Archaeomagnetic field intensity evolution during the last two millennia

3. Synthesis and perspectives
Throughout the development of my PhD project, which resulted in this thesis, I have had the pleasure of exploring a significant range of research topics about the Earth’s magnetic field. The main contributions of this thesis, as well as the immediate implications and perspectives, will be summarized below.

3.1. Contributions for archaeointensity methods
3.1.1. Microwave archaeointensity method
The first part of the project was essentially methodological. In Poletti et al (2013), archaeointensity measurements were performed on archaeological materials using the Microwave method (MW – Shaw et al., 1996). The samples used were those previously investigated by Hartmann et al. (2010), coming from Northeast Brazil with ages covering the last 500 years. In Hartmann et al. (2010), they presented 14 new archaeointensity results obtained from the modified Thellier-Thellier method (TT – Coe et al., 1978; Riisager and Riisager, 2001; details in Genevey et al., 2009) and Triaxe method (TR – Le Goff and Gallet, 2004). In addition, they did a detailed investigation of the magnetic mineralogy. In this way, these well-characterized archeological materials were ideal to study with the MW method. Under this light, an extensive set of measurements was carried out, and the results obtained by the MW method presented some significant discrepancies in relation to those obtained from TT and TR methods (up to 25%). Theoretical and experimental investigations showed that although the MW method directly excite the magnetic minerals by high-frequency microwaves, not heating the material in a conventional way, the samples were indeed heated. Consequently, once the samples are heated, they incorporate an adverse effect called cooling rate effect, which is associated to the difference between the cooling times during its manufactory and that of the heating steps during the archaeointensity experiment (e.g. Fox and Aitken, 1980; Dodson and McClelland-Brown, 1980; Halgedahl et al., 1980). To correct for this effect, Poletti et al. (2013) proposed a simple experimental procedure to be performed on sister samples (i.e., samples from a same fragment). It was observed that this cooling rate correction provides a concordant final result among the three methods (MW-TT-TR). It is important to emphasize that the physical theory behind the heating during MW application is still not well understood, but it is well known that it is proportional to the increase of the power integral (power x time) during the experiment. Since the equipment operates exclusively with the resonance frequency of magnetite (i.e., 14 GHz) (Shaw et al., 1996, 1999; Hill and Shaw, 1999, 2000; Hill et al., 2002a, 2002b), we hypothesize that since archaeological materials have a range of magnetic minerals in its composition, the absorption of the power integral by non-magnetite minerals is converted into heat.
Based on the above mentioned contribution I suggest that from now on all microwave archaeointensity estimates need to be corrected from the cooling rate effect. In addition, it would be interesting if the theoretical basis of the MW method was more explored. Thus, it would be possible to obtain a better understanding of the physics behind the interaction between high-frequency microwaves and bulk samples. Also, this would contribute to reduce the empirical character of this method.

