Geomagnetic Intensity Research Articles

Uncertainty Estimation in the Neural Model for Aeromagnetic Compensation

Measuring the performance of an aeromagnetic compensation system is usually difficult. The standard deviation of the signal has been used as an index in the industry. While the standard deviation is drawn from frequency statistics, it cannot represent the performance on a single sampling point. On the other hand, as the true geomagnetic intensity is unknown, the signal’s deviation is actually an approximate measurement of the residual error. This letter first analyzes the traditional neural model for aeromagnetic compensation to reveal the fact that the model can only estimate the expectation of interference. Then, we introduce a stochastic hidden variable to predict the standard deviation synchronously. The proposed model is derived from variational inference and trained as a stochastic gradient variational Bayes estimator. Simulations are performed to show the correlation between the true residual error and the estimated standard deviation.

Geomagnetic Dipole Changes and Upwelling/Downwelling at the Top of the Earth's Core

The convective state of the top of Earth's outer core is still under debate. Conflicting evidence from seismology and geomagnetism provides arguments for and against a thick stably stratified layer below the core-mantle boundary. Mineral physics and cooling scenarios of the core favor a stratified layer. However, a non-zero secular variation of the total geomagnetic energy on the core-mantle boundary is evidence for the presence of radial motions extending to the top of the core. We compare the secular variation of the total geomagnetic energy with the secular variation of the geomagnetic dipole intensity and tilt. We demonstrate that both the level of cancellations of the sources and sinks of the dipole intensity secular variation, as well as the level of cancellations of the sources and sinks of the dipole tilt secular variation, are either larger than or comparable to the level of cancellations of the sources and sinks of the total geomagnetic energy secular variation on the core-mantle boundary, indicating that the latter is numerically significant hence upwelling/downwelling reach the top of the core. Radial motions below the core-mantle boundary are either evidence for no stratified layer or to its penetration by various dynamical mechanisms, most notably lateral heterogeneity of core-mantle boundary heat flux.

Variations of Earth Magnetic Field Intensity for the Past 5 Myr Derived From Marine Magnetic Anomalies in a Slow‐to‐Intermediate Spreading South Atlantic Ridge

AbstractWe investigated sea‐surface magnetic anomaly data for the past 5 Myr in the slow‐to‐intermediate spreading South Atlantic Ridge. After error analysis and signal processes, the sea surface magnetic anomaly profiles were downward continued to 1.5 km below sea level, and then the distance from spreading axis was converted to time by matching the observed anomalies with forward models of known polarity reversals. The stacked anomaly profiles from South Atlantic Ridge exhibit short‐wavelength wiggles superimposed on the first‐order variations of magnetic anomalies. The stacked anomaly profiles were first compared with commonly used geomagnetic palaeointensity data synthesized from sedimentary relative intensity records in the past and were further correlated with other available magnetic profiles derived from Central Indian Ridge, East Pacific Rise, and Pacific‐Antarctic Ridge. We found that short wavelength variations in the South Atlantic Ridge can be ascribed to geomagnetic intensity variations from excursions or short polarity events. Spectral analysis of marine magnetic anomalies records reveals that there is no obvious dominant periodicity for the geomagnetic field behavior during the past 5 Myr.

Archaeomagnetic evidence of pre-Hispanic origin of Mezcal

For centuries, and until a few years ago, it was considered that the distillation process had been brought to the new world by the Spaniards, who in turn learned it from the Arabs. For this reason, it was believed that the only alcoholic beverage of the Mesoamerican societies was pulque - a ferment of maguey. However, recent archaeological investigations revealed that the alcohol distillation was known in Mesoamerica long before the arrival of Europeans, for at least 25 centuries. The direct evidence comes from the ceremonial and administrative center of Xochitécatl-Cacaxtla (state of Tlaxcala) with several ovens where cooked maguey remains were discowered. The corresponding archaeological context was radiometrically dated from 600 to 400 BCE. Here, we report a detailed archaeomagnetic study on burned archaeological artifacts found in these cooking ovens. 35 specimens belonging to two pottery fragments, one burned rock and two burned soil samples were pre-selected for archaeointensity experiments. Pottery samples exhibited essentially reversible behavior during thermomagnetic experiments pointing to Ti-poor titanomagnetite (almost magnetite phase) as main magnetic carrier while two ferromagnetic phase seems to co-exist in burned soils. In contrast, burned rock samples exhibited some instabilities during the heating at high temperatures and indirect evidence of the presence of antiferromagnetic hematite grains. In total, 29 specimens allowed the estimation of absolute geomagnetic intensity recorded during the last use of the furnace. Archaeomagnetic dating yielded two possible time intervals between 878 to 693 BCE and 557 to 487 BCE. These new data reinforce the initial hypothesis and corroborate the temporality of these pre-Hispanic kilns.

