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Associated with non-steady magnetohydrodynamic (MHD) flow in the liquid metallic core of the Earth, with typical relative speeds of a fraction of a millimetre per second, are fluctuations in dynamic pressure of about 103 N m−2. Acting on the non-spherical core-mantle boundary (CMB), these pressure fluctuations give rise to a fluctuating net topographic torque Lt(t) (i=1, 2, 3)—where t denotes time—on the overlying solid mantle. Geophysicists now accept the proposal by one of us (RH) that Li-(t) makes a significant and possibly dominant contribution to the total torque Li*(t) on the mantle produced directly or indirectly by core motions. Other contributions are the ‘gravitational’ torque associated with fluctuating density gradients in the core, the ‘electromagnetic’ torque associated with Lorentz forces in the weakly electrically conducting lower mantle, and the ‘viscous’ torque associated with shearing motions in the boundary layer just below the CMB. the axial component L3*(t) of Li* (t) contributes to the observed fluctuations in the length of the day [LOD, an inverse measure of the angular speed of rotation of the solid Earth (mantle, crust and cryosphere)], and the equatorial components (Li* (t)) L* (t) contribute to the observed polar motion, as determined from measurements of changes in the Earth's rotation axis relative to its figure axis.
In earlier phases of a continuing programme of research based on a method for determining Li(t) from geophysical data (proposed independently about ten years ago by Hide and Le Mouël), it was shown that longitude-dependent irregular CMB topography no higher than about 0.5 km could give rise to values of L3(t) sufficient to account for the observed magnitude of LOD fluctuations on decadal time-scales. Here, we report an investigation of the equatorial components (L1(t), L2(t)) = L(t) of Li(t) taking into account just one topographic feature of the CMB—albeit possibly the most pronounced—namely the axisymmetric equatorial bulge, with an equatorial radius exceeding the polar radius by 9.5 ± 0.1 km (the mean radius of the core being 3485 2 km, 0.547 times that of the whole Earth). A measure of the local horizontal gradient of the fluctuating pressure field near the CMB can be obtained from the local Eulerian flow velocity in the ‘free stream’ below the CMB by supposing that nearly everywhere in the outer reaches of the core—the ‘polosphere’ (Hide 1995)—geostrophic balance obtains between the pressure gradient and Coriolis forces. the polospheric velocity fields used were those determined by Jackson (1989) from geomagnetic secular variations (GSV) data on the basis of the geostrophic approximation combined with the assumption that, on the time-scales of the GSV, the core behaves like a perfect electrical conductor and the mantle as a perfect insulator.
In general agreement with independent calculations by Hulot, Le Huy & Le Mouël (1996) and Greff-Lefftz & Legros (1995), we found that in magnitude L (t) for epochs from 1840 to 1990 typically exceeds L3(t) by a factor of about 10, roughly equal to the ratio of the height of the equatorial bulge to that strongly implied for irregular topography by determinations of L3(t) (see Hide et al. 1993). But L (t) still apparently falls short in magnitude by a factor of up to about 5 in its ability t o account for the amplitude of the observed time-series of polar motion on decadal time-scales (DPM), and it is poorly correlated with that time-series. So we conclude that unless uncertainties in the determination of the DPM time-series from observations-which we also discuss-have been seriously underestimated, the action of normal pressure forces associated with core motions on the equatorial bulge of the core-mantle boundary makes a significant but not dominant contribution to the excitation of decadal polar motion. Other geophysical processes such as the movement of groundwater and changes in sea-level must also be involved.

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... For topographic coupling and the associated pressure torque, we will refer to the literature (e.g. Hinderer et al., 1987Hinderer et al., , 1990Jault and Le Moue¨l, 1989;Hide et al., 1996;Hulot et al., 1996). ...

... In his model, the relative inner-core rotation is excited by the torsional oscillation of the outer-core fluid and fricition at the inner-core boundary, while the restoring gravitational forces constrain this rotation to be nearly locked to the mantle. The role of the inner core for Ám is outlined in Section 3. Fig. 2 shows that there is probably no reasonable M -model by which the excitation of decadal polar-motion variations, Ám, can be explained by EM core mantle coupling (see also Hide et al., 1996;Greff-Lefftz and Legros, 1995). Hinderer et al. (1987) suggested that Ám can possibly be excited by pressure torques resulting from the interaction of temporally variable flows near the CMB with the CMB-topography (topographic coupling). ...

... In addition, such coupling would excite variations of LOD with larger amplitudes than are observed (see also Hinderer et al., 1990). Hide et al. (1996) found that the topographic torque is too small by a factor of 5 to excite the decadal Ám. ...