3.1.2. Double-heating archaeointensity method
In Poletti et al. (2016) two methodological aspects were explored. The first one is the influence of the anisotropy of thermoremanent magnetization (ATRM) on archaeological materials and how to correct it. The second was the successful implementation of the archaeointensity methodology (TT method) at the Laboratório de Paleomagnetismo, Universidade de São Paulo, Brazil.
Since the late 1970s it has been known that ATRM has adverse effects on the final estimate of archaeointensity estimates obtained from archaeological materials (Rogers et al., 1979). Veitch et al. (1984) proposed an elegant way to correct such effect from the calculation and application of an ATRM-tensor. However, due to the significant increase in laboratory time that this procedure represents as it adds six additional heating steps to the already laborious palaeointensity routine, several researchers looked for alternative methods to correct for the anisotropy effect. The most popular ones were those that corrected the ATRM effect from tensors built through anhysteretic remanent magnetization (ARM) or magnetic susceptibility (MS) measurements. However, these approaches require some caution, since they imply in assuming that the thermoremanent magnetization (TRM) behavior is equivalent to ARM and/or MS, which is not always true (Stephenson et al., 1986; Yu et al., 2003). Therefore, the application of these alternative methods to correct ATRM effect must be accompanied by tests that demonstrate the correspondence between the ATRM and the ARM or MS for each studied case. Another way used by some researchers is to correct for the ATRM effect by measuring six samples extracted from a single fragment, positioned experimentally orthogonal to each other (e.g., Morales et al., 2009; Goguitchaichvili et al. 2012). Fortunately, in Poletti et al. (2016) we had the opportunity to test whether this correction methodology is appropriate or not.
Following Veitch et al. (1984), the samples studied by Poletti et al. (2016) were subjected to six additional heating steps, in a fixed laboratory field, at the temperatures of 350 °C and 500 °C for the ATRM correction. In these additional heating steps, the arbitrary adopted positions were +X, -X, +Y, -Y, +Z and -Z. The different temperatures were strategically chosen in order to calculate the ATRM-tensors in samples that had at least 40% of the NRM removed. This strategy gave us, in addition, a set of measurements that enabled to test the hypothesis of the correction made from an arithmetic mean of six independent sister samples, positioned orthogonally to each other during the experiment.
To test the validity of the six orthogonal samples approach, the following procedure was adopted: i) only samples that showed a demagnetization proportional to at least 30% of NRM between 350 °C and 500 °C, respectively, and complied to all selection criteria proposed by Paterson et al. (2014), were selected; ii) archaeointensity for each position (+X, -X, +Y, -Y, +Z and -Z) between 350 °C and 500 °C were estimated; iii) final results were calculated from the arithmetic mean of the six results obtained in (ii); and iv) the results obtained from the arithmetic mean described in (iii) were compared with the results corrected by the method proposed by Veitch et al. (1984) for each same fragment. At the end, we show that the results obtained by the two correction methods disagree. Therefore, we prove that the ATRM correction from the arithmetic mean of six orthogonal samples is not valid (Poletti et al., 2016).
A great effort has been put forth by the paleomagnetic community to try to reduce the experiment time of the TT method. Yet, based on the above discussion, I suggest that more care should be exercised in the application of alternative methods to correct for the ATRM effect and that the six sample average method, in particular, should be abandoned.

3.1.3. Double-heating archaeointensity method at Universidade de São Paulo, Brazil
As previously stated, another methodological contribution from this thesis was the successful implementation of the modified Thellier-Thellier method for archaeointensity measurements in the Laboratório de Paleomagnetismo, Universidade de São Paulo. Before obtaining new archaeointensity estimates from unpublished materials, in Poletti et al. (2016) we also performed a series of measurements on samples remaining from the works already published by Hartmann et al. (2010 and 2011) and Poletti et al. (2013). In this way, we were able to implement and test the entire protocol of measurements and corrections, and intercalibrate the final results with those obtained at the Institut de Physique du Globe de Paris, France (Hartmann et al., 2010, 2011) and Geomagnetic Laboratory, University of Liverpool, UK (Poletti et al., 2013), therefore demonstrating that results obtained in São Paulo are of equivalent quality to those produced by some of the reference research centers in the world.

3.2. Archaeomagnetic field intensity evolution in South America
3.2.1. Reassessment of the South America database
In Poletti et al. (2016), a detailed reassessment of the available archaeointensity data for South America during the last 2000 years was carried out. For this, a list of selection criteria was established in order to retain only high-quality entries. A detailed description of this list can be found in Poletti et al. (2018). To be an important point of this thesis, the list of selection criteria used will be re-presented below according to Poletti et al. (2018, pages 73 and 74), where it reads:

