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ISSN 0016 7932, Geomagnetism and Aeronomy, 2012, Vol. 52, No. 7, pp. 944952. © Pleiades Publishing, Ltd., 2012.

Manifestation of Solar and Geodynamic Activity in the Dynamics of the Earth's Rotation
V. L. Gorshkov, N. O. Miller, and M. V. Vorotkov
Central Astronomical Observatory, Russian Academy of Sciences, Pulkovo, St.Petersburg, Russia e mail: vigor@gao.spb.ru
Received March 5, 2012

Abstract--The relationships between different manifestations of solar and geomagnetic activity and the structural peculiarities of the dynamics of the pole wobble and irregularities in the Earth's rotation are studied using singular spectrum analysis. There are two close major peaks and several lower ones in the same fre quency range (1.11.3 years) in the Chandler wobble (CW) spectrum. Components in the geomagnetic activ ity were distinguished in the same frequency band (by the Dst and Ap indices). Six to seven year oscillations in the Earth's rotation rate with a complex dynamics of amplitude variations are shown in variations in geo magnetic activity. It is revealed that secular (decade) variations in the Earth's rotation rate on average repeat global variations in the secular trend of the Earth's geomagnetic field with a delay of eight years during the whole observation period. DOI: 10.1134/S0016793212070043

1. INTRODUCTION The causes of low frequency decade and secular variations in geophysical processes are difficult to inter pret because monitoring instruments have only been available for a short period of time (200300 years). At the same time, their significance permanently increases both in terms of scientific and applied (prog nostic for climate changes) aspects. Low frequency interannual variations are also present in the Earth's rotation dynamics, represented by the series of the Earth's rotation parameters (ERP), such as the pole coordinates {Xp,Yp} and variations in the Earth's rotation rate (variations in the length of the day LOD = 86400 LOD s). These variations are of a complex irregular nature, which reflects the interac tion of the lithosphere, where all instruments for ERP monitoring are located, with geophysical processes mainly in the Earth's fluid layers and in the liquid core. The geophysical functions of the atmospheric (AAM), ocean (OAM), hydrosphere (HAM), and inner core angular momenta (CAM) are calculated using corre sponding (mainly model) data. Thus, if one solves the inverse problem, then varia tions in the Earth's rotation vector can serve as an indicator of these processes. At the same time, the dynamics of geophysical processes is supported by the influence of solar activity and the activity of the Earth's interior (core and mantle), including the Earth's geomagnetic activity. Two groups of hypotheses try to explain the causes of the appearance of long term variations in the Earth's rotation dynamics. Hypotheses about the excitation of ERP variations by electromagnetic and

gravitational interactions at the coremantle bound ary are the most popular (Holme, 1998; Dumberry and Bloxham, 2002; Spiridonov and Yakimenko, 2003). However, to build an adequate theory, the avail able data on the model parameters are insufficient; therefore, estimation of the possible effect of angular momenta, which appear at this boundary and are recorded in the form of geomagnetic variations, is used more often (Hide et al., 2000; Bellanger et al., 2002). The second group of hypotheses assumes that the Sun ^ is a source of excitation (Djurovic and PБquet, 1996; Abarca del Rio et al., 2003). Statistical relationships between the index of solar and geomagnetic activity and variations in the Earth rotation rate (LOD) or variations in the CW amplitude are mainly considered in these works. In this work, variations in the LOD and CW ampli tudes are studied using the multidimentional singular spectrum analysis (MSSA) method along with solar and geomagnetic indices. This method allows us to reveal the general structure in a set of jointly studied series with an assumed interdependence. The method has good frequency and time resolutions, which allows one to develop a new approach to the joint analysis of a large volume of dissimilar data. Only interannual and secular variations in the Earth's rotation vector are studied in this work, along with solar activity, among the whole variety of varia tions, and only those, the nature of which is unclear, including decade variations in the Earth's rotation rate, with periods of 4070 years and amplitudes of 3 4 ms and 57 year variations with amplitudes up to 0.3 ms. The excitation of 2 to 3 year variations in