In this work, we review the processes in the Earth's core that influence the Earth's rotation on the decadal time scale. While core–mantle coupling is likely to be responsible for the decadal length-of-day variations, this hypothesis is controversial with respect to polar-motion variations. The electromagnetic-coupling torques are strongly dependent on the assumed electrical conductivity of the lower mantle, while the topographic torques are influenced by the topography of the core–mantle boundary (CMB). Because no comprehensive theoretical framework for determining the topographic and material parameters of the CMB region is currently available, the modeled results about the coupling torques can only be verified by their consistency with the observed variations of the Earth's rotation and the geomagnetic field. A second path of investigation is to consider the relative angular momentum of the core. Recently, the axial angular-momentum balance has been found to coincide with observed variations in the geomagnetic field and the length of day. However, with respect to polar-motion variations, the angular-momentum balance is not yet closed. We also discuss the role of an irregular motion of the figure axis of the oblate inner core with respect to the outer core and mantle in the excitation of polar motion. In particular, we assume that the associated changes of the Earth's inertia tensor cause the observed decadal variations in polar motion. From this assumption, we can derive the temporal variation of the orientation of the figure axis of the inner core from polar-motion data. Finally, we calculate the gravity variations caused by this relative inner-core motion and compare them with the accuracy of current and planned satellite missions.

... Core flow may also produce non-axial torques at the CMB and ICB and thus influence polar motion as well as LOD (e.g. Greff-Lefftz & Legros 1995;Hide et al. 1996;Hulot et al. 1996;Dumberry & Bloxham 2002;Greiner-Mai et al. 2003). ...

... Electromagnetic and topographic coupling between the fluid core and mantle have been investigated and found to be unable to provide the torque required to produce the observed polar motions (e.g. Greff-Lefftz & Legros 1995;Hide et al. 1996;Hulot et al. 1996;Greiner-Mai et al. 2003). Investigations that assumed that inertial forces supply the restoring torque suggested that the inner core might play a role in the generation of the Markowitz wobble (Busse 1970;Kakuta et al. 1975). ...

Motion of the rotation axis of the Earth contains decadal variations with amplitudes on the order of 10 mas. The origin of these decadal polar motions is unknown. A class of rotational normal modes of the core–mantle system termed torsional oscillations are known to affect the length of day (LOD) at decadal periods and have also been suggested as a possible excitation source for the observed decadal polar motion. Torsional oscillations involve relative motion between the outer core and the surrounding solid bodies, producing electromagnetic torques at the inner-core boundary (ICB) and core–mantle boundary (CMB). It has been proposed that the ICB torque can explain the excitation of the approximately 30-yr-period polar motion termed the Markowitz wobble. This paper uses the results of a torsional oscillation model to calculate the torques generated at Markowitz and other decadal periods and finds, in contrast to previous results, that electromagnetic torques at the ICB can not explain the observed polar motion.

... But a significant effect of electromagnetic coupling on polar motion cannot be excluded for extreme assumptions about the distribution and the magnitude of the mantle conductivity at the core-mantle boundary Ž . Hide et al., 1996 . Its responsibility for the decadal variations of the length of day under such assump-Ž . ...

... Greff-Lefftz and Legros 1995 concluded from their numerical investigations that the topographic torque has an effect on the decadal variations of polar motion, which is by a factor 10 Ž . too small; Hide et al. 1996 estimated a factor 5. ...

Provided that the figure axis of the inner core coincides with the dipole axis of the geomagnetic field, the relative rotation of the oblate inner core with respect to the outer core and the mantle can be determined. Because of the density difference between the inner and outer core, the assumed precessional motion of the inner core relative to the mantle is accompanied by a mass redistribution causing variations of polar motion. Assuming standard density models, it is found that variations of polar motion caused by variations of relative inner-core rotation due to that of the real dipole axis are similar to the decadal variations derived from observed pole coordinates. Calculations of the gravity potential show that the assumed relative rotation of the inner core causes gravity changes which may be detectable by modern satellite methods during the next decade.

... This is the so-called Markowitz wobble (Markowitz 1960(Markowitz , 1961. The coupling between core and mantle is believed to be insufficient to explain that term (Hide et al. 1996). As the associated observation errors were too large to definitely conclude about it prior to the use of space geodesy, longer and more precise geodetic time-series should help to further characterize the Markowitz wobble. ...

