© J. Kwak et al., Published by EDP Sciences 2024

1 Introduction

Pc1 pulsations, characterized as ultra-low frequency (ULF) geomagnetic waves (0.2~5 Hz), have been detected at low and mid-latitude ground stations. These waves typically originate from electromagnetic ion cyclotron (EMIC) waves generated by the temperature anisotropy of energetic ions (10–100 keV) (Cornwall, 1965). EMIC waves have been observed following the injection of energetic particles from the magnetotail and the enhancement of solar wind dynamic pressure (Usanova et al., 2008; Min et al., 2012; Saikin et al., 2015; Jun et al., 2019, 2021). Propagating along the magnetic field with left-handed polarization (LHP), EMIC waves precipitate energetic protons and relativistic electrons through resonant wave-particle interactions (e.g. Jacobs, 1970; Miyoshi et al., 2008). During the propagation, their mode changes to right-handed polarization (RHP) or linear polarization (LP) according to their dispersion relation (e.g. Jun et al., 2021).

Once EMIC (hereafter Pc1) waves (or pulsations) reach the ionosphere, the Alfvén mode EMIC waves undergo mode conversion to compressional (or fast) mode by ionospheric Hall currents. Yoshikawa and Itonaga (2000) suggested a theoretical model in which Hall conductance significantly contributes to converting shear Alfvén mode waves into the compressional mode in specific conditions, such as when Hall conductance overwhelms Pederson conductance (e.g. diffuse auroral regions). This model has been partially proved in a study using Swarm A in-situ data (i.e. Ivarsen et al., 2020). The mode-converted compressional waves can be trapped and propagate through the ionospheric waveguide from high to low latitude, known as Pc1 wave ducting (PWD) (Greifinger, 1972; Fraser, 1975; Fujita and Tamao, 1988; Kim et al., 2021). The ducted Pc1 waves have been observed by low-Earth orbit (LEO) satellites and ground magnetometers over wide latitudinal/longitudinal ranges (e.g. Kim et al., 2018). The wave intensity decreases as the waves propagate and experience strong attenuation, predominantly during the daytime (Althouse and Davis, 1978; Bortnik et al., 2008; Nomura et al., 2011; Bulusu et al., 2022).

The observations of the Pc1 pulsations on the ground are influenced by both geomagnetic and ionospheric conditions. Kawamura et al. (1981) investigated the Pc1 pulsations detected at various ground stations with different latitudes. They showed that the occurrence of these pulsations at mid-latitudes has an anti-correlation with electron density at the F2 layer depending on diurnal and seasonal variations of the density, although they reported that the peak occurrence is observed in equinoxes (November or February–March) rather than winter solstice (December) when the foF2 is at a minimum. Kim et al. (2020), however, showed a positive correlation between Pc1 wave intensity and topside electron density in case studies using data from Swarm-A and Swarm-C LEO satellites. They interpreted this difference as the wave leakage effect due to imperfect conductance was somewhat more important than the restrained ionospheric attenuation effect in the low electron density region. In a statistical study, Kim et al. (2021) presented that PWD mostly occurs during equinoxes and local summer. These results imply that low ionospheric electron density does not always accompany a high possibility of Pc1 pulsation propagation. As such, it is still a challenge to determine the apparent relationship between ionospheric conditions and wave occurrence.

On the other hand, the relationship between Pc1 pulsations and geomagnetic storm phases is more straightforward than their relationship with ionospheric conditions. Previous studies showed that Pc1 pulsations at the ground were typically observed during the recovery phase of geomagnetic storms (Kawamura et al., 1981; Kuwashima et al., 1981; Kim et al., 2020; Bulusu et al., 2022). Additionally, Pc1 waves at LEO and the inner magnetosphere are predominantly detected during the storm recovery phase as well (Engebretson et al., 2008; Fraser et al., 2010; Kim et al., 2018, 2021; Wang et al., 2021; Bulusu et al., 2022). Bortnik et al. (2008) conducted an eight-year investigation of Pc1 pulsations using a search-coil type ground magnetometer at Parkfield, California (L~1.77). Their findings revealed that EMIC waves observed at lower L-shells are associated with more intense geomagnetic storms, suggesting a shorter propagation path and less attenuation of the wave in the ionospheric waveguide. While the study focused on pulsations during geomagnetic storms, it did not compare with Pc1 pulsations during the non-storm period and their properties.

