The secular variation of the core geomagnetic field is generally characterized by smooth variations in time. However, since the end of the 1970s with the works of Courtillot et al. (1978) and Malin et al. (1983), the geomagnetic community has been interested in the occurrence of abrupt changes, not globally simultaneous (Brown et al., 2013), observed in the trend of the first derivative of the field elements, mostly Y (East) component, recorded at geomagnetic observatories, called geomagnetic jerks.

There exist many techniques to detect geomagnetic jerks, from spectral decomposition methods such as wavelet analysis (e.g., Alexandrescu et al., 1996) and Slepian functions expansions (Kim and von Frese, 2013) to nonlinear techniques such as nonlinear forecasting approach (Qamili et al., 2013). However, up to date, the most used technique to find out geomagnetic jerks is that based on the direct identification of V-shape in the secular variation of one geomagnetic field component (X, Y, Z) registered in ground geomagnetic observatories, mainly in the East component (Y) because it is the least affected by external fields at midlatitudes (Pinheiro et al., 2011; Torta et al., 2015). Following this approach, Pinheiro et al. (2011) used annual means of the geomagnetic components X, Y, and Z coming from geomagnetic observatories distributed around the world to estimate the occurrence time of the 1969, 1978, 1991, and 1999 geomagnetic jerks. Brown et al. (2013) improved the methodology applied by Pinheiro et al. (2011) using monthly means of the three geomagnetic components in more than 100 observatories, and then histograms with periods of most frequent jerk activity from 1957 to 2008 were estimated. Later, Torta et al. (2015) estimated the 2007, 2011, and 2014 jerks occurrence times following an analogous procedure to that described in Pinheiro et al. (2011) but using only the geomagnetic component Y. They used between six and four geomagnetic observatories to estimate the occurrence times of the most recent geomagnetic jerks.

In the last 2 decades, five well-defined geomagnetic jerks have been widely accepted by scientific community (see, e.g., Brown et al., 2013; Torta et al., 2015). These most recent geomagnetic jerks, reported in 1999 (Mandea and Macmillan, 2000), 2003 (Olsen and Mandea, 2008), 2007 (Olsen et al., 2009; Chulliat et al., 2010), 2011 (Chulliat and Maus, 2014), and 2014 (Torta et al., 2015), have been found to occur at a regular rate of one every 3–4 years. This suggests that they are caused by a quasi-oscillatory phenomenon within the outer core. New high-resolution satellite data provided by the last satellite missions, such as Swarm from European Space Agency (ESA) (Friis-Christensen et al., 2006), have improved the geomagnetic field models and, in turn, the knowledge of the dynamic processes occurring close to the outer core. As a result, one can obtain reliable estimations of the secular acceleration (SA) of the geomagnetic field and its time variations at the Core-Mantle Boundary (CMB). However, it is important to mention that the SA is less constrained for short wavelengths, which increases the difficulty to study rapid fluctuations at these scales (Gillet, 2019). Chulliat et al. (2010) and Chulliat and Maus (2014) observed that the geomagnetic jerks happened between two peaks of SA at the CMB and applied a Principal Component Analysis (Chulliat and Maus, 2014) to establish the principal modes of variability of the SA associated with the occurrence of the geomagnetic jerks. They found maxima and minima lobes of the SA located on the equatorial region in South Atlantic Ocean and South America and in the Indian Ocean. In a very recent work, Kloss and Finlay (2019) found that in these same sectors magnetic field acceleration pulses are produced by alternating prominent bursts of nonzonal azimuthal flow acceleration in the equatorial region beneath the CMB. Moreover, they found alternated sign of the acceleration at some regions that, when associated with large spatial scale structures, could cause geomagnetic jerks at the Earth’s surface.

By using global geomagnetic field models based on paleomagnetic data, Terra-Nova et al. (2016) observed that the reversed flux patches (RFPs) present at the CMB, that is, regions with an opposite polarity to that expected for an axial dipole, for the last three millennia, were mostly located in the Southern Hemisphere, especially in the South Atlantic and Indian regions.