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MANIFESTATION OF SOLAR AND GEODYNAMIC ACTIVITY

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LOD is satisfactorily explained by AAM, while the excitation of 5 to 7 year variations remains hypothet ical (Gorshkov, 2010). The CW with a period of 428 435 days is the most questionable in the pole wobble in view of both excitation and amplitude modulation. 2. DATA Data on the solar and geomagnetic indices were taken from the Geophysical Data Center in Boulder (ftp.ngdc.noaa.gov/STP/SOLAR_DATA/). We used data on the radio flux at an F10.7 cm wavelength (beginning from 1947), the FI flare activity index (from 1966), and the Ap (19322010) and Dst (1957 2008) geomagnetic indices. These data have been reduced to an equal time interval of 0.05 year. Monthly average series of areas (SSAr) and sunspot numbers (SSN) in 17502010 were taken from (Nagovitsyn, 2005). The composite series ACRIM(1,2,3) Nimbus7 of total solar irradiance (TSI) for 1978 2010, described in (Wilson and Mordvinov, 2003), were used after 27 day moving averaging with a further interpolation to 0.05 year. Annual average geomagnetic data (X, Y, Z) for 18432010 were taken from the World Data Center (ftp.nmh.ac.uk/wdc/obsdata/) in Edinburgh. Monthly INTERMAGNET geomagnetic data (Chulliat and Telali, 2007) for 18832007 were also used for com parison. Observatory data were used for calculations of secular variations in the Earth's magnetic field (SVN, SVE, SVU). ERP series C01 from 1846, C04 from 1962, AICAS for 19561992, and LUNAR97 for 18321997 were taken from the data of the International Earth Rotation Service (http://hpiers.obspm.fr/eop pc/), as well as the functions of the atmospheric (AAM, NCEP/NCAR reanalysis, 19482009) and ocean (OAM, ECCO_50y, 19492002) angular momenta. To increase the length of the ERP series, their combinations after valid proce dures of their conjunction were also used. In particular, the AICAS series extended by the C04 series is desig nated in the work as eopAO. All known tidal variations from 5 days to 18 years were removed from the LOD series. It should be kept in mind that an increase in the length of the day corresponds to a decrease in the Earth's rotation rate. Since data on the AAM and OAM momenta excit ing the Earth's rotational dynamics are available starting from the second half of the 20th century, the geophysical excitation reduction of ERPs is also pos sible beginning from this time only. Therefore, LOD was studied separately for the data after 1956 with an interannual resolution of 0.05 years and geophysical reduction; for all available data, with one year resolu tion without taking into account the above mentioned reduction. A sum of "mass" terms, taking into account the inverse barometer, which is responsible for changes in the moment of inertia, and "motion"
GEOMAGNETISM AND AERONOMY Vol. 52 No. 7

terms, originated due to ocean currents and air mass travel, was used in the angular momenta. 3. MAIN RESEARCH METHOD To study the series, the method of singular spectrum analysis (SSA) and its multivariate version for the joint study of the series (MSSA) from (Golyandina et al., 2001) were used. SSA relates to the class of intrinsic (empirical) orthogonal functions, for which basic decomposition functions are determined from initial data. MSSA analyzes data sets jointly, distinguishing the general regularities or revealing special features. Using this method, we can obtain the components of different series, which are similar in frequency, and estimate their significance during decomposition. This method is based on the transformation of a time series into a matrix using parameter M (the specified window length) and singular decomposition of the matrix, which results in the additive decomposition of the ini tial series. The eigenvalues of correlation matrix i are the sampling variances of the corresponding main components, which are ranged so that the first one has the maximum contribution to the total variance. The percentage of the contribution of the i th component is calculated by the formula Vi = i /M в 100%, where i is the i th eigenvalue. All series were standardized before using MSSA by (xi xm)/s where xm and s are the mathematical expectation and standard variation of the {xi} series. The series were studied jointly using MSSA. How ever, to determine the spectral compositions of each series, except for the pole coordinates {Xp,Yp}, the SSA method was used. Using this method, we can obtain the components of different series, which are similar in frequency, and estimate their significance dur ing decomposition. When using MSSA, we should take into account how significant (in view of the contribu tion and amplitude) are the obtained components. Only equivalent components, distinguished at a cer tain frequency, can be considered interdependent. Therefore series standardization is particularly advised when using MSSA. 4. SSA DECOMPOSITION OF THE STUDIED SERIES 4.1. CW and Geophysical Excitation Functions There are two close peaks with maximal amplitudes and several small bursts in the same frequency range in the CW spectrum. Six components have been obtained at the CW frequency. The main CW component is the sum of the first two components (with a period of 1.183 years), which makes 40%, and the other four components make 7% (Fig. 1, left hand side). The weak component consists of a sum of five components with periods of 1.16, 1.21, 1.22, and 1.24 years.
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GORSHKOV et al. LOD(ms) 4 2 0 2 4 4 2 0 2 4 0.2 0 0.2