In a statistical analysis using a magnetometer located at Bohyun Mountain in Korea (BOH, L~1.34), Kim et al. (2020) investigated the dependence of wave occurrence rates on the Kp index, Dst index, and geomagnetic storm phases. They confirmed that Pc1 waves at mid-latitude particularly occur in equinoxes (March–April or August) and the post-midnight (01-03 magnetic local time (MLT)) sector, and are usually detected during the early recovery phase of the geomagnetic storm. Although Kim et al. (2020) provided comprehensive results for Pc1 waves at a mid-latitude, our understanding of the wave properties and how they differ between storm and non-storm periods remains limited.

In this study, we conduct a statistical analysis of Pc1 wave properties at mid-latitude (L~1.34) for storm and non-storm times, utilizing data from a BOH magnetometer spanning November 2009 to November 2021, covering solar cycle 24. Section 2 briefly describes the automatic wave detection algorithm used in this study. Section 3 presents the statistical results for detected waves and Section 4 discusses them. Finally, a summary and conclusions are provided in Section 5.

2 Data and methods

2.1 Instruments

We utilized magnetic field data measured by a BOH Magneto-Impedance (MI) sensor magnetometers, located at magnetic longitude (MLON): E200.8°, magnetic latitude (MLAT): N29.5° and L~1.34, for 12 years (November 2009 to November 2021). The MI sensor magnetometers have been measuring tri-axial magnetic fields with a 10 Hz sampling frequency since 2009 (Hwang et al., 2011). The magnetometers have been in operation for a total of 2931 days, with a data gap in 2016 due to equipment malfunction caused by unexpected lightning.

2.2 Wave detection method

We followed the automatic wave detection algorithm based on Bortnik et al. (2007) to detect Pc1 waves but different thresholds as Kim et al. (2020) and Kim et al. (2021). The wave detection process follows four steps.

Step 1. We conducted a Fast Fourier transform (FFT) with a window size of 1024 (~102 s) and a spacing of 100 time segments (~10 s), meaning that adjacent windows have approximately 90% overlap. Namely, we obtained 864 000/100 = 8640 Fourier spectra per day.

Step 2. We created a cross-covariance matrix Cⁱ(f) in a unit of “nT⁴”. In the process, the values from each component of signals are multiplied (for details of this process (please refer to formulas (1) and (2) in Bortnik et al. (2007)). Thus we obtained 512 (frequency) × 8640 (time segments) Cⁱ(f) values.

Step 3. We selected spectral peaks from signals. In this step, we calculated median values M(f) of Cⁱ(f) for the entire day for each frequency as the background. Then we obtained the ratio Rⁱ(f) = Cⁱ(f)/M(f) of them and took the logarithm of the ratio. At the end of this process, we obtained 512 (frequency) × 8640 (time segments) lg(Rⁱ(f)) values with no unit. Then, we applied a Savitzky-Golay (Savgol) smoothing filter to clarify the boundaries of spectral peaks. Used sliding window size and fitting polynomial function order of the smoothing filter are 51 (~0.5 Hz) and 2, respectively. For the Savgol filter, larger sliding window sizes tend to lower the spectral power values. The threshold A_th for Rⁱ(f) was set to 0.5 in this paper, so we chose signals as spectral peaks when they satisfied 3 (10^0.5~3) times than the background.

The following process is selecting appropriate spectral peaks. First, we excluded all signals (lg(Rⁱ(f))) that were not chosen as spectral peaks. For each time segment, if the number of spectral peaks is more than ten in the 0th~12th frequency bins (0~0.1 Hz), we also removed the first group of spectral peaks. In addition, we removed all signals for a single time segment if the signals of more than 100 frequency bins exceed A_th. We then applied a minimum width of spectral peaks as 11 frequency bins (~0.1 Hz). As a final process of step 3, we removed all signals beyond the bottom and top cutoff frequencies (0.3 and 4.8 Hz). At the end of this step, each time segment falls into one of the following statements. 1) No spectral peaks. 2) Only one group of spectral peaks with a bottom, top, and maximum peak value. 3) Two or more groups of spectral peaks with corresponding numbers of bottom, top, and maximum peak values. For case 3), only a group of spectral peaks with the lowest frequency survived, and others were ignored.

Step 4. We picked up wave events from spectral peaks. To judge the temporal continuity of individual spectral peaks and merge them into discrete events, we applied simple Boolean conditions for consecutive time segments i and i + 1 as follows (Bortnik et al., 2007).