Basement structure and properties of the southern Junggar Basin

We have investigated the detailed structures of velocity, density and magnetization intensity along a nearly east-west profile from Liugou to Dajing across the southern Junggar Basin using the seismic converted wave profiling and joint inversion of gravity and geomagnetic data. Our observations reveal such important interfaces as interface B (the top surface of the folded basement), interface G (the top surface of the crystalline basement), interfaces C1 and C2 (interfaces within the crust), and the Moho (the bottom of the crust). Our results indicate that the crust of southern Junggar Basin with a thickness of 45–50 km and the average velocity of ∼6.3 km/s is mainly composed of an upper crust (including a deposited cover), a middle crust and a lower crust. The top surface of the crystalline basement (G) and the bottom of the crust (Moho) undulate in a same way, indicating an integrated crustal deformation. A series of faults developed in the basin are oriented nearly north-south and cut through the crystalline crust. The faults serve as passageways connecting the crust and upper mantle and are inferred to have formed by north-south compression and east-west extension. We propose that materials from the upper mantle migrate upward into the crust, intrude laterally, and mix up with the crustal materials, producing a crystalline crust in the basin with high velocity, high density and high geomagnetic intensity. Our observations suggest that the southern Junggar Basin bears a single basement layer whose properties have been changed by the exchange of the materials and the energy of the crystalline crust with those from the upper mantle.

A compensation method for the carrier interference of a three-component magnetic measurement system using a Cuckoo search algorithm

The magnetic interference field generated by ferromagnetic materials on the carrier decreases measurement precision, which has been a crucial factor limiting the application of three-component magnetic measurement. In this paper, a magnetic compensation method based on the Cuckoo search (CS) algorithm is proposed. The method can be separated into three steps. First, a measurement error model is established, based on which a formula of the absolute error sum will be derived. Then, compensation parameters are estimated using the CS algorithm by minimizing the absolute error sum. Finally, the geomagnetic intensity is calculated using estimates of the compensation parameters and measured data. As the CS algorithm possesses the advantages of insensitivity to iterative initial values and strong global search ability, optimal estimates of the compensation parameters can be obtained accurately using this method, which ensures high compensation precision. The experimental results show that, after compensation, the maximum error of the x-component can be reduced from 622 nT to 26 nT, the y-component from 329 nT to 19 nT, and the z-component from 669 nT to 15nT.

Last three millennia Earth’s Magnetic field strength in Mesoamerica and southern United States: Implications in geomagnetism and archaeology

Earth’s Magnetic Field variation strength may provide crucial information to understand the geodynamo mechanism and elucidate the conditions on the physics of the Earth’s deep interiors. Aimed to reveal the fine characteristics of the geomagnetic field during the last three millennia in Mesoamerica, we analyzed the available absolute geomagnetic intensities associated to absolute radiometric dating as well some ages provided by historical documents. This analysis is achieved using thermoremanent magnetization carried by volcanic lava flows and burned archaeological artefacts. A total of 106 selected intensities from Mesoamerica and other 100 from the southern part of the United States represent the main core of the dataset to construct the variation curve using both combined bootstrap method and temporal penalized B-spline methods. The obtained intensity paleosecular variation curve for Mesoamerica generally disagrees with the values predicted by the global geomagnetic field models. There is rather firm evidence of eastward drift when compared to similar reference curves in Western Europe, Asia and Pacific Ocean. The recent hypothesis about the relationship between the geomagnetic field strength and paleoclimate is also critically analyzed in the light of this new data compilation.