Xch(arcsec) 0.2 0 0.2 0.2 0 0.2 0.2 0 0.2 1840 1860 1880 1900 1920 194 1960 1980 2000

LUNAR 97

eopAO

1840 1860 1880 1900 1920 194 1960 1980 2000

Fig. 1. SSA decomposition of the X CW coordinate (left part): (top) total CW, (center) sum of the main components (40%), (bot tom) sum of weak components (7%); SSA decomposition of LOD series (right part): (top) composition of LOD series (eopAO series corrected for AAM and OAM), (center) decadal variations in LOD, (bottom) 5 to 7 year variations in LOD.

The main components have about 80 year modula tion with intervals of a strong amplitude damping and a simultaneous phase change by about 180°. The first minimum is at the very beginning of the series (around 1853), the second well known minimum is around 1928, and a sharp damping in the CW amplitude is observed at the end of the series (around 2005). The CW behavior is described in more detail in (Malkin and Miller, 2010; Miller, 2011). In addition, an about 40 year period of amplitude variations can be noted. This regularity was first noted in (Kostina and Sakharov, 1985); the authors connected it with the effect of solar activity. Weak components cause addi tional decade CW amplitude modulations. The nature of the excitation of these variations in the amplitude and sharp changes in the CW phase cannot be com pletely explained (like the nature of the CW excita tion). The seasonal components (1 and 0.5 years), which constitute 34 and 29%, respectively, are the main ones in the 2 and 2 angular momentum functions (AAM and OAM). 4.2. LOD and Geophysical Excitation Functions Figure 1 (right hand side) shows the SSA decom position of LOD. In addition to decade variations, exceeding all other oscillations by more than one order of magnitude (92%), quasi 6 year variations are the next largest contributors (3%) to the spectrum of interannual variations in LOD. These variations are formed from a set of components in the band of 5 to 8 year periods. The causes of their excitation are questionable (interaction between the mantle and the inner core, atmosphericocean dynamics, and solar activity). Quasi periodic 2 to 3 year variations in LOD are completely determined by variations in the

corresponding 3 function (AAM) at the same fre quency, thus reflecting quasi 2 year variations in zonal winds in the tropical stratosphere (Sidorenkov, 2002). Therefore, no variations with a period of 23 years are revealed in the variations in LOD of the eopAO series (from 1956), where the effect of the atmospheric ocean dynamics is taken into account. The main com ponents in the 3 functions (AAM and OAM) have a seasonal nature (a year and half of a year). 4.3. Solar and Geomagnetic Activity Quasi periodic 5 to 6 year components are present in the structure of SSN and SSAr series, as well as in the structure of shorter F10.7 and FI series, with a contribution to the total spectral power of about 1 2%, while 2 to 3 year components are only present in the FI series with a contribution of 1% (Fig. 2). There is a common quasi harmonic ~1.2 year component in the structure of geomagnetic indices (Ap and Dst) in the low frequency band; it contributes about 2% to Dst and about 1% to Ap. There is also a 5 to 6 year component in the Dst series with a contribu tion of about 6%. We have already mentioned that no adequate excitation factors are revealed for the 5 to 7 year component in the LOD series; therefore, the presence of similar components in the solar activity and, especially, Dst series allows one to suppose the geomagnetic excitation of this component in the LOD series. There is a set of components in the range 1.1 1.3 years in the data on total solar irradiance (TSI). Excluding the contribution of the main solar cycle, these components contribute 11.5% in total. Despite the insignificant contribution of this component to the total variability of the solar constant, the effect of this factor on CW modulations should not be excluded.
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MANIFESTATION OF SOLAR AND GEODYNAMIC ACTIVITY 0.3 0.2 0.1 0 0.1 0.2 0.3 56 years
F10.7 (2.1%) SSAr (2%)