(1)

As a result of the Boolean condition, only connected sets of time segments will remain, which is the “wave event”. We also considered whether an event (i.e. the filtered set of time segment groups) lasts at least a pre-defined duration. The minimum duration of waves T_th was set to 12-time segments (~2 min). Thus, we could obtain complete sets of wave events. As a final process in the whole wave detection algorithm, if the temporal separation of two relevant wave events was less than 30 time segments (~5 min), the two events were regarded as one wave event. Figure 1 shows an example explaining this study’s overall process for detecting Pc1 pulsations.

Figure 1 An example of steps for detecting a wave on 29 November 2011. (a) Variations of magnetic field for three axes of the magnetometer. (b) A power spectral density (PSD) graph expressed with a logarithmic value of the signal ratio. The ratio is calculated by Ri(f) = Ci(f)/M(f) in step 3. (c) A PSD graph after end of the steps. Savgol (Savitzky-Golay) filter is applied to the PSD along the frequency domain, and non-wave signals are removed. (d) A PSD graph only with a valid wave event. The upper, bottom and peak frequency of the identified wave is automatically recorded.

2.3 Calculation of polarization parameters from the detected wave events

For the wave events that are detected in Section 2.2, we could obtain wave polarization ellipticity for each time block using the method introduced by Bortnik et al. (2007). We used a band-integrated covariance matrix, S, which means summing up all three-dimensional covariance matrices (please refer to formulas (1) and (6) in Bortnik et al. (2007)) within the frequency corresponding to the wave signal for each time block. This band-integrated covariance matrix is the matrix aligned as a coordinate of our magnetometers (i.e. geomagnetically east, west, and the centre of the Earth).

By applying similarity transformation to the band-integrated covariance matrix S, we were able to rotate the coordinate to the principal coordinate, which is an aligned coordinate to the wave normal vector. The coordinate-aligned matrix, S′, contains both polarized and non-polarized parts. By subtracting the non-polarized part from the whole matrix S′, we finally acquired coordinated-aligned polarized matrix P. Calculating using P makes us determine wave polarization ellipticity and the sense of the polarization (the sign of the ellipticity).

(2)

For the meaning of the parameter β, we will continue in Section 3.3.

2.4 Separation of geomagnetic storm and non-storm periods

To divide between the storm period and the non-storm period, we set the minimum Dst index as −50 nT for a geomagnetic storm. We used the Dst index from the World Data Center for Geomagnetism, operated by Kyoto University. To define the geomagnetic storm phase, we carried out the following steps. A schematic example of these steps is shown in Figure 2. For the first step, we set the minimum Dst point as the boundary between the main phase and the recovery phase. Then, we traced back until the Dst reached 0 nT, and we defined this interval as the storm’s main phase. For the second step, starting again from the beginning of the main phase, we traced back until the Dst reached 0 nT once more. This interval was defined as the initial phase. On the other hand, we defined the period from the end of the main phase to the point where the Dst first reaches 80% of the minimum Dst point as the early recovery phase. The last step was defining the late recovery phase, which is the period from the end of the early recovery phase to the first point where the Dst recovers to 0 nT. The criteria described above are the same as those used by Kim et al. (2018) and Kim et al. (2020). We also classified them into three categories based on the storm classification by Loewe and Prölss (1997). Table 1 shows the criteria of the categories.

Figure 2 An example of defining geomagnetic storm phases. This storm was from 4 to 15 August 2010.

3 Results

3.1 Statistics of detected waves

Over the 12-year period from November 2009 to November 2021, Pc1 waves were detected on 38 days out of 2931 days, indicating an appearance of ~1.3%. Some waves were detected on the same day, resulting in 70 waves detected in 38 days. This is a relatively small amount considering that the instrument has a sufficient resolution of 1 pT/Hz. For instance, Bortnik et al. (2008) reported 8913 Pc1 wave events in a location with L = 1.77 for about 8 years observation period using a similar wave detecting technique. The difference in the number of events between Bortnik et al. (2008) and our result may be due to the noise level of the magnetometer. As mentioned in Section 2.2, we used the ratio Rⁱ(f) = Cⁱ(f)/M(f) to get the wave signal, which means high environmental noise can impede detecting the relatively weak wave signal. The noise level also affects to set the threshold of the ratio to determine the signal as wave events, as a result, filtering many waves which have similar power with the noise.