Observation of the variations in the Earth’s rotation at time scales ranging from subdiurnal to multidecadal allows us to learn about its deep interior structure. We review all three types of motion of the Earth’s rotation axis: polar motion (PM), length of day variations (ΔLOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \text {LOD}$$\end{document}) and nutations, with particular attention to how the combination of geodetic, magnetic and gravity observations provides insight into the dynamics of the liquid core, including its interactions with the mantle. Models of the Earth’s PM are able to explain most of the observed signal with the exception of the so-called Markowitz wobble. In addition, whereas the quasi-six year oscillations (SYO) observed in both ΔLOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \text {LOD}$$\end{document} and PM can be explained as the result of Atmosphere, Oceans and Hydrosphere Forcing (AOH) for PM, this is not true for ΔLOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \text {LOD}$$\end{document} where the subtraction of the AOH only makes the signal more visible. This points to a missing—possibly common—interpretation related to deep interior dynamics, the latter being also the most likely explanation of other oscillations in ΔLOD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \text {LOD}$$\end{document} on interannual timescales. Deep Earth’s structure and dynamics also have an impact on the nutations reflected in the values of the Basic Earth Parameters (BEP). We give a brief review of recent works aiming to independently evaluate the BEP and their implications for the study of deep interior dynamics.

... Nastula et al., 2011). Core-mantle coupling has been a suggested source (Hide et al., 1996), but lacks confirmation by a geophysical model. With the launch of GRACE in 2002, time variable gravity fields have shown significant ice mass loss in polar regions (Chen et al., 2006;Chen et al., 2008). ...

... For generation of plate tectonic forces the convection in the mantle is responsible (Bercovichi, 1998), which in turn is related to the processes into the fluid outer core (e.g. Hide et al., 2007). Simultaneously, the processes into the fluid outer core are responsible for generation of the Earth's main magnetic field (Glatzmaier and Roberts, 1995). ...

The integrated studies involving seismology, geodynamics and geomagnetism are essential for advances in understanding of the dynamics of our planet. In this report, the results obtained in this direction in the Institute of seismology of Kazakhstan are presented. To obtain these results, the data on earthquakes with M≥4.0 were taken from the NEIC catalogue, and for each of the epicenters the parameters of the main geomagnetic field were estimated with using the International Geomagnetic Reference Field (IGRF) model. Then, spatial scale distribution of earthquake epicenters in relation to geometry of the main geomagnetic field was investigated. It is found: 1) local peaks of seismic activity in the northern and southern hemispheres are better organized according to geomagnetic latitude or angle of geomagnetic inclination then the geographic latitude; 2) the western and southern boundaries of the now-forming Somalian plate are defined very well using traced earthquakes, if one presents the map of epicenters not in the usual geographic coordinates but in a plot of geomagnetic inclination versus geographic longitude; 3) spatial location of three main seismotectonic areas: orogeny, subduction zones, and rift systems show systematization according to the angle of geomagnetic declination (D): for earthquake epicenters occurred in orogeny, D values are rather small (vary from ~-1.0 to +5.0); for epicenters occurred in subduction zones, D values are rather large and positive, while they are rather large and negative for epicenters occurred in rift systems. It is concluded that geographical distribution of seismic zones at the Earth is controlled by the geometry of its main magnetic field.

... Finally, we insert drag into our model. If we assume that any excess velocity formed from the tidal acceleration in the atmosphere is quickly dissipated into the Earth through surface interactions with a damping factor Γ = 1 τ (with τ defined as the total energy over power loss of the system, such that Q = ω0τ ), and that this surface motion is relatively quickly dissipated into the rotational motion of the entire Earth, as given by Hide, et al. [1996], we obtain: ...

Stromatolite data suggest the day length throughout much of the Precambrian
to be relatively constant near 21 hours; this period would have been resonant
with the semidiurnal atmospheric tide. At this point, the atmospheric torque
would have been nearly maximized, being comparable in magnitude but opposite in
direction to the lunar torque, halting Earth's angular deceleration, as
suggested by Zahnle and Walker [1987]. Computational simulations of this
scenario indicate that, depending on the atmospheric $Q$-factor, a persistent
increase in temperature larger than ~10K over a period of time less than $10^7$
years will break resonance, such as the deglaciation following a snowball event
near the end of the Precambrian. The resonance was found to be relatively
unaffected by other forms of climate fluctuation (thermal noise). Our model
provides a simulated day length over time that matches existing records of day
length, though further data is needed.

... Since core-mantle processes are known to cause decadal variations in the length of the day, they may also excite decadal variations in polar motion. But electromagnetic coupling between the core and mantle appears to be two to three orders of magnitude too weak (Greff-Lefftz and Legros, 1995) and topographic coupling appears to be too weak by a factor of three to ten (Greff-Lefftz and Legros, 1995;Hide et al., 1996;Hulot et al., 1996;Asari et al., 2006). In addition, the modeled decadal polar motion variations resulting from these studies show little agreement in phase with the observed variations. ...

