the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Feb 2025
An analysis of the SAMA’s interference on Pc3 pulsations using data from conjugate stations
Abstract. In this study, we analyzed Pc3 pulsation data from pairs of conjugate stations located at low latitudes (L-shell <2). One pair of stations is situated in the Americas under the influence area of the South Atlantic Magnetic Anomaly (SAMA). As a reference, we selected a pair of stations located at a distant longitude in the Asia-Pacific region. This choice of regions facilitates meaningful comparisons. We conducted a signal spectral analysis using the Fast Fourier Transform (FFT), Continuous Wavelet Transform (CWT), and Wavelet Coherence to characterize the dynamics of Pc3 pulsations at conjugate stations in the time-frequency domain. The Pc3 pulsations exhibited similar waveforms and occurred simultaneously at the conjugate stations in both regions. Spectral power plots and wavelet scalograms revealed notable similarities between the stations. However, we observed an increase in pulsation amplitude and wavelet coefficients at the station located near the SAMA center. Additionally, high coherence and in-phase signals were observed in the Asia-Pacific region, while moderate to high coherence signals were observed at the station in the SAMA region. We suggest that the observed differences at the SAMA station may result from the unique characteristics of the region. The presence of the SAMA facilitates the precipitation of energetic particles from the inner radiation belt, thereby enhancing ionospheric conductivity.
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RC1: 'Comment on egusphere-2025-794', Anonymous Referee #1, 25 Apr 2025
This is an interesting study aimed to assess the impact of the South Atlantic Magnetic Anomaly (SAMA) on the Pc3 pulsations in the Earth’s magnetic field. For this, authors studied the Pc3 signal features in the magnetic data from two pairs of conjugate (i.e. located in the Northern and Southern magnetic hemispheres symmetrically with respect to the magnetic equator) ground-based stations in order to compare the pulsation dynamics within the SAMA area with the one outside it.
The authors have examined not only spectral characteristics of the Pc3 pulsations but also the coherence features. The capabilities of the group of wavelet-based techniques are well demonstrated as applied to the data analysis. The results show the difference in the Pc3 pulsation patterns inside and outside the SAMA region, indicating its influence on the wave processes in the Earth’s magnetosphere.
All in all, this is the first comparative analysis performed for geomagneticdatasets from conjugate stations. Moreover, this is the one of the studies that present a valuable display of the interaction of the Earth’s core magnetic field and the magnetospheric wave processes and, furthermore, can bring to light the details of the nature of both internal and external magnetic field sources. The manuscript is definitely worth publishing in the GI journal.
The presentation of the results is good, but there are some issues to improve.
To me, in Section 3.1, such detailed description of the basics of spectral analysis is excessive, as well as the well-known wavelet functions and their equations. I recommend some reduction of this theoretical part, so that it doesn't look like a lecture note on mathematics. Also please check the period axis labels in wavelet coherence plots in Fig. 6.
Citation: https://doi.org/10.5194/egusphere-2025-794-RC1 -
AC1: 'Reply on RC1', Edwin Camacho, 25 Apr 2025
We thank the reviewer for their positive feedback and for highlighting the novelty of using conjugate stations and wavelet techniques to study the impact of SAMA on Pc3 pulsations.
Below we address the specific comment made by the reviewer:Comment #1:
To me, in Section 3.1, such detailed description of the basics of spectral analysis is excessive, as well as the well-known wavelet functions and their equations. I recommend some reduction of this theoretical part, so that it doesn't look like a lecture note on mathematics.Response: We agree with the comment and will summarize the basic concepts more concisely, removing some of the mathematical expressions and sentences that are already well known in the field.
Comment #2:
Also please check the period axis labels in wavelet coherence plots in Fig. 6.Response: Thank you for pointing this out. Figure 6 wil be updated to correctly reflect the period values and improve the clarity of the graphs.
We will incorporate the reviewer’s comments during the final revision of the manuscript.
Sincerely,
Edwin CamachoCitation: https://doi.org/10.5194/egusphere-2025-794-AC1
-
AC1: 'Reply on RC1', Edwin Camacho, 25 Apr 2025
-
RC2: 'Comment on egusphere-2025-794', Anonymous Referee #2, 11 Jun 2025
In the manuscript "An analysis of the SAMA’s interference on Pc3 pulsations using data from conjugate stations" Authors analyse three hours of synchronuous data from four observatories in Brazil, Puerto Rico, Japan, and Australia for pc3 pulsations. They find synchronuous coherent events in the according frequency band with enhanced amplitudes in Brazil which they interprete as caused by the South Atlantic Magnetic Anomaly (SAMA).