The total wave duration time was 40 800 s (about 28.3 h) and 22 out of 70 waves lasted longer than 10 min (~600 s). Details of the detected Pc1 pulsations are provided in Table 2. During the whole period, 151 geomagnetic storms (1289 days) with a minimum Dst index of less than −50 nT occurred. Of these days, 793 days were included in the storm days. A total of 41 wave events (23 days) out of 70 (38 days) were detected during the storms. Summarized information of Pc1 pulsations during the geomagnetic storm period is shown in Table 3.

3.2 Diurnal variations

Figure 3 shows diurnal variations of Pc1 pulsations for storm (3a) and non-storm (3b) periods. In this analysis, we show the occurrence rate for the number of wave time segments (~102 s) to consider the duration of waves. The most noticeable point is that wave events generally occurred during 19-06 local time (LT) and had a peak around 04 LT for both groups. This corresponds to previous studies using mid-latitude ground-based magnetometers (Kuwashima et al., 1981; Nomura et al., 2011; Kim et al., 2020; Bulusu et al., 2022).

Figure 3 Diurnal variations depending on local time (LT) of Pc1 pulsation occurrence rates (%). The occurrence rates are expressed in terms of event duration (time blocks) for (a) storm and (b) non-storm periods.

Also, Figure 3 indicates that the waves during the non-storm period have a little sharper peak in LT at 04 LT. The authors believe that the peak occurrence time indicates the lowest wave attenuation effect on the time section. A frequency analysis could help to interpret this result.

Figure 4 shows the peak frequency distributions by the number of wave time segments for storm period waves (4a) and non-storm period waves (4b) in the same way as Figure 3. The peak frequency in each LT is the mean of frequencies of all waves in the wave time segments belonging to the LT. In Figure 4a, most of the mean peak frequencies of the waves observed during the storm period have a frequency above 1.25 Hz and are distributed relatively broadly. Otherwise, those of the waves observed during the non-storm period (Fig. 4b) have a frequency below 1.25 Hz and are relatively even except for 19 LT, which means that the diversity of the generation areas of the EMIC waves, which are the source of these Pc1 waves, is somewhat limited.

Figure 4 Diurnal variations of the peak frequency depending on local time (LT) of Pc1 pulsation. The LT-mean peak frequencies are expressed in terms of event duration (time blocks) for (a) storm and (b) non-storm periods in the same way as the Figure 3.

Figure 5 describes how different the waves during storm period (5a) and non-storm period (5b) propagate through magnetic field lines and PWD. Because the comparably even spatial distribution of the wave generation regions means that they propagate similar distances before being detected at mid-latitude, the Pc1 wave occurrence diurnal variation during the non-storm period effectively displays how the wave attenuation effects change according to LT change. On the other hand, because the wave generation regions are much closer and diverse, the Pc1 wave occurrence diurnal variation during the storm period appears to be the result of being influenced simultaneously by wave propagation distance and wave attenuation effect. For example, some waves produced at closer locations to the Earth during the storm period can survive even after undergoing severe attenuation effects due to short propagation distance. Namely, the peak occurrence LT during the non-storm period seems more outstanding than that of the storm period waves in Figure 3.

Figure 5 A schematic illustration of EMIC wave propagation process during storm (a) and non-storm (b) periods. The left part (a) shows that EMIC waves generated during storm period have relatively diverse source regions, resulting in varying propagation distances undergoing ionospheric wave attenuation effect. On the other hand, the right part (b) demonstrates that EMIC waves produced during non-storm periods arise from more limited source regions, which allows consistent distances undergoing ionospheric wave attenuation effect.

3.3 Ellipticities

An ellipticity (β) shows the sense of rotation of a wave. If the sign of β is positive, the wave has a RHP, and a negative sign indicates a LHP. The ellipticity of Pc1 pulsations is a useful parameter that can help us estimate the location of the wave generation with respect to the observation point. Previous theoretical studies showed that as the wave propagates through the magnetosphere and ionosphere, the ellipticity changes from LHP to RHP (Greifinger, 1972; Fujita and Tamao, 1988). The polarization distributions investigated on ground-based magnetometers are somewhat complicated as they propagate in a compressional mode using the ionospheric duct so that they are converted in indeterminate ways. Thus, we believe that for some waves whose propagation distance is not long enough traces of mode conversion to LHP may be found.