Effects of solar activity and galactic cosmic ray cycles on the modulation of the annual average temperature at two sites in southern Brazil

Abstract. Quasi-periodic variations in solar activity and galactic cosmic rays (GCRs) on decadal and bidecadal timescales have been suggested as a climate forcing mechanism for many regions on Earth. One of these regions is southern Brazil, where the lowest values during the last century were observed for the total geomagnetic field intensity at the Earth's surface. These low values are due to the passage of the center of the South Atlantic Magnetic Anomaly (SAMA), which crosses the Brazilian territory from east to west following a latitude of ∼ 26∘. In areas with low geomagnetic intensity, such as the SAMA, the incidence of GCRs is increased. Consequently, possible climatic effects related to the GCRs tend to be maximized in this region. In this work, we investigate the relationship between the ∼ 11-year and ∼ 22-year cycles that are related to solar activity and GCRs and the annual average temperature recorded between 1936 and 2014 at two weather stations, both located near a latitude of 26∘ S but at different longitudes. The first of these stations (Torres – TOR) is located in the coastal region, and the other (Iraí – IRA) is located in the interior, around 450 km from the Atlantic Ocean. Sunspot data and the solar modulation potential for cosmic rays were used as proxies for the solar activity and the GCRs, respectively. Our investigation of the influence of decadal and bidecadal cycles in temperature data was carried out using the wavelet transform coherence (WTC) spectrum. The results indicate that periodicities of 11 years may have continuously modulated the climate at TOR via a nonlinear mechanism, while at IRA, the effects of this 11-year modulation period were intermittent. Four temperature maxima, separated by around 20 years, were detected in the same years at both weather stations. These temperature maxima are almost coincident with the maxima of the odd solar cycles. Furthermore, these maxima occur after transitions from even to odd solar cycles, that is, after some years of intense GCR flux. The obtained results offer indirect mathematical evidence that solar activity and GCR variations contributed to climatic changes in southern Brazil during the last century. A comparison of the results obtained for the two weather stations indicates that the SAMA also contributes indirectly to these temperature variations. The contribution of other mechanisms also related to solar activity cannot be excluded. Keywords. Meteorology and atmospheric dynamics (climatology)

Last two millenia Earth's Magnetic Field strength: New archaeointensity determinations from Ichkaantijo, Early to Late Maya Classic period

We report a detailed rock-magnetic and absolute geomagnetic intensity analysis performed on forty eight samples belonging to eight pre-Columbian potteries from the Ichikaantijo area, near Merida city in the Yucatan Peninsula. Twenty six samples out of 48 analyzed, yielded reliable archaeointensity determinations which allowed estimating the geomagnetic field strength fluctuations for the central and northern Maya region during the Early to late Classic periods. The combined analysis of archaeointensity results obtained in this study with existing similar quality determinations indicate the persistence of substantially low geomagnetic field strength during the time interval involved, contrasting with the values predicted by the global geomagnetic field models. It seems that a large period of low geomagnetic field strength prevailed at the Maya area just before the so-called Mayan Collapse.

A Study on the Model of Detecting the Variation of Geomagnetic Intensity Based on an Adapted Motion Strategy.

By simulating the geomagnetic fields and analyzing the variation of intensities, this paper presents a model for calculating the objective function of an Autonomous Underwater Vehicle (AUV) geomagnetic navigation task. By investigating the biologically inspired strategies, the AUV successfully reaches the destination during geomagnetic navigation without using the priori geomagnetic map. Similar to the pattern of a flatworm, the proposed algorithm relies on a motion pattern to trigger a local searching strategy by detecting the real-time geomagnetic intensity. An adapted strategy is then implemented, which is based on the specific target. The results show the reliability and effectiveness of the proposed algorithm.

A Geomagnetic Paleointensity Record of 0.6 to 3.2 Ma From Sediments in the Western Equatorial Pacific and Remanent Magnetization Lock‐In Depth