Whereas the applied analysis methods and the presentation of the background and the research itself are fine, there are serious issues with the significance of the results and with the soundness of the research concept. As to the first, it is of course not serious to make general statements about the SAMA's influence on pulsations based on such a short data set - there is no prove that it is representative and not just by chance that intensities at one station are larger that at some other. As to the latter, it is misleading to include the concept of conjugate points to such an analysis in such a simplistic way. It certainly is intriguing to investigate if an anomaly of the main magnetic field has a visible impact on some field variations, but this should be done in a way that is not self-contradictory. The problem is that the concept of conjugate points (as Authors describe correctly) is based on the footpoints of the same dipole field line. However, the essence of SAMA is that there are significant deviations from the dipole approximation in this region and field lines are not dipole-like. I am afraid that it is impossible to find footpoints of the same field line with a dipole approximation for the SAMA region and hence that the distribution of the used stations is not really relevant for the study.
Authors correctly mention various interesting chances for research on the topic and judging from the elaborateness of their tools, have ambitious plans so I hope to see more of them in the future. As to the presented work, I am sorry to say that I regard it as conceptually too problematic and results as too insignificant to justify publication.
Citation: https://doi.org/10.5194/egusphere-2025-794-RC2 -
AC2: 'Reply on RC2', Edwin Camacho, 18 Jun 2025
We thank the reviewer for their feedback. Below we address the specific comment made by the reviewer:
Comment #1: “As to the first, it is of course not serious to make general statements about the SAMA's influence on pulsations based on such a short data set - there is no prove that it is representative and not just by chance that intensities at one station are larger that at some other.”
We thank the reviewer for their valuable feedback and acknowledge the concern regarding the generalizability of our findings based on a limited dataset. In response, we will revise the Discussion and Results sections to clearly state that our analysis constitutes a case study. We will ensure that the text avoids implying broader generalizations and instead emphasizes that our conclusions are specific to this particular event.
Regarding the reviewer’s concern about the observed pulsation intensities, we respectfully point out that previous studies have reported comparable findings. For example, Obana et al. (2005), Yumoto et al. (1985), and Engebretson et al. (2000) observed that magnetic pulsations at conjugate stations, outside the South Atlantic Magnetic Anomaly (SAMA), typically exhibit similar amplitude and phase characteristics. Additionally, investigations focused on the SAMA region (though not necessarily at conjugate stations) have demonstrated that pulsations tend to show enhanced amplitudes in this area (e.g., Da Silva et al., 2020; Trivedi et al., 2005). Therefore, our observations are consistent with prior work, supporting the notion that elevated pulsation amplitudes in the SAMA region are a recurrent feature, rather than a result of chance.
We also emphasize that our study employs 1-second resolution data from conjugate stations, an uncommon and valuable dataset in this field. The limited availability of such high-resolution conjugate data constrains our ability to perform a more statistically comprehensive analysis at this stage. Moreover, the current scope of our project does not provide the resources required for a broader investigation. Nevertheless, we fully agree with the reviewer that a more extensive statistical study would be highly beneficial, and we intend to pursue this direction in future work, contingent on project extension and data access.
As a positive aspect, we highlight that our study employs a robust methodological framework by integrating three complementary techniques to address the objective proposed in the manuscript. We believe that this integrated approach offers novel insights and contributes meaningfully to the advancement of the field. Finally, we would like to underline the scientific value of well-documented case studies, especially when they involve rare datasets or provide unique observational perspectives. Numerous peer-reviewed publications have advanced knowledge in their respective areas through detailed case studies (e.g., Takahashi, 1994; Trivedi, 1997; Sarafopoulos, 2005; Francia et al., 2012). In this context, we believe our work offers a meaningful contribution.
Comment #2: "As to the latter, it is misleading to include the concept of conjugate points to such an analysis in such a simplistic way. It certainly is intriguing to investigate if an anomaly of the main magnetic field has a visible impact on some field variations, but this should be done in a way that is not self-contradictory. The problem is that the concept of conjugate points (as Authors describe correctly) is based on the footpoints of the same dipole field line. However, the essence of SAMA is that there are significant deviations from the dipole approximation in this region and field lines are not dipole-like. I am afraid that it is impossible to find footpoints of the same field line with a dipole approximation for the SAMA region and hence that the distribution of the used stations is not really relevant for the study"
We appreciate the reviewer’s second comment and acknowledge the concern regarding the determination of conjugate points. To calculate conjugate points, we employed the Altitude-Adjusted Corrected Geomagnetic (AACGM) coordinate system. This coordinate conversion involves tracing a magnetic field line to the dipole magnetic equatorial plane using the full-resolution International Geomagnetic Reference Field (IGRF) model, including its non-dipolar components. From that point, a dipole field line is then traced back to the Earth's surface (Shepherd, 2014; Laundal and Richmond, 2017). These steps ensure a more physically meaningful mapping between conjugate locations.