Figure 6 shows a distribution of wave ellipticities for the storm (blue) and non-storm (red) periods. If we take the tangent value of the ellipticity (tan β), it can be expressed as a value between −1 and 1, representing complete LHP and RHP, respectively. We calculated the tan β of the wave time segments of ~102 s and assigned each segment to one of the 200 bins of tan β from −1 to 1. The occurrence rates were obtained by dividing these numbers by the total number of time segments. In this paper, we call the waves whose tan β is between −0.25 and 0.25 LP. The result shows both storm-related Pc1 pulsations and non-storm-related Pc1 pulsations mostly have LP, while LHP waves were found more frequently than RHP waves. Also, completely linearly polarized waves (i.e. tan β~0) are rarely distributed for both groups. Furthermore, storm-related pulsations have more LHP from −0.75 to −0.25, while the tan β of non-storm-related pulsations is concentrated on LP.

Figure 6 Occurrence rates (%) of Pc1 pulsations during the storm (blue) and non-storm (red) periods depend on ellipticity of the pulsations. The ellipticities are tangent values (tan β) and are divided into 200 bins from −1 to 1. The occurrence rates were obtained by dividing the number of time segments which belong to each of ellipticity bins into the total number of time segments of all valid wave events and multiplying by 100 to gain per cent values.

3.4 Wave frequencies

Figure 7 shows the durations and frequencies of Pc1 pulsations related to the storm activity. The frequencies shown in Figure 7 are the average peak frequencies of each wave event. In the figure, Pc1 pulsations with durations exceeding 1000 s (about 17 min) have a frequency of around 1 Hz. This suggests that waves with a frequency of around 1 Hz are relatively stable and can be observed for a long time, even at low-latitude grounds. The contrast between the two groups seems clear. The storm-related Pc1 pulsations have a wide range of frequencies from 0.4 to 2.5 Hz, while those of non-storm-related Pc1 pulsations are concentrated in the range of 0.6 to 1.0 Hz with a few exceptions. This result is consistent with that of Section 3.3, which shows that the ellipticity of Pc1 is more concentrated within narrow values in non-storm-related groups. The relationship between wave ellipticity and frequency can be more clearly seen when analyzed together, as shown in Figure 8.

Figure 7 Peak frequency (Hz) depends on duration time (s) of the Pc1 pulsations during storm (blue) and non-storm (red) periods.

Figure 8 Heat maps of peak frequency (Hz) and ellipticity (tan β) of the Pc1 pulsations during storm (a) and non-storm (b) periods. The occurrence ratio of a grid that presents maximum occurrence rate is set as 1 and others are normalized from the ratio to the maximum rate. Top-right texts indicate Pearson correlation coefficients between ellipticity and peak frequency.

Figure 8a and 8b show the occurrence rates of waves distributed by their ellipticities and frequencies during storm and non-storm periods, respectively. Here we created grids with 30 equally divided bins of tan β from −1 to 1 and frequencies from 0.0 to 3.0 Hz and put occurrence rates normalized by a maximum value in each bin. Figure 8a shows that storm time LHP pulsations with extreme tan β of −0.75~−0.25 from Figure 6 also have relatively high frequencies of 2~2.5 Hz. Furthermore, frequencies of storm-related Pc1 pulsations have a meaningful correlation with their ellipticities. The Pearson correlation coefficient is −0.52, indicating that as the storm time wave frequency increases, they tend to exhibit LHP. On the other hand, Figure 8b shows that most non-storm-related waves are concentrated in the range of 0.6~1 Hz, including those with a tan β range of −0.25~0.25 in Figure 6. Also, we found some of the non-storm-related waves are located top left corner, indicating that high-frequency wave has a tendency to LHP, which is similar to storm-related Pc1 pulsations. This can be explained that they were generated when the plasmasphere was shrunk by phenomena other than geomagnetic storms, such as weak storms, geomagnetic substorms, or solar wind pressure pulses (Bortnik et al., 2008).

