THE RELIABILITY OF EARTH S MAGNETIC POLES IN THE MODERN, HISTORICAL AND ANCIENT MODELS. T.I. Zvereva, S.V. Starchenko

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1 THE RELIABILITY OF EARTH S MAGNETIC POLES IN THE MODERN, HISTORICAL AND ANCIENT MODELS T.I. Zvereva, S.V. Starchenko Pushkov institute of Terrestrial Magnetism, ionosphere and Radio wave Propagation (IZMIRAN), Moscow, Troitsk, 14219, Russia, zvereva@izmiran.ru Abstract. We used daily averaged vector magnetic field data from the CHAMP satellite to construct spherical harmonic models of the main geomagnetic field up to n = m = 1 for the period from May 21 to the end of 29 at an interval of 4 days. The Earth s magnetic poles (the points where magnetic field lines are vertical) were modelled on the Earth s surface for each half year average with Gaussian decomposition degree n from 1 till 1. Final result is that models with n = 6 are virtually indistinguishable with n =7, 8, 9, 1 models. Therefore, the spherical harmonic models for the calculation of the virtual magnetic poles should be build at least up to n=6. For this reason the majority of the available ancient (archeo/paleo) magnetic reconstructions are not suitable for magnetic poles modeling, while the historical models (e.g. gufm1) are suitable for that because they are based on real measurements allowing modeling with n=6 and more. Introduction A magnetic pole is viewed as a point on the planetary surface where the magnetic field is entirely vertical. The Earth s magnetic poles located in the North and South hemisphere wander independently of each other. They can migrate rapidly: movement of the North pole up to 63 km per year in 23 have been observed. The direct measurements of the magnetic poles are hard and so scare that the first motivation of this study was to model the magnetic poles for the last decade that is actually not properly covered. In generic planetary respect magnetic poles are determining magnetosphere shape and dynamics of its most active places cusps. However the intrinsic magnetic field of the planets is estimated not so well comparing to the Earth where having Gaussian decomposition degree n up to 13 we could perfectly model magnetic poles positions and dynamics. So, in this research we are looking for the lowest degree n at which the model properly resembles the magnetic poles modeled at the highest degree n. In the same fashion we are modeling geomagnetic field at core-mantle boundary of the Earth in order to set up the lower resolution limit for satellite magnetic measurements capable to detect at least some generic planetary dynamo properties. Data and methods The vector measurements of the magnetic field on the CHAMP German satellite ( performed from May 21 until the end of 29 were used as data. The spherical harmonic models of the Earth s magnetic field were obtained using Janovsky (1978) formulas: n+ 1 N n a m m m U(r, θ, λ) = a (g n cosmλ + h n sin mλ)pn (cosθ), n= 1m= r 1 du 1 du du X = Y = Z =, r dθ rsin θ dλ dr where U is the geomagnetic potential at a point with geographic coordinates r, θ, λ (radius, co-latitude, and longitude); X, Y, and Z are the northern, eastern and vertical (downward) field components; а is the average radius of the Earth; P m n (cosθ) are the Legendre associated functions of power n and order m in the Schmidt normalization; and g m and h m n n are constant Gaussian coefficients. The available field measurements are used to calculate the g m and h m n n coefficients, which make it possible to calculate the field at any point, e.g., to find the poles coordinates. 66

2 Average daily spherical harmonic models of the main geomagnetic field were constructed for the above period at an interval of four days. All available measurements within one day with a 1_s resolution were taken (about 86 points). The models up to n = m = 1 (the number of spherical coefficients is 12) and the time variations in each coefficient were finally obtained for the above interval. It is clear that it is not necessary to use such a discreteness of the constructed models in order to reveal the tendency in pole motion variations, and models could be constructed without such a time resolution. However, after a half year averaging and having obtained only 16 points, we partially eliminated the model errors related to the neglect of the contribution of external fields to the models by Zvereva (212). Results Gaussian coefficients for intrinsic geomagnetic field were found on each fourth day using satellite data. The magnetic poles were modeled on the Earth s surface for each half year average with Gaussian decomposition degree n from 1 till 1. The results are shown in Fig. 1-3 for the magnetic pole located in the Northern hemisphere n=3 n=2 8 n= n=1 n=2 n=3 Fig. 1. The North geomagnetic pole tracks for n = 1, 2, 3, 1 n=9 n=7 n= Fig. 2. The North geomagnetic pole tracks for n = 7, 8, 9, 1 n=9 n=8 n=7 67