We utilized Python-based tools that implement AACGM coordinates for this purpose. While it is true that AACGM coordinates are traditionally undefined in certain regions, particularly near the magnetic equator and parts of the South Atlantic Ocean, recent updates to Shepherd’s (2014) original code now provide coordinate estimates in these regions through interpolation and fitting techniques. Importantly, the software is designed to alert users when a location falls within a region where the coordinate calculation is invalid. In such cases, the code returns a NaN value, indicating that the conjugate point could not be determined.
In our study, we verified that none of the stations used were located within these "forbidden" regions. Therefore, it was possible to compute valid conjugate points, even within or near the South Atlantic Magnetic Anomaly (SAMA), and to base our analysis and discussion on those results. We will revise the manuscript to better clarify the methodology used for conjugate point calculation, including the steps taken to ensure data validity within this challenging geomagnetic region. Finally, we consider it important to mention that an online calculator for transformations between geographic and AACGM-v2 coordinates is also available (https://sdnet.thayer.dartmouth.edu/aacgm/aacgm_calc.php). This tool allows any interested reader to independently verify that the station coordinates used in our study are appropriate for calculating geomagnetic conjugate points.
References:
TRIVEDI, N. B. et al. Global Pc5 geomagnetic pulsations of March 24, 1991, as observed along the American sector. Geophysical Research Letters, v. 24, n. 13, p. 1683-1686, 1997.SARAFOPOULOS, D. V., 2005. A case study testing the cavity mode model of the magnetosphere. Annales Geophysicae. Göttingen, Germany: Copernicus Publications.
Francia, P., M. Regi, M. De Lauretis, U. Villante, and V. A. Pilipenko. 2012, A case study of upstream wave transmission to the ground at polar and low latitudes, J. Geophys. Res., 117, A01210, doi:10.1029/2011JA016751.
The other references mentioned are found in the manuscript.Citation: https://doi.org/10.5194/egusphere-2025-794-AC2
-
AC2: 'Reply on RC2', Edwin Camacho, 18 Jun 2025
-
EC1: 'Comment on egusphere-2025-794', Emmanuel Nahayo, 19 Jun 2025
Thank you for valuable comments from Referee#1 and Referee#2 on the manuscript regarding some identified concerns that need attention of the authors. The responses of authors to raised issues for the improvement of the manuscript, i.e., revisiting section 3.1, changing the narrative of the manuscript on the issue of generalization of the possible interference of SAMA on PC3 pulsations and presenting the method used to determine magnetic conjugate points, will be attended to before the resubmission of the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-794-EC1
Status: closed
-
RC1: 'Comment on egusphere-2025-794', Anonymous Referee #1, 25 Apr 2025
This is an interesting study aimed to assess the impact of the South Atlantic Magnetic Anomaly (SAMA) on the Pc3 pulsations in the Earth’s magnetic field. For this, authors studied the Pc3 signal features in the magnetic data from two pairs of conjugate (i.e. located in the Northern and Southern magnetic hemispheres symmetrically with respect to the magnetic equator) ground-based stations in order to compare the pulsation dynamics within the SAMA area with the one outside it.
The authors have examined not only spectral characteristics of the Pc3 pulsations but also the coherence features. The capabilities of the group of wavelet-based techniques are well demonstrated as applied to the data analysis. The results show the difference in the Pc3 pulsation patterns inside and outside the SAMA region, indicating its influence on the wave processes in the Earth’s magnetosphere.
All in all, this is the first comparative analysis performed for geomagneticdatasets from conjugate stations. Moreover, this is the one of the studies that present a valuable display of the interaction of the Earth’s core magnetic field and the magnetospheric wave processes and, furthermore, can bring to light the details of the nature of both internal and external magnetic field sources. The manuscript is definitely worth publishing in the GI journal.
The presentation of the results is good, but there are some issues to improve.
To me, in Section 3.1, such detailed description of the basics of spectral analysis is excessive, as well as the well-known wavelet functions and their equations. I recommend some reduction of this theoretical part, so that it doesn't look like a lecture note on mathematics. Also please check the period axis labels in wavelet coherence plots in Fig. 6.