AbstractInformation of past geomagnetic intensity variations is important for better understanding of the geodynamo, and efforts to recover continuous paleointensity records continue, in particular for ages older than 2 Ma. In this study, a new relative paleointensity (RPI) record of 0.6 to 3.2 Ma was obtained from a sediment core in the western equatorial Pacific, which has good age control by the oxygen isotope stratigraphy from 2.0 to 3.2 Ma. The RPI record could well be correlated to existing RPI templates despite the low sedimentation rate of ~5 m/Ma and will be useful for future construction of a stacked paleointensity curve beyond 2 Ma. Magnetic minerals of the core consist mainly of biogenic and terrigenous oxidized magnetite. Some rock magnetic contamination to long‐term RPI changes is recognized; RPI inversely correlates with the ratio of anhysteretic remanent magnetization to saturation remanent magnetization, which may be caused by differences in remanence acquisition efficiency between the biogenic and terrigenous magnetic components. The lock‐in depth of the studied core is estimated to be approximately 0 from a line of evidence including no apparent offset between RPI and cosmogenic beryllium nuclide flux changes across some polarity boundaries. Lock‐in depths vary locally from core to core or even within a single core and have no obvious relation with sedimentation rates and carbonate contents. Lock‐in depths may be controlled by factors that are currently difficult to be evaluated, such as variations in sediment flocculation sizes and biogeochemical remanent magnetization dependent to chemical conditions of sediments.

Archaeomagnetic Dating of Pyrotechnological Contexts: a Case Study for Copper Smelting Sites in the Central Timna Valley, Israel

This study is focused on establishing age constraints for several copper slag deposits at the centre of the Timna Valley (Israel) via reconstruction of their ancient geomagnetic intensities as recorded by the individual slag samples at the time of their formation. The results show a correlation between the location of the slag deposits (labelled as individual ‘mounds’ in our survey) and their inferred ages, reflecting varying socio‐economic and political dynamics in the region. While the slag mounds found at the unprotected foothills represent a variety of dates (mostly Early Islamic), the slag mounds on the hilltops are chronologically constrained to the early Iron Age (late 11th to 10th centuries bce), supporting the idea for a need for protection during this period. Furthermore, in comparing the new data with previous archaeomagnetic studies from Timna, we can assert the existence of simultaneous copper production at the archaeological Sites 30, 30a and 34. This gives further support to the claim of intense smelting in the central Timna Valley during the early Iron Age. Finally, this project demonstrates the potential of archaeomagnetic experiments to provide chronological insights, and their particular advantage in addressing pyrotechnology‐related cases.

A 17,000 yr paleomagnetic secular variation record from the southeast Alaskan margin: Regional and global correlations

High-resolution sedimentary records on two cores from the Gulf of Alaska margin allow development of a ∼17,400-yr reconstruction of paleomagnetic secular variation (PSV). General agreement between the two records on their independent chronologies confirms that local PSV is recorded, demonstrating that such archives, notwithstanding complexities due to variable sedimentary regimes, deposition rates, and diagenetic conditions, provide meaningful information on past changes of the geomagnetic field. Comparisons with other independently dated sedimentary paleomagnetic records from the NE Pacific indicate largely coherent inclination records that in combination create a NE Pacific sedimentary inclination anomaly stack (NEPSIAS) capturing the common signal over an area spanning >30° longitude and latitude from Alaska through Oregon to Hawaii. Comparisons of NEPSIAS with high quality declination records from the northern North Atlantic (NNA) show that negative (shallow) inclination anomalies in NEPSIAS are associated with eastward NNA declinations while positive (steep) inclination anomalies in NEPSIAS are associated with westward NNA declinations. Comparison of these directional records to regional geomagnetic intensities over the past ∼3000 yrs in North America and back nearly 8000 yrs in the Euro/Mediterranean region, are consistent with a driving mechanism of oscillations in the relative strength of the North American and Euro/Mediterranean flux lobes. The persistence of these dynamics through the Holocene implicates a long-lived organizing structure likely imposed on the geomagnetic field by the lower mantle and/or inner core. These observations underscore a fundamental connection between directional PSV in the North Pacific with that of the North Atlantic, supporting the potential for long-distance correlation of directional PSV as a chronostratigraphic tool.

Absolute geomagnetic intensity record from pre-Columbian pottery dates elite Tlailotlacan Woman in ancient Teotihuacan

A detailed rock-magnetic and archaeomagnetic investigation were carried out on seven pottery fragments (49 specimens) found within the burial of an individual with the most body/dental modifications and prestige elements found so far in the ancient Teotihuacan city. The skull of this 35 to 40years old woman (at the time of death) shows an intentional cephalic modification with frontal-occipital compression. This is very uncommon within the Teotihuacan population and indicating the southern provenance (Oaxaca or Maya area). The age estimations, based on relative datings, placed the archaeological context between 350 and 400CE. The magnetic mineralogy experiments were characterized by a single remanence component, occasionally accompanied by a soft overprint, probably of viscous origin and Curie temperatures between 540°C and 565°C. Only twelve specimens, belonging to two distinct pottery fragments, yielded reliable determinations meeting very strict selection criteria. The values retrieved from both fragments are statistically undistinguishable. The absolute age estimation of the Tlailotlacan Woman archaeological context obtained in this study contradicts the early estimations and indicates a late time interval between 650 and 800CE corresponding to the decline of Teotihuacan, where the social differences of their inhabitants became much more evident.

