1. Introduction

The variation of the geomagnetic field in the archaeological past can be obtained from the well dated burned archaeological artifacts, bearing some spinels like titanomagnetites, as principal carriers. Archaeomagnetic data retrieved from thermoremanent magnetization are considered the most accurate and reliable compared to the data from lakes and sediments which may be smoothed and/or offset due to their magnetization acquisition process. These data are used to draw up regional PSV reference-curves or global prediction models building upon the knowledge of the geomagnetic field variations for the periods covering the last few millennia. Reference PSV curves can also be used for dating purposes by comparing the archaeomagnetic field information (direction and/or intensity) of archaeological material within a region with the known PSV curve of the Earth’s magnetic field for the corresponding region (^{Lanos and Dufresne, 2008}; ^{Pavón-Carrasco et al., 2011}).Well-defined PSV curves in southwest USA are scarce (^{Sternberg and McGuire, 1990}; ^{Eighmy et al.,1990}; ^{Wolfman, 1990}a) in contrast to Europe, where several well-defined PSV curves are available for different regions (^{Gómez-Paccard et al., 2006}; ^{Schnepp and Lanos, 2005}; ^{Gallet et al., 2002}).

Mesoamerican culture in Mexico had great development, since the Olmec civilization, which left strong evidence of numerous big cities with trade networks that covered all of Mexico and Central America. Many investigations headed by the INAH (Instituto Nacional de Antropología e Historia) were carried out in the XX century elaborating regional sequences with ceramics and architectonic styles as chronological controls. The chronology was divided into three broad periods: The Formative or Preclassic from 2000 BC. to AD. 300, the Classic from AD. 300 to 950 and the Postclassic from AD. 950 to the contact with the Spaniard in AD. 1521. A period denominated Epiclassic between AD. 800-1200 corresponds to a brief flowering of secondary-states that grew with the collapse of great cities such as Teotihuacan and Monte Albán (^{López-Austin & López-Luján, 2014}). By 1960 the radiocarbon method began to be employed, but due to the relatively high cost, the poorly constrained laboratory techniques or the lack of a rigorous sampling methodology, some aberrant dates were obtained and consequently unreliable sequences were developed. ^{Wolfman (1990b)} visualized the archaeomagnetic dating as a great tool to provide an unattainable precision for the chronometric results solving cultural-historical problems. He then published the first directional secular variation for Mesoamerica with samples of twelve sites in Mexico, two in Guatemala, one of Honduras and six in El Salvador. A total of 81 burned samples were measured in the Wolfman research and only one directly related to a radiocarbon date.

A compilation of previously available results for Mexico is here reported, 35 of Wolfman, 39 published in refereed journals, 12 of them unburned samples that includes 4 of pictorial origin. 38 samples complete the catalog of 112 archaeomagnetic directions to build upon a reliable PSV curve for central and southem Mexico. For each individual study, the main information has been detailed, including the field sampling procedures, laboratory treatment and archaeological and chronological information. Rock magnetic studies have been carried out to identify the main magnetic minerals and their thermal stability. In addition, these data may largely contribute to better constraining the variation of the Earth’s magnetic field in the North and Central Mesoamerica during the last two millennia.

2. Archaeomagnetic studies in Mexico

The directional component of the geomagnetic field from Preclassic to Postclassic (AD. 1-1200) recorded in burned materials of 12 sites of Mexico were reported by ^{Wolfman (1990b)}. The site locations are mentioned in Table 1 and Figure 1. The measurements were carried out in the paleomagnetic laboratories of Oklahoma, Pittsburgh and California. In Oklahoma the samples were measured in a Princeton Applied Research (PAR) spinner magnetometer. In Pittsburgh, most of the samples were measured in a Superconducting Technology (SCT) cryogenic magnetometer, and some in a PAR spinner magnetometer. A SCT cryogenic magnetometer and a Schoendsted spinner magnetometer (SSM-1A) were used in almost all cases.

Figure 1 Location of the archaeological sites in Mexico sampled for archaeomagnetic research. 

Most directions of the Natural Remanent Magnetization (NRM) showed good clustering with α₉₅ less than 4° and their temporalities consistent with other chronological contexts. Alternative-field demagnetization was done in Oklahoma and Pittsburg laboratories using over 10 samples, only 4 of Teotihuacan. With the 35 data samples from of Mexico in addition to the 29 samples from Guatemala, El Salvador and Honduras, Wolfman constructed the first secular variation curve for Mesoamerica. All the samples were dated by architectural style, ceramics or stratigraphy, which potentially decreases the accuracy of the curve.