In the last decades, the presence of two RFPs located beneath South America and South Africa from 1840 has been observed (Gubbins et al., 2006), although recent studies (Tarduno et al., 2015; Campuzano et al., 2019) point out that they could be even older (950 AD or earlier). These RFPs are commonly associated with the internal origin of the South Atlantic Anomaly (SAA) (e.g., Hulot et al., 2002; Olson and Amit, 2006; Laj and Kissel, 2015; Pavón-Carrasco and De Santis, 2016; Terra-Nova et al., 2017), a region with anomalously low values of geomagnetic field intensity at the Earth’s surface. In Figure 1, the present situation of the intensity and the radial component (Br) of the geomagnetic field at the surface and CMB, respectively, are shown. The SAA is also related to the continuous decreasing of the dipole moment of the geomagnetic field in the last 150 years (Finlay et al., 2016a; Terra-Nova et al., 2017). This has motivated some authors to study this feature as a possible precursor of a next geomagnetic transition, such as an excursion or a reversal (De Santis et al., 2013; Laj and Kissel, 2015; Pavón-Carrasco and De Santis, 2016).

In the search for understanding geomagnetic jerks, an important element is to investigate possible correlations between these events and some other geophysical phenomena (see Mandea et al., 2010 for a review on some of the up-to-date suggested links). In the present paper, we suggest that the minima of the acceleration of the areal extent of SAA could be a reliable indicator of the occurrence of geomagnetic jerks, being able to register all of the well-defined geomagnetic jerks for the last 2 decades.

In the next sections, we describe the methods, together with the most important results, and then provide a discussion about the dynamic processes at the CMB that could be involved in this link and the possible identification of future geomagnetic jerks occurrence from this result.

This study has been carried out using the CHAOS-7.2 model, the release of the CHAOS-7 model (Finlay et al., 2020) that uses the Swarm preliminary baseline 0603 data up to the end of March 2020 and ground observatory data as available in February 2020. The Swarm satellite mission (Olsen and Haagmans, 2006 and references therein) was launched by ESA in November 2013. This mission, based on a constellation of three identical satellites (Alpha, Bravo, and Charlie), provides high quality measurements of the geomagnetic field in three different orbital planes, with Alpha and Charlie flying almost in parallel and Bravo orbiting alone at a higher altitude. These data, along with those given by other previous satellite missions (Cryosat-2, CHAMP, SAC-C, and Ørsted) and the global network of magnetic observatories at ground level, provide the possibility of obtaining high-resolution time-dependent geomagnetic field models such as the CHAOS-7 model and later releases.

According to Domingos et al. (2017), there are several ways to define the SAA position and, depending on the choice, the shape and evolution of the SAA could be slightly different. An operative and simple way to define the SAA in terms of its areal extent is to consider the area within the contour of 32,000 nT at the Earth’s surface following De Santis et al. (2012). We calculate its area (S) monthly from January 1998 to March 2020 using the CHAOS-7.2 model until maximum spherical harmonic degree 13 that corresponds to the main geomagnetic field. As can be observed in Figure 2A, the areal extent of the SAA has been continuously growing during the entire period, from 9.49 ∙ 10⁷ km² to 10.47 ∙ 10⁷ km². In order to evaluate in detail the evolution of this increase, we also study the rate of change of the areal extent of the SAA by applying the first and second derivatives to the previously calculated area (S) (Figures 2B–C). For the first derivative estimation, S ˙ , we use the finite differences between successive times, t_i and t_i+1, from January 1998 to March 2020, centered in the mean time, using S ˙ t i + 1 2 = S t i + 1 − S t i ( t i + 1 − t i ) , (1) with t_i+1/2 = t_i + 3 months and t_i+1 = t_i + 6 months, in order to provide smooth changes.

For the second derivative, S ⋅ ⋅ , we use the finite differences method of second order following Tozzi et al. (2009), with t_i+1 = t_i + 6 months and t_i−1 = t_i−6 months for the same period.

Prior to the estimation of these derivatives, we smooth the areal extent of the SAA series by fitting the data using a cubic splines basis with knot points every year from 1998 to 2020.2 in order to avoid subsequent mathematical artifacts from the derivatives (orange line in Figure 2A).

