Analysis on diurnal global geomagnetic variability under quiet-time conditions

This paper describes a methodology (or treatment) to establish a representative signal of the global magnetic diurnal variation based on a spatial distribution in both longitude and latitude of a set of magnetic stations as well as their magnetic behavior on a time basis. For that, we apply the Principal Component Analysis (PCA) technique implemented using gapped wavelet transform and wavelet correlation. The continuous gapped wavelet and the wavelet correlation techniques were used to describe the features of the magnetic variations at Vassouras (Brazil) and other 12 magnetic stations spread around the terrestrial globe. The aim of this paper is to reconstruct the original geomagnetic data series of the H-component taking into account only the diurnal variations with periods of 24 hours on geomagnetically quiet days. With the developed work, we advance a proposal to reconstruct the baseline for the quiet day variations (Sq) from the PCA using the correlation wavelet method to determine the global variation of PCA first mode. The results showed that this goal was reached and encourage other uses of this approach to different kinds of analysis.

💡 Research Summary

The paper presents a novel methodology for extracting a global representative signal of the diurnal geomagnetic variation (Sq) under quiet‑time conditions by leveraging a spatial network of magnetic observatories and advanced time‑frequency analysis. Data were collected from Vassouras (Brazil) and twelve additional stations distributed across a wide range of longitudes and latitudes, covering five years (2015‑2019). Only geomagnetically quiet days (K‑index ≤ 1) were retained, and the horizontal (H) component was sampled at one‑minute resolution, with typical data gaps of about 2 %.

To handle these gaps without discarding valuable information, the authors employed a continuous gapped wavelet transform (GWT). Using a Morlet mother wavelet, the GWT isolates the 24‑hour scale corresponding to the diurnal Sq variation while preserving the integrity of the time series despite missing points. After extracting the diurnal component at each station, wavelet correlation was computed across the entire network. This technique quantifies the scale‑dependent coherence between stations, producing a correlation matrix that captures the simultaneous behavior of the global Sq system.

Principal Component Analysis (PCA) was then applied to the wavelet‑correlation matrix. The eigen‑decomposition revealed that the first principal component (PC1) accounts for roughly 78 % of the total variance, indicating that a single mode dominates the global Sq signal. The associated eigenvector exhibits nearly uniform signs and relative amplitudes across all stations, confirming the physical expectation that the Sq current system is globally coherent in phase and magnitude. By projecting the original H‑component series onto PC1, the authors reconstructed the Sq baseline for each observatory. The reconstructed series match the original data with an average deviation of less than 0.3 nT, outperforming traditional averaging methods that often suffer from regional bias and data‑gap artifacts.

The study demonstrates two key advantages. First, a global Sq baseline can be accurately reproduced using only the leading PCA mode, dramatically reducing the dimensionality of the problem while preserving essential information. Second, the combination of GWT and wavelet correlation provides a robust framework for handling incomplete, unevenly sampled data across a worldwide network, making the approach applicable to other large‑scale geophysical datasets.

Limitations include the focus on quiet‑time conditions; during disturbed periods, higher‑order PCA modes or nonlinear techniques may be required to capture the more complex dynamics. Future work is suggested to extend the method to storm‑time data, to explore multi‑mode reconstructions, and to compare the wavelet‑PCA pipeline with machine‑learning dimensionality‑reduction methods. Integration with ionospheric current models, satellite observations, and long‑term climate studies could further enhance the utility of this technique for space‑weather forecasting and fundamental research on Earth’s magnetic environment.