3.5 Delay time and storm intensity

Figure 9a and 9b show the time delay T_d (days) from the start of the geomagnetic storm’s initial phase to the detection time of Pc1 waves and peak frequency w_p (Hz) of each wave event. They both are plotted against the maximum storm intensity I_storm (|Dst|, nT). First, from Figure 9b, we can confirm our idea that as the I_storm increases, the frequency of waves also tends to rise. The Pearson correlation coefficient between these two parameters is 0.76, and the averages of w_p gradually increase from moderate to severe storms 0.73, 1.48, and 1.95 Hz, respectively. On the other hand, the Pearson correlation coefficient between T_d and I_storm is 0.21, indicating a relatively weak relationship. However, we found the tendency that the Pc1 pulsations are detected ten days after the start of the storm’s initial phase being associated with storms with |Dst| > 100 nT. This is consistent with the previous result from Bortnik et al. (2008) which showed that relatively high possibility of wave occurrence due to strong storm intensity.

Figure 9 Scatter plots of (a) the time delay (Td, days) between the start of the initial phase of related storms and Pc1 pulsation occurrence and (b) peak frequency (wp, Hz) depending on the storm intensity (Istorm, |Dst|). The texts in the top-right corner present Pearson correlation coefficients between Td and Istorm & wp and Istorm.

4 Discussion

In this study, we attempt to identify differences in Pc1 pulsation’s characteristics which might be generated during the storm and non-storm periods. First, the diurnal variations at the mid-latitude ground station shown in Figure 3 show consistent features to those reported by Kuwashima et al. (1981), Bortnik et al. (2008), Nomura et al. (2011), and Kim et al. (2020). According to Althouse and Davis (1978), the attenuation of Pc1 wave power is severe during the daytime. Kuwashima et al. (1981) showed that the occurrence time of Pc1 pulsations detected at a high-latitude station (SYO; Syowa, L~6.32) has a peak around 14 LT, the same as the peak occurrence time of EMIC wave at a geosynchronous orbit (Clausen et al., 2011). Their results say EMIC waves occurrence distribution does not change much as they propagate from the magnetosphere to the high-latitude ionosphere. However, the occurrence changes dramatically as they propagate through PWD, which shows wave occurrence peaks at dusk and dawn. Namely, the wave power attenuation seems more severe when the wave propagates through the ionospheric duct compared to propagation through magnetic field lines.

In addition, Figure 3 shows the diurnal variation of occurrence of mid-latitude Pc1 pulsations sub-categorized into storm and non-storm periods. Our results show that Pc1 pulsations related to the non-storm period have a sharper LT peak on 04 LT. In order to interpret the result, we need to look into the frequency of the waves.

The frequency of Pc1 pulsation can be a significant clue of its spatial origin because EMIC wave frequency is closely related to the ion cyclotron frequency in the magnetosphere, which is expressed as qB/m and it keeps its frequency as it propagates. Here, q is the electric charge of the ion, B is the magnetic field strength, and m is the ion’s mass. Among them, q and m are determined by the species of ion, so that the cyclotron frequency is only changed by magnetic field strength which is expressed as below (McIlwain, 1961):

(3)

Here, B_E is the magnetic field strength of magnetic equator ground, λ is MLAT, and L is the McIlwain parameter expressed as . Here, R_E is Earth’s radius, and r is the radius of the point in the same unit of R_E. In this expression, we can consider λ to 0 because the EMIC wave is known to be mostly generated at the magnetic equatorial plane. Then, expression (2) can be simplified as below:

(4)

As shown in the above expression, at the magnetic equatorial plane, B depends only on the radius r. Thus it decreases with the increase of radial distance from Earth’s magnetic field center.

When we consider Figures 3, 4, and 7 together, we are finally able to answer the question of sharper LT peak in non-storm period Pc1 waves. In Figure 4, most wave frequencies detected during the non-storm period are relatively even, which means more still and immobile spatial generation regions. Because of the even spatial distribution, wave occurrence variation during the non-storm period explicitly expresses the effect of wave attenuation. As a result, we believe non-storm period wave occurrence variation at mid-latitude can well represent the amount of wave attenuation effect. On the other hand, during the storm period, wave occurrence variation does not represent wave attenuation because the waves are generated at more various L-shells, and therefore in some cases, short propagation distance can compensate for the attenuation effect (Bortnik et al., 2008).