3 87 86 n=5 n=4 Latitude, [deg] n= Longitude, [deg] n=6 n=5 n=4 Fig. 3. The North geomagnetic pole tracks for n = 4, 5, 6, 1 In the same fashion neglecting by the mantle conductivity we also modeled magnetic flux space-time distributions on core-mantle boundary. The maps of the Z-component of the magnetic field on core-mantle boundary for the models with n = 1, 7, 4 on Fig. 4-6 are shown. N= Fig.4. The Z/1 - component of the magnetic field on core-mantle boundary. core radius is taken equal to half the radius of the Earth. This map is constructed on the model with n = 1 for 29 N= Fig.5. The Z/1 - component of the magnetic field on core-mantle boundary. The core radius is taken equal to half the radius of the Earth. This map is constructed on the model with n = 7 for 29 68

4 N= Fig.6. The Z/1 - component of the magnetic field on core-mantle boundary. The core radius is taken equal to half the radius of the Earth. This map is constructed on the model with n = 4 for 29 Final result is that models with n = 7 are virtually indistinguishable with n = 8, 9, 1 models, while magnetosphere and geodynamo related integral properties start to converge at n=5 already. Thus planetary magnetic field should at least be known up to n=6 degree in order to make plausible conclusions about related to the dip poles magnetosphere properties and related to the magnetic fluxes hydromagnetic dynamo features. Discussion Up to five centuries buck from the present time many direct geomagnetic measurements were performed (Bondar et al., 22; Jackson et al., 2) first by marine explorers and then in the specially designed observatories started by Gauss and Weber in 1 s. Those measurements quality and quantity allow geomagnetic modelling with Gaussian coefficients n sufficiently more than 5 as, for example that was done in gufm1 model by Jackson et al. (2). Therefore the geomagnetic pole position could be successfully modelled up to the beginning of 16th century, while it was not done properly yet. Besides the geomagnetic intensity measurements are started in 1 s only. So, it is not clear are the previous data enough reliable for such pole modelling or not? Going deeper in time we start to experience difficulties with the number and especially with the quality of the geomagnetic data. Archeomagnetic records operate with millenniums time-scale, but they could hardly reach n=4 as it is in the model by Korte et al. (25). Millions years paleomagnetic models are obviously even worst with their highest n=2, e.g. see Hatekayama and Kono (22). For this reason such ancient (archeo/paleo) magnetic reconstructions are not suitable for magnetic poles modeling at the Earth s surface. However, the magnetosphere and its cusps are forming many thousands kilometers above this surface. The magnetic poles at those positions should be much smaller affected by the higher n spherical harmonics. Thus archeomagnetic or even paleomagnetic models could become suitable for such super-higher altitude dip pole modelling and this is the subject for our future researches. Conclusion The Earth models with n about 7 are virtually indistinguishable with models, while magnetosphere and dynamo related polar properties start to converge at n=m=5 already. Therefore, the spherical harmonic models for the calculation of the virtual magnetic poles should be build at least up to n=6. For this reason the majority of the available ancient (archeo/paleo) magnetic reconstructions are not suitable for magnetic poles modeling at the Earth s surface, while the historical (up to 16th century) models are suitable when they are based on real measurements allowing modeling with n=6 and more. 69

5 References Bondar, T.N., Golovkov V.P., Yakovleva S.V. (22) Spatial-temporary model of the secular variation of geomagnetic field from 1 till 2, Geomagnetism and Aeronomy 42, 1-7. Jackson, A., Jonkers, A.R.T., Walker, M.R. (2) Four centuries of geomagnetic secular variation from historical records, Philos. Trans. R. Soc. Lond. 358, Janovsky, B.M. (1978) Terrestrial magnetism, Leningrad: Leningrad State University, 4 p. Hatekayama, T., Kono, M. (22) Geomagnetic field model for the last 5 My: time-averaged field and secular variation, Phys. Earth Planet. Inter., 133, Korte, M., Genevey A., Constable C. G., Frank, U., Schnepp, E. (25) Continuous geomagnetic field models for the past 7 millenia: 1. A new global data compilation, Geochem. Geophys. Geosyst. 6(2), Q2H15, doi:1.129/24gc8. Zvereva, T.I. (212) Motion of the Earth s Magnetic Poles in the Last Decade, Geomagnetism and Aeronomy 52, , doi: /S