As expected, the S ˙ values are positive (Figure 2B); that is, the areal extent of the SAA is increasing in the analyzed time interval with an average rate of 4.4 ∙ 10⁵ km²/yr. In Figure 2C it is observed that this increase of the SAA is not continuously accelerated (see also Pavón-Carrasco and De Santis, 2016), alternating periods of accelerations (beginning –1999.0, 1999.9–2000.9, 2002.2–2004.0, 2005.1–2006.1, 2006.8–2008.8, 2011.0–2012.0, 2013.3–2016.0, and 2017.8–2019.6) and decelerations (1999.0–1999.9, 2000.9–2002.2, 2004.0–2005.1, 2006.1–2006.8, 2008.8–2011.0, 2012.0–2013.3, 2016.0–2017.8, and 2019.6– end). The time intervals when the S ⋅ ⋅ reaches positive values (2000.7–2001.1, 2003.6–2004.4, 2007.4–2010.3, 2011.6–2012.5, 2014.8– end) are characterized by longer displacements of the areal extent of the SAA. These intervals present a duration from 1 to 3 years, being the longest period of positive S ⋅ ⋅ , that is, the maximum increase of areal extent of the SAA for the last 2 decades, between 2007 and 2010. Actually, the longest period with positive S ⋅ ⋅ would be from 2014.8 up to now, but this result must be considered carefully because it could be affected by edge problems of the CHAOS-7.2 model. These edge problems could also be present at the beginning of the model, the borders being the periods most subject to change. On the other hand, in the minima of S ⋅ ⋅ (1999.9, 2002.2, 2005.1, 2006.8, 2011.0, 2013.3, and 2017.8) the areal extent of the SAA is slowing down its advancement.

The comparison between the occurrence of these minima and the well-defined geomagnetic jerks reported during the last 2 decades is shown in Figure 2C. Since the geomagnetic jerks are not registered simultaneously in all geomagnetic observatories, we can find differences between observations of the same jerk in two different observatories even of around two years (e.g., Mandea et al., 2010). The shaded bands in Figure 2 give information about this fact. For representation of shaded bands, we have taken the occurrence times from previously published works. In detail (the following occurrence times for the different jerks are summarized in Supplementary Table S1):

- The 1999 geomagnetic jerk occurrence time: occurrence dates of the 1999 geomagnetic jerk were given in Supplementary Table A4 by Pinheiro et al. (2011). They are 54 occurrence dates calculated from the annual means of the geomagnetic components X, Y, and Z in 42 observatories. The mean (and standard deviation) of these 54 occurrence dates provides the value of 1999.0 (±0.9) plotted in Figure 2C.

As we can observe, the minima of the acceleration ( S ⋅ ⋅ ) of the areal extent of the SAA (Figure 2C) coincide quite well with the geomagnetic jerks occurrence for the last 2 decades.

To reinforce the obtained link, we have performed several tests to verify the independence of the results with 1) the model used to calculate the SAA areal extent and 2) the SAA definition. For the first objective, we have compared our results with those given by a previous version of the CHAOS model, the CHAOS-6-x8 (Finlay et al., 2016b), that used a previous version of Swarm data (v.0505) up to the end of August 2018 and ground observatory data available at the same epoch, and with the GRIMM-3 model (Lesur et al., 2011). This last model is mainly an improvement of GRIMM-2 (Lesur et al., 2010), which was generated from CHAMP satellite data and observatory hourly means, and it is valid from January 2001 to July 2009. As we can see in Supplementary Figures S1–S2 of the Supplementary Material, the minima of the acceleration of the areal extent of SAA are detected in similar times as when the CHAOS-7.2 is used (Figure 2C). The main differences are found in the earlier times but within the uncertainty shown by shaded bands.

For the second objective, we have changed the definition of the SAA using 1) a different contour line of 28,000 nT, which corresponds to the lowest value of geomagnetic field intensity registered over the interest area in 1840 AD, computed using the historical geomagnetic field model GUFM1 (Jackson et al., 2000), and 2) the new measure to characterize the SAA area proposed by Amit et al. (2020). The results (Supplementary Figures S3–S4 in the Supplementary Material) are in agreement with those obtained previously. The most notable discrepancies are seen using the definition proposed by Amit et al. (2020) in the second derivative of the SAA areal extent, especially in the recent times, where the edge effects could be more significant by the effect of the smoothing of the splines basis used to represent the temporal variations during the modeling process.