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0.4 0.2 0 0.2 0.4

56 years

F10.7 (2.1%) Dst (5.8%)

1850 1950 1900 2000 1750 1800 1925 1875 1775 1825 1875 0.6 0.4 0.2 0 0.2 0.4 0.6 23 years
Ap (1%) Dst (0.7%)

1950

1960

1970

1980

1990

2000

2010

0.3 0.2 0.1 0 0.1 0.2 0.3

23 years
F1 (1%)

1940 1950 1960 1970 1980 1990 2000 2010

1975 1980 1985 1990 1995 2000 2005 2010

Fig. 2. (Top) 5 to 6 and (bottom) 2 to 3 year components in the SSA decomposition of solar (SSAr, F10.7, FI) and geomagnetic solar (, Dst) activities.

The presence of similar components in the series of geomagnetic indices and Dst intensifies the possi ble effect of the solar factor on CW modulation. 5. JOINT (MSSA) ANALYSIS OF DATA SERIES 5.1. Solar Activity, Geomagnetic Indices, and CW The atmosphericocean dynamics is assumed to be one of the factors exciting free wobble of the poles (CW) (unk and cdonald, 1960). We have per formed an MSSA series decomposition of the pole coordinates {, Yp}, SSN, and the corresponding 1 and 2 functions (AAM, OAM). It turned out that the functions of angular momenta of the atmosphere and ocean (1 and 2) oscillate concurrently at the annual frequency of pole wobbles, but no concurrent solar activ ity (SSN) is observed in this case. However, four compo nents with significant amplitudes and corresponding to weak CW components of 1.16 (1.8%), 1.24 (0.9%), and 1.22 (2.8%) years have been distinguished from the MSSA decomposition of {Xp, Yp} and SSN. This can be an indication of the solar activity effect on the mod ulation of the CW amplitude without an atmosphere and ocean mediated influence. The results of a joint MSSA series decomposition of {, Yp} and Dst, where three components with significant amplitudes were dis tinguished, corresponding to three weak CW compo nents of 1.24 (1.9%), 1.1 (0.7%), and 1.16 (0.5%) years, can indicate the same (Fig. 3). The amplitudes of the components behave synchronously; i.e., a change in the amplitude of a component of the pole coordinates
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corresponds to an analogous change in the amplitude of the corresponding Dst component--a period of low magnetic activity corresponds to an increase in the CW amplitude. A comparison of {Xp, Yp} and Ap gives a similar result, i.e., 1.16 (1.7%), 1.22 (2.8%), and 1.1 (0.4%) years. The joint MSSA decomposition of SSAr and the RCW centroid radius (Fig. 4, left part), estimated after the removal of the mean pole wobble from the {, Yp} series, gives the most interesting result in the region of secular variations. About 40 year variations in the CW amplitude agree with solar activity (the significance level is 9%) with minimal phase discrepancies: the CW amplitude increases with solar activity. Forty year variations in the CW amplitude were first noted in (Kostina and Sakharov, 1985). The cross correlation function of these components shows just a 40 year maximum and about a 10 year phase shift. 5.2. Solar Activity, Geomagnetic Indices, and LOD A joint MSSA decomposition of SSAr and the functions of atmosphericocean angular momenta for the axial component (3) shows a good spectral corre spondence between these series in the region of our inter est (Fig. 5). Components of the angular momenta with 5 to 6 year periodicity are almost synchronous (AAM to a low degree) with SSAr and spectrally equivalent at 1.6% level. The 2 to 3 year AAM component (1.2%) is almost opposite in phase with SSAr, while the corre
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GORSHKOV et al. (a) dst

1980 (b)

1990

2000

2010

1980 (c)

1990

2000

2010

1980

1990

2000

2010

Fig. 3. MSSA decomposition of the pole coordinates {, Yp} and Dst series (scaled). The periods of the components are equal to (a) 1.24, (b) 1.1, and (c) 1.16 years, respectively.