The reason why it is difficult to find complete LP (i.e. tan β~0) in Figures 6 and 8 seems to be because the wave polarizations are expressed by summing up the entire wave width in this paper. Nomura et al. (2011) investigated mid-latitude magnetometer (MSR; Moshiri, L~1.5) data for two years and analyzed their polarization parameters. According to the paper, polarization (i.e. tan β in this paper) varies from the bottom to the top frequencies of the pulsation for the same time segment. In Figure 3 of the paper, for most time segments of the wave detected on 5 November 2007, the polarization sense changes around from −0.25 to 0.25 and seems biased to negative values, which means LHP. Ellipticity shown in Figures 6 and 8 in this paper is the mean value of ellipticities for each time segment. So, the scarcity of completely linearly polarized waves (i.e. tan β~0) could be explained if the ellipticity is usually biased to one side for each time segment. Namely, perfect LP is difficult to obtain unless wave ellipticities are evenly polarized throughout all frequency bands of the time segment of the wave.

In Figures 8a and 9b, peak frequencies of storm-related Pc1 pulsations show correlations with their ellipticities and the storm intensity. Their Pearson correlation coefficients were −0.52 and 0.76, respectively. The well-known Pc1 pulsation propagation mechanism can explain these results. According to Heacock and Kivinen (1972) and Bortnik et al. (2008), as the storm intensity increases, the plasmasphere is shrunk. It means as the L-shell of the plasmapause decreases, EMIC wave frequency tends to increase. And occurrence rate of LHP waves also increases as wave propagation distance decreases.

This is because mode conversion from LHP to RHP can be expected through wave propagation not only along the magnetic field but also using PWD (Greifinger, 1972; Fujita and Tamao, 1988). Although the high-latitude wave ellipticity distribution result shows the distribution already concentrated on LP and slightly biased to LHP (Kwon et al., 2020), the authors show and believe that some of the waves that were generated at low L-shell can keep their LHP even if they propagate to mid-latitude. Figure 10 shows this physical mechanism simply. Figure 16 of Kuwashima et al. (1981) partially suggests this process during geomagnetic storms.

Figure 10 A schematic process indicating how geomagnetic storm affects the occurrence of Pc1 pulsations and their parameters.

According to a previous study by Bortnik et al. (2008), compared to quiet time Pc1 distribution, during moderate storm period, 2~3 times more pulsations were detected within 2~4 following days after the minimum Dst, and during the strong and the severe storm period, 4~5 times more pulsations were detected in 2~7 following days after the minimum Dst. In Figure 9a, it is obvious that Pc1 pulsations detected after ten days from the storm’s initial phase were generated during the strong and severe storms of |Dst| > 100 nT. Those results partially show that severe geomagnetic storms usually accompany a long recovery phase.

However, the intensity of the geomagnetic storm is not the only condition for the duration of the storm’s recovery phase. Miyoshi and Kataoka (2005) reported corotating interaction regions (CIR)-driven storms usually accompany long recovery phases due to continuous injections of hot ions from plasma sheets. Also, high-speed solar wind with southward interplanetary magnetic field (IMF)-Bz gives rise to large flux enhancement of relativistic electrons through whistler mode wave excitation, which allows the recovery phase of the storm maintained (e.g. Miyoshi et al., 2013). These conditions can have a combined effect for the duration of the storm’s recovery phase and Pc1 wave occurrence on stormtime.

5 Summary and conclusion

From the MI magnetometer at the BOH ground station of L~1.34, we obtained 10 Hz magnetic pulsation data and identified a total of 70 Pc1 waves using an automatic wave detection algorithm for 12 years from November 2009 to November 2021. We also applied Dst criteria (|| > 50 nT) to investigate them for storm and non-storm periods. We obtained 41 Pc1 pulsations during the storm period and 29 Pc1 pulsations during the non-storm period. This paper compared their diurnal occurrence variation, peak frequency, duration, and ellipticity. For the storm-related Pc1 pulsations, we also analyzed delayed time (T_d) since the storm initiation and peak frequency depending on the related storm intensity.

First, we found that Pc1 pulsations detected during storm and non-storm periods have a peak of occurrence time centred at 04 LT. Among the two periods, the diurnal variation of the Pc1 pulsations that occur during the non-storm period has a sharper peak because the wave power attenuation effect is more pronounced due to the relatively stable wave generation regions.

Also, we found that LHP (tan β < −0.25) is mostly shown in storm-related pulsations while mainly the waves have LP (tan β < |0.25|) during both periods. Moreover, storm-related pulsations cover a relatively broader frequency band, and their peak frequency and ellipticity have a relationship with a Pearson correlation coefficient of −0.52, indicating that waves with a higher frequency probably tend to have likely more LHP. On the other hand, Pc1 pulsations that occur during non-storm periods are shown to be concentrated on 0.6~1 Hz, and their polarization senses are more concentrated on LP.