The Earth is a dynamic system—it has a fluid, mobile atmosphere and oceans, a continually changing global distribution of ice, snow, and water, a fluid core that is undergoing some type of hydromagnetic motion, a mantle both thermally convecting and rebounding from the glacial loading of the last ice age, and mobile tectonic plates. In addition, external forces due to the gravitational attraction of the Sun, Moon, and planets also act upon the Earth. These internal Gross, R. S., Earth Roation Variations – Long Period, in Physical Geodesy, edited by T. A. Herring, Treatise on Geophysics, Vol. 11, Elsevier, Amsterdam, in press, 2007. 2 dynamical processes and external gravitational forces exert torques on the solid Earth, or displace its mass, thereby causing the Earth's rotation to change. Changes in the rotation of the solid Earth are studied by applying the principle of conservation of angular momentum to the Earth system. Under this principle, the rotation of the solid Earth changes as a result of: (1) applied external torques, (2) internal mass redistribution, and (3) the transfer of angular momentum between the solid Earth and the fluid regions with which it is in contact; concomitant torques are due to hydrodynamic or magneto-hydrodynamic stresses acting at the fluid/solid Earth interfaces. Here, changes in the Earth's rotation that occur on time scales greater than a day are discussed. Using the principle of conservation of angular momentum, the equations governing small variations in both the rate of rotation and in the position of the rotation vector with respect to the Earth's crust are first derived. These equations are then rewritten in terms of the Earth rotation parameters that are actually reported by Earth rotation measurement services. The techniques that are used to monitor the Earth's rotation by the measurement services are then reviewed, a description of the variations that are observed by these techniques is given, and possible causes of the observed variations are discussed.

... Topographic core-mantle coupling has been of interest for understanding the axial torques (Hide 1969;Anufriev & Braginsky 1975, 1977aMoffatt 1978;Jault & Le Mouël 1989;Jault & Le Mouël 1990Kuang & Bloxham 1993;Kuang & Chao 2001) and the equatorial torques (Hide et al. 1996;Hulot et al. 1996) that the fluid core exerts on the mantle. Comparatively fewer studies have examined the explicit role that CMB topography plays in altering the convective dynamics of the core (Bell & Soward 1996;Bassom & Soward 1996;Herrmann & Busse 1998;Westerburg & Busse 2003). ...

We present the first investigation that explores the effects of an
isolated topographic ridge on thermal convection in a planetary
core-like geometry and using core-like fluid properties (i.e. using a
liquid metal-like low Prandtl number fluid). The model's mean azimuthal
flow resonates with the ridge and results in the excitation of a
stationary topographic Rossby wave. This wave generates recirculating
regions that remain fixed to the mantle reference frame. Associated with
these regions is a strong longitudinally dependent heat flow along the
inner core boundary; this effect may control the location of melting and
solidification on the inner core boundary. Theoretical considerations
and the results of our simulations suggest that the wavenumber of the
resonant wave, LR, scales as Ro-1/2, where Ro is
the Rossby number. This scaling indicates that small-scale flow
structures [wavenumber ?] in the core can be excited by a topographic
feature on the core-mantle boundary. The effects of strong magnetic
diffusion in the core must then be invoked to generate a stationary
magnetic signature that is comparable to the scale of observed
geomagnetic structures [?].

... It is also recognized that seismic excitation can only lead to a secular trend in polar motion [e.g., Chao and Gross, 1987;Gross and Chao, 2005], and that continental water storage mainly contributes to the seasonal and interseasonal wobbles [e.g., Chen and Wilson, 2005]. However, the mechanism for decadal polar motions is still not quite certain, though the topographic core-mantle coupling seems to be effective [e.g., Hide et al., 1996] while the electromagnetic one is probably not [Greff-Lefftz and Legros, 1995;Mound, 2005]. Many recent progresses are still not covered in this short discussion, and one can find them in relevant journals. ...