“i) Age uncertainty. For this study, we accepted data with age uncertainty less than or equal to 100 years (sage = 100). This rather strict choice was made to enable the comparison between archaeomagnetic and observatory/satellite data in the Gauss era (i.e., 181 years). Data were not filtered by the dating technique (except for archaeomagnetic dating);
ii) The archaeointensity method used and the protocol adopted. We only accepted intensity data performed exclusively with the classical double-heating method at room-temperature (Thellier-Thellier, 1959) in one of its modified versions (TT) (Coe, 1967; Aitken et al., 1988; Yu et al, 2004), the microwave method (MW) (Shaw et al., 1996; Hill and Shaw, 1999), or the high-temperature Triaxe method (TR) (Le Goff and Gallet, 2004). Our choice was based on palaeointensity methods that perform a gradual and progressive replacement between the magnetizations acquired from the nature and laboratory. The results obtained from these three specific methods are more likely to be high-quality and concordant as highlighted by several works published in the last few decades (e.g., Hill et al., 2002a; Genevey et al., 2009; Poletti et al., 2013);
iii) Additional steps to check alterations during the experiment. For TT and MW, we required additional steps in the laboratory protocol, referred to as pTRM checks, to monitor possible (thermo)chemical alterations during the gradual increase of temperature (TT) or power (MW) steps on the experiment (Coe et al., 1978). For TR, these additional steps are unnecessary (Le Goff and Gallet, 2004);
iv) Evaluation of the influence of multi-domain (MD) grains. We required at least one test-type to verify possible MD grains influence (e.g., Riisager and Riisager, 2001; Krása et al., 2003; Yu et al., 2004), in order to avoid the violation of the principles of additivity and reciprocity, which are part of the backbone of the Thellier-Thellier method (Yu and Dunlop, 2003; Dunlop, 2011);
v) Anisotropy thermoremanent magnetization (ATRM) correction. We accepted only data largely unbiased by anisotropy effects either by having the laboratory field applied in a direction within 10 degrees of the principal component of the natural remanent magnetization (NRM) (Rogers et al, 1979; Aitken et al., 1981), or by the correction of the tensor of ATRM being obtained experimentally and calculated through the formulation proposed by Veich et al. (1984). Although there are other ways to correct the ATRM effect, for example, through the tensor obtained from measures of anhysteretic remanent magnetization (ARM) or magnetic susceptibility (MS), we restrict our analysis to results that take into account the same physical basis between anisotropy correction and Thellier-Thellier method (see ii). Data corrected by the ATRM effect using ARM or MS technique implicitly assume equivalence between the pairs of anisotropy tensors TRM-ARM or TRM-MS, which are not always true (Stephenson et al., 1986; Yu et al., 2003), although we acknowledge the need for further advances in this topic.
vi) Cooling rate correction. We accepted only archaeointensity data that were corrected for cooling rate effects following the experimental procedure described by Chauvin et al. (2000) and Genevey and Gallet (2002) for data from TT, and Poletti et al. (2013) for data from MW, in order to avoid possible bias in the final archaeointensity result due to the difference between natural (NRM) and experimental (pTRMs imparted) cooling times (e.g., Fox and Aitken, 1980; Dodson and MaClellend-Brown, 1980; Halgedhal et al., 1980; Biggin et al., 2013). All results from TR were accepted without this correction, since TR routinely produces results consistent with cooling rate-corrected TT and MW estimates (e.g., Genevey et al., 2009; Hartmann et al., 2010; 2011; Poletti et al., 2013);
vii) Standard deviation of final archaeointensity estimates. We only accepted data with standard deviation up to 15% of the mean intensity (Paterson et al., 2014), and a minimum of three samples/specimens (N=3) per age.”

The above mentioned list of selection criteria was established for archaeological materials. In the case of geological materials (i.e., volcanic rocks) criteria (v) and (vi) were not applied (see Poletti et al., 2018).
From 205 initial data, which represents about 5% of the world intensity data for this period, only 39 passed by the selection criteria. On the one hand, the number of values has been drastically reduced, implying in a huge gap of data for this region, both temporally and geographically (Poletti et al., 2016). On the other hand, this new list is composed only of high-quality archaeointensity data that can be used as a reference for regional studies of the Earth’s magnetic field intensity variations.
Based on the analysis put forward by Poletti et al. (2016), it is evident the immediate necessity to acquire new high-quality archaeointensity results for different regions of the South America, as well as for different ages. In addition to the importance of understanding the regional field evolution, the increase in the number of data for this region is essential to better understand the field variations in the Southern Hemisphere, which presents a high secular variation and is the location of the largest and most enigmatic magnetic field anomaly of the present-day field: the South Atlantic Anomaly (SAA).

3.2.2. New archaeointensity data for South America and implications
Another important contribution from this thesis was the acquisition of nine new high-quality archaeointensity data from archaeological materials collected in South Brazil, covering the last 400 years. All archaeointensity data were obtained in the Laboratório de Paleomagnetismo, Universidade de São Paulo, Brazil, and obey the selection criteria listed below, extracted from Poletti et al. (2016, page 39):

“At the specimen level, an intensity estimate is considered valid if:
– it uses a minimum of four temperature steps (N = 4) including at least 35% of the total NRM (f = 0.35) (Coe et al., 1978);
– standard errors of the slope are below 15% (ß = 0.15) (Selkin and Tauxe, 2000);
– the overall quality index of the paleointensity estimate is above 5 (q = 5) (Coe et al., 1978);
– the intensity value is obtained along the same temperature interval in which the characteristic magnetic component was isolated with an unanchored MAD = 10°;
– the angular difference between anchored and free-floating best-fit directions on a vector component diagram is below 15° (a = 15);
– maximum difference produced by a pTRM check normalized by the TRM is smaller than 9% (dCK = 9) (Leonhardt et al., 2004);
– the measure of cumulative alteration determined by the ratio of the alteration-corrected intensity estimate (Valet et al., 1996) to the uncorrected estimate, normalized by the uncorrected estimate is below 18% (dpal = 18) (Leonhardt et al., 2004);
– maximum difference produced by a pTRM tail check normalized by the NRM is below 20% (dTR = 20) (Leonhardt et al., 2004).