Citation: https://doi.org/10.5194/egusphere-2025-794-RC1 -
AC1: 'Reply on RC1', Edwin Camacho, 25 Apr 2025
We thank the reviewer for their positive feedback and for highlighting the novelty of using conjugate stations and wavelet techniques to study the impact of SAMA on Pc3 pulsations.
Below we address the specific comment made by the reviewer:Comment #1:
To me, in Section 3.1, such detailed description of the basics of spectral analysis is excessive, as well as the well-known wavelet functions and their equations. I recommend some reduction of this theoretical part, so that it doesn't look like a lecture note on mathematics.Response: We agree with the comment and will summarize the basic concepts more concisely, removing some of the mathematical expressions and sentences that are already well known in the field.
Comment #2:
Also please check the period axis labels in wavelet coherence plots in Fig. 6.Response: Thank you for pointing this out. Figure 6 wil be updated to correctly reflect the period values and improve the clarity of the graphs.
We will incorporate the reviewer’s comments during the final revision of the manuscript.
Sincerely,
Edwin CamachoCitation: https://doi.org/10.5194/egusphere-2025-794-AC1
-
AC1: 'Reply on RC1', Edwin Camacho, 25 Apr 2025
-
RC2: 'Comment on egusphere-2025-794', Anonymous Referee #2, 11 Jun 2025
In the manuscript "An analysis of the SAMA’s interference on Pc3 pulsations using data from conjugate stations" Authors analyse three hours of synchronuous data from four observatories in Brazil, Puerto Rico, Japan, and Australia for pc3 pulsations. They find synchronuous coherent events in the according frequency band with enhanced amplitudes in Brazil which they interprete as caused by the South Atlantic Magnetic Anomaly (SAMA).
Whereas the applied analysis methods and the presentation of the background and the research itself are fine, there are serious issues with the significance of the results and with the soundness of the research concept. As to the first, it is of course not serious to make general statements about the SAMA's influence on pulsations based on such a short data set - there is no prove that it is representative and not just by chance that intensities at one station are larger that at some other. As to the latter, it is misleading to include the concept of conjugate points to such an analysis in such a simplistic way. It certainly is intriguing to investigate if an anomaly of the main magnetic field has a visible impact on some field variations, but this should be done in a way that is not self-contradictory. The problem is that the concept of conjugate points (as Authors describe correctly) is based on the footpoints of the same dipole field line. However, the essence of SAMA is that there are significant deviations from the dipole approximation in this region and field lines are not dipole-like. I am afraid that it is impossible to find footpoints of the same field line with a dipole approximation for the SAMA region and hence that the distribution of the used stations is not really relevant for the study.
Authors correctly mention various interesting chances for research on the topic and judging from the elaborateness of their tools, have ambitious plans so I hope to see more of them in the future. As to the presented work, I am sorry to say that I regard it as conceptually too problematic and results as too insignificant to justify publication.
Citation: https://doi.org/10.5194/egusphere-2025-794-RC2 -
AC2: 'Reply on RC2', Edwin Camacho, 18 Jun 2025
We thank the reviewer for their feedback. Below we address the specific comment made by the reviewer:
Comment #1: “As to the first, it is of course not serious to make general statements about the SAMA's influence on pulsations based on such a short data set - there is no prove that it is representative and not just by chance that intensities at one station are larger that at some other.”
We thank the reviewer for their valuable feedback and acknowledge the concern regarding the generalizability of our findings based on a limited dataset. In response, we will revise the Discussion and Results sections to clearly state that our analysis constitutes a case study. We will ensure that the text avoids implying broader generalizations and instead emphasizes that our conclusions are specific to this particular event.
Regarding the reviewer’s concern about the observed pulsation intensities, we respectfully point out that previous studies have reported comparable findings. For example, Obana et al. (2005), Yumoto et al. (1985), and Engebretson et al. (2000) observed that magnetic pulsations at conjugate stations, outside the South Atlantic Magnetic Anomaly (SAMA), typically exhibit similar amplitude and phase characteristics. Additionally, investigations focused on the SAMA region (though not necessarily at conjugate stations) have demonstrated that pulsations tend to show enhanced amplitudes in this area (e.g., Da Silva et al., 2020; Trivedi et al., 2005). Therefore, our observations are consistent with prior work, supporting the notion that elevated pulsation amplitudes in the SAMA region are a recurrent feature, rather than a result of chance.
We also emphasize that our study employs 1-second resolution data from conjugate stations, an uncommon and valuable dataset in this field. The limited availability of such high-resolution conjugate data constrains our ability to perform a more statistically comprehensive analysis at this stage. Moreover, the current scope of our project does not provide the resources required for a broader investigation. Nevertheless, we fully agree with the reviewer that a more extensive statistical study would be highly beneficial, and we intend to pursue this direction in future work, contingent on project extension and data access.