Asymmetry in growth and decay of the geomagnetic dipole revealed in seafloor magnetization

Geomagnetic intensity fluctuations provide important constraints on time-scales associated with dynamical processes in the outer core. PADM2M is a reconstructed time series of the 0–2 Ma axial dipole moment (ADM). After smoothing to reject high frequency variations PADM2M's average growth rate is larger than its decay rate. The observed asymmetry in rates of change is compatible with longer term diffusive decay of the ADM balanced by advective growth on shorter time scales, and provides a potentially useful diagnostic for evaluating numerical geodynamo simulations. We re-analyze the PADM2M record using improved low-pass filtering to identify asymmetry and quantify its uncertainty via bootstrap methods before applying the new methodology to other kinds of records. Asymmetry in distribution of axial dipole moment derivatives is quantified using the geomagnetic skewness coefficient, sg. A positive value indicates the distribution has a longer positive tail and the average growth rate is greater than the average decay rate. The original asymmetry noted by Ziegler and Constable (2011) is significant and does not depend on the specifics of the analysis.A long-term record of geomagnetic intensity should also be preserved in the thermoremanent magnetization of oceanic crust recovered by inversion of stacked profiles of marine magnetic anomalies. These provide an independent means of verifying the asymmetry seen in PADM2M. We examine three near-bottom surveys: a 0 to 780 ka record from the East Pacific Rise at 19°S, a 0 to 5.2 Ma record from the Pacific Antarctic Ridge at 51°S, and a chron C4Ar–C5r (9.3–11.2 Ma) record from the NE Pacific. All three records show an asymmetry similar in sense to PADM2M with geomagnetic skewness coefficients, sg>0. Results from PADM2M and C4Ar–C5r are most robust, reflecting the higher quality of these geomagnetic records. Our results confirm that marine magnetic anomalies can carry a record of the asymmetric geomagnetic field behavior first found for 0–2 Ma in PADM2M, and show that it was also present during the earlier time interval from 9.3–11.2 Ma.

Reconstructing the Geomagnetic Field in West Africa: First Absolute Intensity Results from Burkina Faso

We present absolute geomagnetic intensities from iron smelting furnaces discovered at the metallurgical site of Korsimoro, Burkina Faso. Up to now, archaeologists recognized four different types of furnaces based on different construction methods, which were related to four subsequent time periods. Additionally, radiocarbon ages obtained from charcoal confine the studied furnaces to ages ranging from 700–1700 AD, in good agreement with the archaeologically determined time periods for each type of furnace. Archaeointensity results reveal three main groups of Arai diagrams. The first two groups contain specimens with either linear Arai diagrams, or slightly curved diagrams or two phases of magnetization. The third group encompasses specimens with strong zigzag or curvature in their Arai diagrams. Specimens of the first two groups were accepted after applying selection criteria to guarantee the high quality of the results. Our data compared to palaeosecular variation curves show a similar decreasing trend between 900–1500 AD. However, they reveal larger amplitudes at around 800 AD and 1650 AD than the reference curves and geomagnetic field models. Furthermore, they agree well with archaeomagnetic data from Mali and Senegal around 800 AD and with volcanic data around 1700 AD.

Causal mechanisms of seismo-EM phenomena during the 1965\u20131967 Matsushiro earthquake swarm