1.0 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1840 1860 1880 1900 1920 1940 1960 1980 2000 SSAr RCW

R 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8

SSAr Rp

80 60 40 20

0

20

40

60 80 Shift in years

Fig. 4. MSSA decomposition of the SSAr series, the RCW centroid radius (left part), and their cross correlation function (right part).

sponding OAM component is weakly visible in the MSSA spectrum at this frequency. This component is weakly visible in long solar activity series too; therefore, only the SSArAAM dependence should be consid ered significant at this frequency band. MSSA decomposition of LOD and SSAr over the whole range from 1750, where the LOD resolution is equal to one value per year, no correspondence between the series in a 5 to 6 year interval is revealed. However, the concurrency between the Earth's rota tion rate and solar and, especially, geomagnetic activ ities in the interval from 1956 is evident (Fig. 6) for shorter and more detailed LOD series (eopAO), in which the influence of the atmosphericocean dynamics is taken into account. Let us note the depen

dence of the decomposition results on the length of representation. This causes difficulties when comparing results with different lengths of representation. There is no noticeable correspondence between LOD and SSAr in the region of secular variations, although both of these series have the highest spectral power there. However, a comparison of low frequency variations in these series gives a good synchronization if the solar activity series is shifted by 94 years towards the past. In this case, a secular increase in solar activity with a delay of 94 years results in the acceleration of the Earth's rotation (Fig. 7). This result, obtained on the basis of 200 year history of observations of the Earth's
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MANIFESTATION OF SOLAR AND GEODYNAMIC ACTIVITY 0.4 0.2 0 0.2 0.4 1950 1960 1970 1980 1990 2000 2.3 years, 1.2%
AAM OAM SSAr

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0.4 0.2 0 0.2 0.4 1950

5.2 years, 1.6%
AAM OAM SSAr

1960

1970

1980

1990

2000

Fig. 5. MSSA decomposition of SSAr and A OAM.

56 years (2%) 0.2
LOD AAM TSI

0.4 0.2 0.2

56 years (1.3%)
LOD AAM SSAr

0

0 0.2

0.2

0.2 1970 1980 1990 56 years (3%)
LOD AAM Dst

0.4 1960 1980 1985 1990 1995 2000 2005 2010 56 years (3.7%) 0.4 LOD AAM 0.4
Ap

2000

2010

0.2 0 0.2 0.4 1960 1970 1980 1990 2000

0.2 0 0.2 0.4 2010 1960 1970 1980 1990 2000 2010

Fig. 6. Components (5 to 6 year) of MSSA of different series of solar and geomagnetic activities in comparison with the LOD series.

rotation rate, was obtained earlier in (Duhau and Martinez, 1996) and, probably, is not random. Since the short eopAO series is corrected for the influence of atmosphericocean dynamics 3 (AAM and OAM), where 2 to 3 year components totally manifest themselves, as has been mentioned above, then no corresponding components are revealed in the joint analysis of LOD and solar activity. 6. EARTH'S GEOMAGNETIC ACTIVITY AND LOD The comparison of low frequency Earth's rotation rate with long term variations in the rate of the secular
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trend in the Earth's geomagnetic field (SVN, SVE, and SVU) is the most interesting. Usually, jerks (points of change in this rate) are compared with the corre sponding momenta of LOD (Greiner Mai, 1995; Holme and de Viron, 2005). Jerks are recorded from observation results at geomagnetic observatories, which is not always done globally and has a long (sometimes up to several years) delay at different observatories. This effect of delays and the spreading of jerks is assigned to regionally varying conductivity of the mantle (Alexandrescu, 1996). The rate of the east component (SVE), averaged over the best Euro pean stations, is commonly used, as it represents vari ations in the Earth's geomagnetic field best of all.
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GORSHKOV et al. 0.8 SSN 0.6 1.0 0.8 0.6 0.4 0.2 0.2 0 1700 1750 1800 1850 1900 1950 2000 1800 1850 1900 1950 2000 LOD LOD SSN 0.4

Fig. 7. Comparison of secular variations in SSN and LOD; (right part) with a 94 year shift towards the past for SSN.