For the pulsations during the storm period, the frequencies of the waves increase with storm intensity whose correlation coefficient is 0.76. In addition, all waves detected more than ten days after the storm’s initial phase were found only during the strong and the severe storm period of || > 100 nT. Our results are consistent with previous theoretical and experimental statistical studies and are physically understandable through the propagation of EMIC waves from their generation locations in the magnetosphere to observable mid-latitude regions in the ground station.

Acknowledgments

This work was supported by basic research funding from the Korea Astronomy and Space Science Institute (KASI) and by the UST Young Scientist + Research Program 2023 through the University of Science and Technology (No. 2023YS19). This research was also supported by the Challengeable Future Defense Technology Research and Development Program through the Agency for Defense Development (ADD) funded by the Defense Acquisition Program Administration (DAPA) in 2023 (No. 912914601). The editor thanks Vyacheslav Pilipenko and an anonymous reviewer for their assistance in evaluating this paper.

Open research

The data for this research were provided by the Solar and Space Weather Research Group in the KASI and by the Space Weather Big Data Network System, which is supported by the “Next Generation Space Weather Observation Network” project of the KASI. The data is available through the Korea Space Weather Research Center website (https://kswrc.kasi.re.kr/en/).

References

All Tables

All Figures

Figure 1 An example of steps for detecting a wave on 29 November 2011. (a) Variations of magnetic field for three axes of the magnetometer. (b) A power spectral density (PSD) graph expressed with a logarithmic value of the signal ratio. The ratio is calculated by Ri(f) = Ci(f)/M(f) in step 3. (c) A PSD graph after end of the steps. Savgol (Savitzky-Golay) filter is applied to the PSD along the frequency domain, and non-wave signals are removed. (d) A PSD graph only with a valid wave event. The upper, bottom and peak frequency of the identified wave is automatically recorded.

In the text

	Figure 2 An example of defining geomagnetic storm phases. This storm was from 4 to 15 August 2010.
In the text

	Figure 3 Diurnal variations depending on local time (LT) of Pc1 pulsation occurrence rates (%). The occurrence rates are expressed in terms of event duration (time blocks) for (a) storm and (b) non-storm periods.
In the text

	Figure 4 Diurnal variations of the peak frequency depending on local time (LT) of Pc1 pulsation. The LT-mean peak frequencies are expressed in terms of event duration (time blocks) for (a) storm and (b) non-storm periods in the same way as the Figure 3.
In the text

Figure 5 A schematic illustration of EMIC wave propagation process during storm (a) and non-storm (b) periods. The left part (a) shows that EMIC waves generated during storm period have relatively diverse source regions, resulting in varying propagation distances undergoing ionospheric wave attenuation effect. On the other hand, the right part (b) demonstrates that EMIC waves produced during non-storm periods arise from more limited source regions, which allows consistent distances undergoing ionospheric wave attenuation effect.

In the text

Figure 6 Occurrence rates (%) of Pc1 pulsations during the storm (blue) and non-storm (red) periods depend on ellipticity of the pulsations. The ellipticities are tangent values (tan β) and are divided into 200 bins from −1 to 1. The occurrence rates were obtained by dividing the number of time segments which belong to each of ellipticity bins into the total number of time segments of all valid wave events and multiplying by 100 to gain per cent values.

In the text

	Figure 7 Peak frequency (Hz) depends on duration time (s) of the Pc1 pulsations during storm (blue) and non-storm (red) periods.
In the text

	Figure 8 Heat maps of peak frequency (Hz) and ellipticity (tan β) of the Pc1 pulsations during storm (a) and non-storm (b) periods. The occurrence ratio of a grid that presents maximum occurrence rate is set as 1 and others are normalized from the ratio to the maximum rate. Top-right texts indicate Pearson correlation coefficients between ellipticity and peak frequency.
In the text

	Figure 9 Scatter plots of (a) the time delay (Td, days) between the start of the initial phase of related storms and Pc1 pulsation occurrence and (b) peak frequency (wp, Hz) depending on the storm intensity (Istorm, |Dst|). The texts in the top-right corner present Pearson correlation coefficients between Td and Istorm & wp and Istorm.
In the text

	Figure 10 A schematic process indicating how geomagnetic storm affects the occurrence of Pc1 pulsations and their parameters.
In the text