The 1965–1967 Matsushiro earthquake swarm in central Japan exhibited two unique characteristics. The first was a hydro-mechanical crust rupture resulting from degassing, volume expansion of CO2/water, and a crack opening within the critically stressed crust under a strike-slip stress. The other was, despite the lower total seismic energy, the occurrence of complexed seismo-electromagnetic (seismo-EM) phenomena of the geomagnetic intensity increase, unusual earthquake lights (EQLs) and atmospheric electric field (AEF) variations. Although the basic rupture process of this swarm of earthquakes is reasonably understood in terms of hydro-mechanical crust rupture, the associated seismo-EM processes remain largely unexplained. Here, we describe a series of seismo-EM mechanisms involved in the hydro-mechanical rupture process, as observed by coupling the electric interaction of rock rupture with CO2 gas and the dielectric-barrier discharge of the modelled fields in laboratory experiments. We found that CO2 gases passing through the newly created fracture surface of the rock were electrified to generate pressure-impressed current/electric dipoles, which could induce a magnetic field following Biot-Savart’s law, decrease the atmospheric electric field and generate dielectric-barrier discharge lightning affected by the coupling effect between the seismic and meteorological activities.

Six centuries of geomagnetic intensity variations recorded by royal Judean stamped jar handles

Earth's magnetic field, one of the most enigmatic physical phenomena of the planet, is constantly changing on various time scales, from decades to millennia and longer. The reconstruction of geomagnetic field behavior in periods predating direct observations with modern instrumentation is based on geological and archaeological materials and has the twin challenges of (i) the accuracy of ancient paleomagnetic estimates and (ii) the dating of the archaeological material. Here we address the latter by using a set of storage jar handles (fired clay) stamped by royal seals as part of the ancient administrative system in Judah (Jerusalem and its vicinity). The typology of the stamp impressions, which corresponds to changes in the political entities ruling this area, provides excellent age constraints for the firing event of these artifacts. Together with rigorous paleomagnetic experimental procedures, this study yielded an unparalleled record of the geomagnetic field intensity during the eighth to second centuries BCE. The new record constitutes a substantial advance in our knowledge of past geomagnetic field variations in the southern Levant. Although it demonstrates a relatively stable and gradually declining field during the sixth to second centuries BCE, the new record provides further support for a short interval of extreme high values during the late eighth century BCE. The rate of change during this "geomagnetic spike" [defined as virtual axial dipole moment > 160 ZAm2 (1021 Am2)] is further constrained by the new data, which indicate an extremely rapid weakening of the field (losing ∼27% of its strength over ca. 30 y).

Analysis of the global ionospheric disturbances of the March 2015 great storm

AbstractThe global ionospheric storm in March 2015 was investigated by using data from over 3000 GPS stations worldwide. In this study, total electron content (TEC), rate of TEC (ROT), and ROT's standard deviation rate of the TEC index, as well as the second‐order difference operator TECT, were considered as main characteristic methods to distinguish ionosphereic disturbances. The results show that (1) based on the multiple methods above, we all observed that for the first time, there were three equatorward traveling ionospheric disturbances (TIDs) in the main phase of this storm. In North America, the disturbance zone expanded to ~40°N; the disturbance periods and AE peak stages were roughly synchronous. We suggest that these three TIDs were induced by the propagation of atmospheric gravity waves to low latitudes under the action of AE. (2) The most intense positive storm occurred over South America and the South Atlantic (over 300% enhancement; 00:00–05:00 UT on 18 March), whereas a negative storm was observed in the corresponding region of the Northern Hemisphere. Such inverse hemispheric asymmetry in intensity and structure can be explained by the variations of the thermospheric composition, the IMF By component, and the geomagnetic intensity. (3) On 18 March, a negative storm dominated globally (except at certain low latitudes), and tended to propagate equatorward and decay with time, which could be largely attributed to the storm circulation theory. And the evolution of the negative storm was further characterized by the foF2 variations of ionosondes.

First evidence of complex dental practice about 1300 BP in Mesoamerica revealed by absolute geomagnetic intensity

Deliberated dental modifications and mutilations are known since prehistoric times. The Mayas and other ancient cultures in Mesoamerica were considered pioneers of such practice. The evidences of therapeutic intervention, however, are still poorly documented and credible examples are extremely scarce. One of the burials excavated at the locality of La Mina (Michoacan, Mexico) corresponds to a 30-35 year old male individual named Alvaro, who presented a well-marked dental deformation. Moreover, Alvaro had a quite deep and symmetrical perforation in the upper right canine–a treatment similar to the procedure of endodontics or root canal. The archaeological context of Alvaro’s habitat was dated using the archaeomagnetic method applied to pottery samples unambiguously correlated to the burial. The analysis supplied a time interval between 647 and 825 AD suggesting the first evidence of complex dental practice in the Americas.