2 1 0 1 2 2 1 0 1 2 1840 1860 1880

LOD SVe

(a) 14 pc, 81% 2 1 0 1 2 (b) 16 pc, 87% 2 1 0 1 2

(c) 19 pc, 90%

(d) 16 pc, 87%

1900

1920

1940

1960

1980

2000 1840

1860

1880

1900

1920

1940

1960

1980

2000

Fig. 8. Steps of MSSA restoration of components and their contributions when studying jointly SVe and LOD (the value cor responds in sign to the Earth's rotation rate); pc means principal components.

According to different assessments, the time of jerk shielding, i.e., the time of its "leakage" from the core mantle boundary to the corresponding recording instruments on the Earth's surface, is from several to 20 years. Therefore, the authors of many works try to detect a corresponding feature in the behavior of the Earth's rotation in the past relative to recorded jerks. The only exceptions are the works (Holme and de Viron, 2005; Nakada, 2009), where direct, i.e., with out any delay, manifestations of jerks have been revealed in certain cases.

A comparison of refined monthly INTERMAGNET geomagnetic data (Chulliat and Telali, 2007) for a part of the material (56 stations beginning from 1901) with annual average observatory data has not revealed dif ferences between them in secular variations, but there were observed seasonal variations in the series. There fore, we used annual average data from all available geomagnetic observatories (172 stations) with obser vational history longer than 25 years to form a com bined SVE series for the Northern Hemisphere. These data were also studied by the MSSA along with com
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28 years 8 years

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ms 4
69 years

2 0 2 4
68 years

0.4 0.6 60 40 20

LOD SVE (smoosed & scaled) CAM LOD CAM

0

20

40

60

1840 1860 1880 1900 1920 1940 1960 1980 2000

Fig. 9. Unbiased estimate of the cross correlation between the LOD and SVE series (left part). A comparison of the SVE, LOD, and CAM series with the LOD series, taking into account CAM (right part).

bined LOD series, which also had a resolution of one value per year (Fig. 8). When series are restored step by step with an increase in the number of the main components, in the SVE series, additional curve breaking points appear sequentially; they should be interpreted as ever weaker (local) jerks. Further addition of components only increases the noise component. As is seen, all peculiarities of SVE precede the corresponding fea tures in the LOD series, which is especially evident beginning from the 20th century, when the accuracy and number of stations increased. This important point can be defined more accurately by means of cal culations of the cross correlation function of these series (Fig. 9, left part). As is seen, the delay is equal to 8 years; i.e., the Earth's rotation rate increases eight years after (for the period of observations on average) an increase in the rate of the eastern component of the Earth's geo magnetic field. The main and, which is most impor tant, common period of their variability is equal to 6869 years. The similarity between the details on the curves in Fig. 9 and the strictly periodic curve of these series do not allow for the possibility of another interpretation; i.e., the recorded features of secular variations in the rate of change in the geomagnetic field precede the corresponding variations in the Earth's rotation rate. The core angular momenta are calculated by the model in (Pais and Hulot, 2000) by the International Earth Rotation Service; therefore, the contribution of these model data to the Earth's rotation rate can be estimated. All of the above mentioned series are com pared in Fig. 9 (right part). It is evident that the model does not exclude real variations in LOD. This is probably related to a strongly underestimated conduc tivity of the mantle in the model, which, according to recent data (Ohta et al., 2012), can be increased signif icantly due to the discovery of FeO conductivity under
GEOMAGNETISM AND AERONOMY Vol. 52 No. 7