At the fragment level, a mean intensity was retained only when:
– the difference between individual intensity values per fragment was less than 5% after anisotropy correction;
– alteration measured by the difference between the two rapidly acquired TRMs during cooling rate experiments was less than 5% (Hartmann et al., 2010, 2011);
– at least two independent intensities were obtained for each fragment.
At site level, a total mean was calculated by averaging results from at least three fragments and the standard deviation of the mean is less than 10%.”

From the nine new results, three of them were obtained from archaeological materials sampled from ruins of Guarani Jesuit Mission reductions, located at the triple border Brazil-Paraguay-Argentina (Poletti et al., 2016) and the remaining six come from the Pelotas city, Rio Grande do Sul, Brazil, from archaeological sites of jerky beef farms (Hartmann et al., Submitted). The compilation of these new results provided a new intensity curve of archaeointensity as a function of time for South Brazil, thus expanding in latitude the works of Hartmann et al. (2010 and 2011) in Northeast and Southeast Brazil.
The southern region of Brazil covers a strategic area and enables us to investigate the SAA evolution. The basic dynamics regarding SAA is that it started its influence in Africa and drifted westward while expanding in area, passing recently over South Brazil (e.g., Jackson et al., 2000; Hartmann and Pacca, 2009). With the new data, and in an unprecedented way, it was demonstrated that the relative increase of non-dipolar components of the field over South America started in 1800 CE, therefore suggesting that this is the age of the arrival of SAA in South Brazil.
Based on the high-quality archaeointensity data discussed here, I emphasize the importance of expanding the number of new archaeointensity data for the southern part of the South American continent, particularly for ages prior to 1600 CE. This is a promising way to understand the SAA evolution, as well as to bring new insights on the supposedly recurrent nature of this feature (Tarduno et al., 2015, Shaah et al., 2016). New data for different latitudes and longitudes close the southern portion of South America are also crucial for determining the geometry of this anomaly.

3.3. The Earth’s magnetic axial dipole evolution for the last millennia
In Poletti et al. (2018) a careful analysis of all absolute magnetic intensity estimates derived from archaeological and geological records for the last two thousand years was carried out. To do it, we applied the list of selection criteria above-described (section 3.2.1), in order to retain only high-quality archaeointensity estimates. The main purpose of this analysis was to understand the evolution of the geomagnetic axial dipole for the last millennia.
As aforementioned (section 1.2. in Chapter 1), the main component of the Earth’s magnetic field can be approximated by a geocentric and axial dipole. Its stability is balanced by the equilibrium of normal and reverse magnetic flux patches (Olson and Amit, 2006). When normal flux patches move to the poles and reverse patches move to the equator the geomagnetic dipole intensity increase and vice-versa (e.g., Olson and Amit, 2006). In this light, the analysis of geomagnetic field models (Gillet et al., 2013) and geodynamo models (e.g., Aubert et al., 2013) suggests an asymmetry in the advective sources of the field implying in the decrease of the Earth’s magnetic dipole intensity in the last 185 years (Finlay et al., 2016). The growth of the SAA is a likely candidate to explain the asymmetry.
Interestingly, the results presented by Poletti et al. (2018) indicated that the geomagnetic dipole is decaying since about 700 CE and this decay can be described on a millennial scale as a constant trend (i.e., linear). Since the dipole decay trend described by the archaeointensity data is very similar to the mean trend observed from data recorded by observatories and satellites, it was suggested that the process responsible for the current fall in magnetic field intensity started more than 1,300 years ago. In other words, the break in the symmetry of advective sources, which balance the average intensity of the Earth’s magnetic field, occurred more than 1000 years before previously thought. Finally, according to Amit et al. (2017) the time-scale for axial dipole secular variation is about 1000 years. Therefore, based on this order of magnitude, we speculate that the dipole will not necessarily continue to drop and therefore the present decay does not represent a sign of an imminent polarity reversal.