3. Methods

4. Results

Many of the new data reported now are included in Bachelor and Master theses of students from Physics, Archaeology and Earth Sciences areas since 2003, whose paleomagnetic experiments and measurements were performed in the Paleomagnetic Laboratories of the Geophysics Institute of the National University of Mexico (CDMX and Morelia). Other data were reported in unpu blished Reports requested by and delivered to the excavation projects headed by the INAH. These reports allow access to data from which there are no digital versions.

In many cases, specimens have a linear and univectorial component of magnetization and the characteristic remanent magnetization (ChRM) may be easily determined as may be observed in examples shown on Figure 2 for well heated and unburnt structures. Principal component analysis was used to get the primary magnetization direction of each sample. Fisher statistics was applied to obtain the mean direction of the samples (^{Fisher, 1953}).

Figure 2 Stereonet, Vectorial Diagram and Demagnetization spectra of representative samples of unburned (TM2601) and burned (CQE1 and Gu15b) stuccos. 

The resulting data are listed in Table 1 and some stereonet examples are shown in Figure 3. We only consider acceptable the samples with α₉₅ less than 10 and until 15 in the case of the unburned stuccos. Nine samples of this type are included in the present catalog belonging to some well identified archaeological contexts and with archaeomagnetic dates that correspond with the chronology of strata.

Figure 3 Stereonet of Mean characteristic magnetization of the unburned samples: Gu1y2, Gu5, TM2604, Xal4, JO01-22, TP78 and of burned samples: Gu13y14, SNE2, TU6, TU17, HT1, LG02. 

Some hysteresis and IRM cycles that exemplify the behavior of many of the samples are reported in Figure 4. The behavior observed corresponds to poor Ti titanomagnetites. Pseudosingle domains are preponderant in the modified Day diagram (^{Day et al., 1977}) by ^{Dunlop (2002)} (Figure 5).

Figure 4 Hysteresis and IRM cycles of the samples Gu10, TU04, Tp30. 

Figure 5 Day diagram of representative samples of Teotihuacan: Ciudadela and Xalla, Sierra de las Navajas, Xalasco, Guachimontones, Tlatelolco, Chapultepec and Xochicalco. 

Temperature-dependent magnetic susceptibility experiments carried out in a Bartington MS2 furnace indicate low-Titanium Titanomagnetites as the principal magnetic carrier. Hematites sometimes co-exist but their contribution in remanent magnetization appears to be minor.

Some examples of the AMS of unburnt and burned stuccos could be observed in the Figure 6. All of the magnetic fabrics are of sedimentary type supporting the hypothesis that the unburned stuccos can record the direction of the geomagnetic field at the time of deposition. Burned samples: CQE1, Tp30 to Tp59 of Teotihuacan and Tu05, 06y7 of Tula. Unburned samples: Tu23 of Tula, Gu10 of Teuchitlán and Jo45 of La Joya.

Figure 6 Magnetic Anisotropy Susceptibility of the burned samples: CQE1 of Teotihuacan TU05,06 & 7 of Tula, TP30 to TP59 of Teotihuacan and Gu10 of Teuchitlan. Anisotropy of Magnetic susceptibility of unburned samples: TU23 of Tula and JO45 of La Joya. (circles - minimum - k3, square - intermediated- k2, triangle -maximum - k1). 

The archaeomagnetic dates of ^{Wolfman (1990b)} were obtained from the curve that he constructed following the distribution of the VGPs and their chronological order based on stratigraphic consideration, ceramics and architecture style. Wolfman proposed two curves: one from AD. 1 to 300 and the other from AD. 300 to 1200.

The curves have a gap between AD. 100 to 300 and between AD. 915 to 1060, because there is a lack of data for these periods. The dating was performed by the intersection of the curve with the direction considering its error (α₉₅).