As a positive aspect, we highlight that our study employs a robust methodological framework by integrating three complementary techniques to address the objective proposed in the manuscript. We believe that this integrated approach offers novel insights and contributes meaningfully to the advancement of the field. Finally, we would like to underline the scientific value of well-documented case studies, especially when they involve rare datasets or provide unique observational perspectives. Numerous peer-reviewed publications have advanced knowledge in their respective areas through detailed case studies (e.g., Takahashi, 1994; Trivedi, 1997; Sarafopoulos, 2005; Francia et al., 2012). In this context, we believe our work offers a meaningful contribution.
Comment #2: "As to the latter, it is misleading to include the concept of conjugate points to such an analysis in such a simplistic way. It certainly is intriguing to investigate if an anomaly of the main magnetic field has a visible impact on some field variations, but this should be done in a way that is not self-contradictory. The problem is that the concept of conjugate points (as Authors describe correctly) is based on the footpoints of the same dipole field line. However, the essence of SAMA is that there are significant deviations from the dipole approximation in this region and field lines are not dipole-like. I am afraid that it is impossible to find footpoints of the same field line with a dipole approximation for the SAMA region and hence that the distribution of the used stations is not really relevant for the study"
We appreciate the reviewer’s second comment and acknowledge the concern regarding the determination of conjugate points. To calculate conjugate points, we employed the Altitude-Adjusted Corrected Geomagnetic (AACGM) coordinate system. This coordinate conversion involves tracing a magnetic field line to the dipole magnetic equatorial plane using the full-resolution International Geomagnetic Reference Field (IGRF) model, including its non-dipolar components. From that point, a dipole field line is then traced back to the Earth's surface (Shepherd, 2014; Laundal and Richmond, 2017). These steps ensure a more physically meaningful mapping between conjugate locations.
We utilized Python-based tools that implement AACGM coordinates for this purpose. While it is true that AACGM coordinates are traditionally undefined in certain regions, particularly near the magnetic equator and parts of the South Atlantic Ocean, recent updates to Shepherd’s (2014) original code now provide coordinate estimates in these regions through interpolation and fitting techniques. Importantly, the software is designed to alert users when a location falls within a region where the coordinate calculation is invalid. In such cases, the code returns a NaN value, indicating that the conjugate point could not be determined.
In our study, we verified that none of the stations used were located within these "forbidden" regions. Therefore, it was possible to compute valid conjugate points, even within or near the South Atlantic Magnetic Anomaly (SAMA), and to base our analysis and discussion on those results. We will revise the manuscript to better clarify the methodology used for conjugate point calculation, including the steps taken to ensure data validity within this challenging geomagnetic region. Finally, we consider it important to mention that an online calculator for transformations between geographic and AACGM-v2 coordinates is also available (https://sdnet.thayer.dartmouth.edu/aacgm/aacgm_calc.php). This tool allows any interested reader to independently verify that the station coordinates used in our study are appropriate for calculating geomagnetic conjugate points.
References:
TRIVEDI, N. B. et al. Global Pc5 geomagnetic pulsations of March 24, 1991, as observed along the American sector. Geophysical Research Letters, v. 24, n. 13, p. 1683-1686, 1997.SARAFOPOULOS, D. V., 2005. A case study testing the cavity mode model of the magnetosphere. Annales Geophysicae. Göttingen, Germany: Copernicus Publications.
Francia, P., M. Regi, M. De Lauretis, U. Villante, and V. A. Pilipenko. 2012, A case study of upstream wave transmission to the ground at polar and low latitudes, J. Geophys. Res., 117, A01210, doi:10.1029/2011JA016751.
The other references mentioned are found in the manuscript.Citation: https://doi.org/10.5194/egusphere-2025-794-AC2
-
AC2: 'Reply on RC2', Edwin Camacho, 18 Jun 2025
-
EC1: 'Comment on egusphere-2025-794', Emmanuel Nahayo, 19 Jun 2025
Thank you for valuable comments from Referee#1 and Referee#2 on the manuscript regarding some identified concerns that need attention of the authors. The responses of authors to raised issues for the improvement of the manuscript, i.e., revisiting section 3.1, changing the narrative of the manuscript on the issue of generalization of the possible interference of SAMA on PC3 pulsations and presenting the method used to determine magnetic conjugate points, will be attended to before the resubmission of the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-794-EC1
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