Despite some discrepancies mainly due to edge effects, these tests confirm the results obtained with CHAOS-7.2.

We suggest a previously unreported link between the minima of the second derivative of the areal extent of SAA at surface and the occurrence of geomagnetic jerks for the last 2 decades. This result has been confirmed at the CMB, by studying the areal extent of the RFPs associated with the presence of the SAA at surface.

We have seen that global SA pulses at the CMB related to the occurrence of the geomagnetic jerks are also detected locally on the area at the CMB affected by the RFPs associated with the presence of the SAA at surface.

A new change of sign in the lobes of the SA of Br at the CMB over the Atlantic sector in 2016.0 epoch seems to reinforce the hypothesis proposed by Chulliat and Maus (2014) on the presence of a standing magnetohydrodynamic wave with a 6-year periodicity that is of the order of the periodicities reported in this work. This was also noted by other authors in more recent works (e.g., Aubert, 2018; Kloss and Finlay, 2019). A new pulse has also been observed in the global averaged squared SA of the Br, which has reached a maximum in 2016.2 and a minimum in 2017.5. This fact, along with the change of sign of the lobes of the SA of Br, the analysis of periodicities, and the minima registered in the second derivative of the areal extent of SAA and RFPs in 2017.8, would point to a new geomagnetic jerk. This argument is supported by recent observatory data analyzed by Hammer (2018) where the characteristic V-shape in the secular variation and the steep change in the secular acceleration are found in observatories in the French Guyana in 2016 and Hawaii in 2017.

We have seen that the areal extent of SAA is able to detect through its relative minima all impulses of the geomagnetic field at surface (and, therefore, observed in magnetic observatories). This fact is of particular interest because it could shed light on geomagnetic jerks identified in some, but not all, studies. In this work, the occurrence of the 2005.0 geomagnetic jerk is discussed. We propose that this event, detected as a minimum of the second derivative of the areal extent of SAA, could be an impulse of the geomagnetic field associated with the asymmetry of the positive and negative lobes of the SA of the geomagnetic field at the CMB. It could be considered as a new kind of impulse of the geomagnetic field but also as a poor-defined jerk. It is also important to take into account that the jerks can be poorly defined particularly when we have to distinguish between successive events in disparate regions of the globe that overlap in time. From this point of view, this work is encouraging because it aims to give links to effects at the CMB that help to simplify the view of the surface expressions.

Finally, we have observed that the RFPs at the CMB are mostly observed in the same sectors related to the geomagnetic jerks occurrence (i.e., Atlantic and Indian sectors). The fact of detecting jerks globally (outside of these regions) does not exclude the fact that singular situations of the core dynamics like the presence of RFPs can favor the detection of jerks. These regions seem to be characterized by upwelling of toroidal field from the core, related to temperature anomalies associated with lower mantle lateral heterogeneities (Terra-Nova et al., 2016). Following Kloss and Finlay (2019), it could be possible that the relation between the arrival of quasi-geostrophic Alfvén waves at the CMB and the presence of nonzonal azimuthal flow accelerations of alternating sign could affect the upwelling of toroidal field present in higher latitudes. When a rapid change of the sign of these flow accelerations is produced, this would coincide with a change of the upwelling regime, observed as a minimum in the second derivative of the areal extent of the RFPs at CMB and of the SAA at surface, and the unfolding of a geomagnetic jerk. This could provide an important hint about the dynamic processes that link the RFPs and, therefore, the evolution of the SAA nowadays, with the geomagnetic jerks at the interior of the Earth.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

SAC developed the project and performed the calculations with the help of FJPC. The interpretation of the results and writing were led by SAC with the help of FJPC, ADS, AGL, and EQ; SAC, FJPC, ADS, AGL, and EQ discussed the results and commented on the manuscript.

The Living Planet Fellowship (TEMPO project) from ESA, Contract No. 4000112784/14/I-Sbo, is the main financial support to this research. ASI Limadou-Science Project has supported this work partially. Grant FPU17/03635 from the Spanish Ministry of Education was funding AGL PhD thesis. FJPC was partially supported by the Spanish research project PGC2018-099103-A-I00.

EQ was employed by the company Serco. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.