the conditions of mantle temperatures and pressures. In any case, the time sequence of the geomagnetic field and Earth rotation rates follows from a compari son of their secular variations; i.e., the first features of the geomagnetic field are recorded and then they show in the Earth's rotation rate. 7. DISCUSSION AND CONCLUSIONS We may assume that the electromagnetic effect of the solar wind during magnetic storms can be one of the excitation factors of variations in the CW amplitude and the Earth's rotation rate. The presence of magnetic interactions between processes that occur at the core mantle boundary provides for the background angular momentum transfer from the core to the mantle. Varia tions in the magnetic field during magnetic storms induce currents in the mantle. The depth distribution of these currents is determined by the conductivity of rocks composing the Earth's interior. Based on the well known estimates of changes in the conductivity with depth, we may assume the origination of variations in the Earth's magnetic field caused by magnetospheric processes at a depth of up to 10002000 km. In this case, rapid variations in the magnetic field are absent at these depths, and only slow variations are observed with periods corresponding to variations in the magnetic activity of the Sun. This can explain the agreement between the solar activity parameters and the varia tions in the ERP within 1 to 8 year intervals, studied in this work. A variation in the magnetic field due to solar activity can be considered as a controlling factor of the coremantle magnetic interaction. In this case, the direct contribution of solar wind particles to variations in the Earth's rotation vector momentum is negligible. Thus, the following conclusions can be drawn from the results of this work. The correspondence between the geomagnetic activity (Dst, Ap) and weak CW components has been
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GORSHKOV et al. Duhau, S. and Martinez, E.A., The Secular Variation of the Geomagnetic Westward Drift in the Last 1000 Years, in Actas 19 Reunion Cientifica de la Asoc. Arg. Geofis. Geodes., 1996, pp. 9195. Dumberry, M. and Bloxham, J., Inner Core Tilt and Polar Motion, Geophys. J. Int., 2002, vol. 151, pp. 377392. Golyandina, N., Nekrutkin, V., and Zhigljavsky, A., Analy sis of Time Series Structure: SSA and Related Techniques, London: Chapman and Hall/CRC, 2001. Gorshkov, V.L., Study of the Interannual Variations of the Earth's Rotation, Sol. Syst. Res., 2010, vol. 44, no. 6, pp. 487497. Greiner Mai, Y., About Possible Geophysical Causes of the Decade Fluctuations in Length of Day, Astron. Nachr., 1995, vol. 316, pp. 311318. Hide, R., Boggs, D.H., and Dickey, J.O., Angular Momen tum Fluctuations within the Earth's Liquid Core and Torsion Oscillations of the CoreMantle System, Geo phys. J. Int., 2000, vol. 143, pp. 777786. Holme, R., Electromagnetic CoreMantle Coupling I. Explaining Decadal Changes in the Length of Day, Geophys. J. Int., 1998, vol. 132, pp. 167180. Holme, R. and De Viron, O., Geomagnetic Jerks and High Resolution Length of Day Profile for Core Studies, Geophys. J. Int., 2005, vol. 160, pp. 435439. Kenji, O., Cohen, R.E., Hirose, K., Haule, K., Shimizu, K., and Ohishi, Y., Experimental and Theo retical Evidence for Pressure Induced Metallization in FeO with Rocksalt Type Structure, Phys. Rev. Lett., p. 2012. Kostina, L.D. and Sakharov, V.I., Analysis of Long Period Amplitude Variations in the Chandler and Annual Components of the Earth Pole Motion, Izv. Glavn. Astron. Obs., 1985, vol. 201, pp. 6063. Malkin, Z. and Miller, N., Chandler Wobble: Two More Large Phase Jumps Revealed, Earth Planet. Space, 2010, vol. 62, pp. 943947. Miller, N., Chandler Wobble in Variations of the Pulkovo Latitude for 170 Years, Sol. Syst. Res., 2011, vol. 45, no. 4, pp. 342353. Munk, W. and Macdonald, G., The Rotation of the Earth, Cambridge, 1960. Nagovitsyn, Yu.A., To