The secular variation curve from 50 BC. to AD. 1600 obtained in the year 2000 for the archaeomagnetic dating, included the ^{Wolfman data (1990b)} from Mexico, Salvador and Guatemala, as well as the lava flow of Xitle volcano (100 BC.-AD. 60) data of ^{Urrutia-Fucugauchi (1996)} and the stalagmite data DAS2 (AD. 750-1975) of ^{Latham and co-workers (1986)}. We employed the crossing point technique (^{Le Goff et al.,2002}; ^{Noel and Batt,1990}) to get the intersections with the curve and achieve the dating. To better constrain the dates, stratigraphic restrictions were considered. The whole dataset was reduced to Teotihuacan (19.7°N, 261.2°E) because the greatest number of samples comes from this emblematic site.

In 2010 with the publication of the software Rendate (^{Lanos, 2008}) a new curve was modeled with cubic splines and the previous directions were processed obtaining better age restrictions. Figure 7 shows the secular variation curves obtained. Most of the new excavation projects have been taking samples for radiocarbon dating improving the local chronologies (^{Beramendi et al., 2009}) providing new data to complete and expand the secular variation curve of central and south Mexico.

Figure 7 Previous Secular variation curve reduced to Teotihuacan (19.7N,261.2E) with their errors ΔI and ΔD. The curve includes geological and archaeomagnetic data. 

Table 1 compiles all the information concerning the location of samples, and their features: burned or unburned (b/ub), number of specimen employed to calculate the statistical means n, the total number of the specimens in the sample N. The Demag column indicates NRM if the samples were not demagnetized or, the maximum peak demagnetizing field in mT. Dec, Inc and α₉₅ are the parameters of the mean direction of the sample resulted from the Fisher statistic; plat and plong are the paleolatitude and paleolongitude of Virtual Geomagnetic Poles (VGP). Estimated date is the date of the sample assigned by ceramic style, stratigraphy (st) or radiocarbon date (rc) related. Archaeomagnetic date is the date obtained by Rendate software. A key to identify the data Published in Referee Journals (PRJr) or the data of thesis and internals reports (uPRr unPublished in Referee Journals). As can be observed the mean α₉₅ of unburned samples is 8.5 and usually greater than 4°. For unburned samples we accept α₉₅ values less than 15° because of the type magnetization and potential inclination error. In all cases of unburned stuccos, the magnetic fabric has been measured confirming the sedimentary fabric (Figure 6).

5. The PSV curve for Central Mexico

The early proposed curve has been improved by including only data supported by dates obtained by other alternative methods, in our case only radiocarbon data are available. The stalagmite data (^{Latham et al., 1986}) have been removed due to controversy in their records. The data of the Xitle (^{Urrutia-Fucugauchi ,1996}) was also removed to include only archaeomagnetic samples.

The new curve presented includes the archaeomagnetic data of ^{Wolfman (1990b)} and those of the researches carried out in the Laboratory of Paleomagnetism of the UNAM (located in CDMX) and of Morelia Laboratory, the current National Archaeomagnetic Service since 1999, all of them compiled in Table 1.

Fisher’s statistic mean-directions and VGP poles were obtained every 50 years with a mobile window of 100 years. Table 2 shows the results and Figure 8 shows them in an equal area projection. It is important to point out that more data is still needed in the Preclassic time-span (500 BC.-AD. 200), and for the Postclassic especially after AD. 1100.

Figure 8 Stereonet of Virtual Geomagnetic Poles for Central and South of Mexico for 300 BC to AD 1500 every 100 years. 

In Figure 9 we can observe the comparison results amongst the available curves for the SW of USA. The employed data are from papers of ^{Eighmy et al., (1990)}, ^{Lengyel and Eighmy (2002)} and ^{Sternberg and McGuire (1990)}. The data comes from the states of Colorado, Arizona, New Mexico, Arkansas, Missouri, Louisiana and Tennessee. ^{Lengyel and Eighmy (2002)} focused on a proposal to solve the problem of damping by the use of the moving window and to the small number of samples in certain periods. Some large differences are observed between AD. 600 to 650 and AD. 925 to 1100 which can be tentatively attributed more to the lack of reliable data in the SW of USA than to the local non-dipole field, but great differences can be observed between AD. 1200 to 1325 where the lack of data is in Mexico. It is evident that more high-quality data supported by radiometric ages are strongly needed to improve the reference curves of Mesoamerica and SW of USA. Special effort should be place on put to the time intervals of 500 BC. to AD. 200 and AD. 1200 to 1325, which represent the major lack of reliable archaeomagnetic results in Mexico.

Figure 9 Polar Secular variation curves of center and south of Mexico and SW of USA from AD 600 to AD 1500.