees elevation angle are considered, and ionospheric pierce points of the observations must be within two degrees of the TIDB location. Multiple days from October 2007 have been analyzed. Results are shown here for 25 and 27 October 2007.
Figure 6 shows the Canberra Pc 3 indices and TIDB TEC variations for 25 October 2007. Similar to the TEC processing for Churchill (previous section), TEC series for different satellites are plotted in different colors and combined 5-min average amplitudes of the TEC variations are also computed. There are periods with larger pulsation indices prior to 0600 UT and also after 1800 UT at Canberra. At TIDB there are larger-amplitude TEC variations observed during these periods. This indicates that the GPS TEC series do provide some measure of the Pc 3 activity, although there is not a direct one-to-one correlation with the Pc 3 indices.
Figure 7 shows the Canberra Pc 3 indices and TIDB TEC variations for 27 October 2007. For the periods 0000–0600 UT and 1000–1130 UT there are larger Pc 3 indices and larger GPS TEC variations observed. This again is a general correlation, which would not allow for direct geomagnetic noise reduction using coherence processing with GPS TEC times series, but results are encouraging for the potential use of airborne GPS observations in a statistical sense to measure and detect Pc 3 pulsation activity in real time for MAD applications. Overall, results for the Australian analysis are similar to those for Canadian site Churchill.
 A novel method for identifying the presence of ULF pulsations using GPS TEC observations has been investigated. This work has focused on Pc 3 pulsation events with the practical consideration of reducing geomagnetic noise for MAD. Ground-based magnetometer data, Pc 3 indices, and GPS TEC observations from Churchill, Canada and Canberra, Australia have been analyzed to determine whether a well defined statistical relationship exists between magnetic and TEC variations. Preliminary results indicate that amplitudes of the magnetic and TEC variations tend to vary in a similar manner. This may allow the use of TEC information alone to at least identify the presence of Pc 3 pulsations, in the form of an index. However, there were intervals during which high TEC indices occurred when no Pc 3 activity was present. In such cases good magnetic data might be rejected based on the TEC information. On the basis of these results, it is recommended that such GPS-TEC statistical indicators be used only as an approximate measure of the level of pulsation effects. Results are encouraging, however, and with continued refinements of the processing and analysis methods potential exists to derive new Pc 3 indices for aeromagnetic survey operations.