the Description of Long Term Vari ations in the Solar Magnetic Flux: The Sunspot Area Index, Astron. Lett., 2005, vol. 31, issue 8, pp. 557562. Nakada, M., Earth's Rotational Variations by Electromag netic Coupling Due to Core Surface Flow on a Time Scale of ~1 year for Geomagnetic Jerk, Geophys. J. Int., 2009, vol. 179, pp. 521535. Pais, A. and Hulot, G., Length of Day Decade Variations, Torsional Oscillations and Inner Core Superrotation: Evidence from Recovered Core Surface Zonal Flows, Phys. Earth Planet. Int., 2000, vol. 118, pp. 291316. Sidorenkov, N.S., Fizika nestabil'nostei vrashcheniya Zemli, (Physics of the Earth Rotation Instabilities), Moscow: Fizmatlit, 2002. Spiridonov, E.A. and Akimenko, Ya.V., Chandler Swing of the Pole Initiated by the Motion of the Earth's Inner Core, Fiz. Zemli, 2003, no. 11, pp. 7478. Wilson, R.C. and Mordvinov, A.V., Secular Total Solar Irra diance Trend during Solar Cycles 2123, Geophys. Res. Lett., 2003, vol. 30, no. 5; doi:10.1029/2002GL016038.
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revealed by MSSA. The behavior of the amplitude of each component is synchronized with geomagnetic activity; i.e., a variation in the amplitude of each CW component corresponds to a similar variation in the amplitude of the corresponding component of geo magnetic activity. In the region of secular variations in the CW amplitude, about 40 year variations in it agree with solar activity: the CW amplitude increases with solar activity. Analyzing the functions of geophysical excitation 3 (OAM and AAM) jointly with variations in solar and geomagnetic activity, ~2.3 and ~5.2 year compo nents have been revealed. The best spectral correspon dence between these processes is observed for the 5.2 year component: the atmosphericocean dynamics at this frequency increases with solar activity. For the 2 to 3 year component, the dynamics of solar activity is opposite in phase only with atmospheric function 3. The Earth's rotation rate is closely related to solar and, especially, geomagnetic activity in the region of 5 to 6 year periods. Beginning from the second half of the 20th century, an increase in solar activity generally corresponds to a decrease in the Earth's rotation rate (vice versa for Dst) in this region of periods, although phase variations sometimes strongly disturb the corre lation between these processes. In the region of the strongest secular variations, no regular correspondence is observed between solar activity and the Earth's rotation rate; however, the results of the work (Duhau and Martinez, 1996) can be confirmed: variations in the Earth's rotation rate repeat secular variations in solar activity with a delay of 94 years. This law has been true for the last 200 years, i.e., almost the entire modern observation history. The time sequence of the Earth's geomagnetic field and rotation rates follows from a comparison of their secular variations; i.e., first, the features of the geo magnetic field are recorded and then they are reflected in the Earth's rotation rate with an average observation delay of eight years. REFERENCES
Abarca del Rio, R., Gambis, D., Salstein, D, Nelson, P., and Dai, A., Solar Activity and Earth Rotation Variabil ity, J. Geodyn., 2003, vol. 36, pp. 423443. Alexandrescu, M., Gilbert, D., Hulot, G., Le Mouёl, J. L., and Saracco, G., Worldwide Wavelet Analysis of Geo magnetic Jerks, J. Geophys. Res., 1996, pp. 21 97521 994. Bellanger, E. Gibert, D., and Le MouКl, J. L., A Geomagnetic Triggering of Chandler Wobble Phase Jumps, Geophys. Res. Lett., 2002, vol. 29, no. 7. doi:10.1029/2001GL014253. Chulliat, A. and Telali, K., World Monthly Means Data Base Project, Publ. Inst. Geophys. Pol. Acad. Sci., 2007, no. 398, p. 99. Djurovic, D. and PБquet, P., The Common Oscillations of ^ Solar Activity, the Geomagnetic Field and the Earth's Rotation, Sol. Phys., 1996, vol. 167, pp. 427439.

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