The Earth's rotation is perturbed by mass redistributions and relative motions within the Earth system, as well as by the torques from both the internal Earth and celestial bodies. The present study aims to establish a theory to incorporate all these factors perturbing the rotation state of the triaxial Earth, just like the traditional rotation theory of the axial-symmetric Earth. First of all, we reestimate the Earth's inertia tensor on the basis of two new gravity models, EIGEN-GL05C and EGM2008. Then we formulate the dynamic equations and obtain their normal modes for an Earth model with a triaxial anelastic mantle, a triaxial fluid core, and dissipative oceans. The periods of the Chandler wobble and the free core nutation are successfully recovered, being ∼433 and ∼430 mean solar days, respectively. Further, the Liouville equations and their general solutions for that triaxial nonrigid Earth are deduced. The Liouville equations are characterized by the complex frequency-dependent transfer functions, which incorporate the effects of triaxialities and deformations of both the mantle and the core, as well as the effects of the mantle anelasticity, the equilibrium, and dissipative ocean tides. Complex transfer functions just reflect the fact that decays and phase lags exist in the Earth's response to the periodic forcing. Our theory reduces to the traditional rotation theory of the axial-symmetric Earth when assuming rotational symmetry of the inertia tensor. Finally, the present theory is applied to the case of atmospheric-oceanic excitation. The effective atmospheric-oceanic angular momentum function (AMF) χeff = χeff1 + iχeff2 for the present theory is compared with the AMF χeffsym = χeff1sym + iχeff2sym for the traditional theory and the observed AMF χobs = χ1obs + iχ2obs; we find that the difference between χeff and χeffsym is of a few milliseconds of arc (mas) and can sometimes exceed 10 mas. In addition, spectrum analyses indicate that χeff is in good agreement with χeffsym and, further, show an increase of coherency with χobs especially in the low-frequency band. The obvious advantage of χeff in the low-frequency band with respect to χeffsym is the critical support of the present theory. However, still better performance of our theory can be expected if the models of the mantle anelasticity and oceanic dynamics were improved. Thus we conclude that the traditional Earth rotation theory should be revised and upgraded to include the effects of the Earth's triaxiality, the mantle anelasticity, and oceanic dynamics. The theory presented in this study might be more appropriate to describe the rotation of the triaxial Earth (or other triaxial celestial bodies such as Mars), though further studies are needed to incorporate the effects of the solid inner core and other possible influences.

... and geodynamical studies Forte et al., 1995 and expanded . Greff- Lefftz and Legros, 1995b;Hide et al., 1996;Hulot et al., 1996 . The pressure torque L is the sum of L o and terms proportional to u c and u c . ...

The theory of the rotation of the fluid core is modified in order to take into account the magnetic field within the core. Because of the conductivity of the lower mantle, there is a frictional magnetic torque which appears at the core–mantle boundary (CMB); the magnitude of this torque depends on the conductivity profile within the mantle and on the magnetic energy at the CMB. It perturbs the rotational eigenmodes involving a damping in the free core nutation (FCN) and in the Chandler wobble. The geostrophic pressure at the CMB acts on the bumps of this interface involving a topographic torque. Because of the geostrophic rigidification, this surface pressure field is advected by the core velocity, and consequently, the topography being fixed in a frame related to the mantle, it appears a restoring torque acting on the core. Such a torque perturbs the FCN and creates a slow new rotational eigenmode.

... The Guinot, 1972; Lambeck, 1980; Wahr, 1988; Cazenave and Feigl, 1994] Dickman, 1981; Vondrdk, 1985], 1954; Guinot, 1972; Pejovi5, 1990] [Wahr, 1988; Dickman, 1993]) [Alexandrescu et al., 1995 [Alexandrescu et al., , 1996Table 1).Table 2 [1989] and McLeod [1989] (1901, 1913, 1925, 1932, 1949, 1970, and 1980 [1989] and McLeod [1989] [Hinderer et al., 1990; Hulot et al., 1996; Hide et al. , 1996]. [1995, 1996] [Wart, 1988; Dickman, 1993; Eubanks, 1993; Wilson, 1993; Furuya et al., 1996] ...

Wavelet analysis is applied to analyze polar motion spanning the years 1890-1997. First, the wavelet transform is used to identify the components (prograde and retrograde) present in the data. This wavelet transform is subsequently used to filter and reconstruct each component. Then we define the ridge of the wavelet transform and show how it can be used to detect rapid phase jumps in a signal. This technique is applied to the reconstructed prograde Chandler wobble component, and several features characteristic of phase jumps are identified. Synthetic signals with adjustable phase jumps (in terms of their dates, durations, and amplitudes) are constructed to produce ridge functions similar to the one obtained for the Chandler wobble. We find that less than 10 phase jumps are necessary to reproduce the observed features. All but one phase jump have durations between 1 and 2 years, and their dates are found to remarkably follow those of geomagnetic jerks with a delay not exceeding 3 years. Elementary statistical tests assign a high probability to the correlation between the dates of the phase jumps and those of the jerks. Simple physical models of core-mantle coupling show that the observed phase jumps can be recovered with torques of about 1020Nm.

... For example, it is well known that interactions between the Earth's core and mantle cause very strong decadal variations in LOD. However, compared to other effects, these processes in the Earth's interior seem to be inferior for the excitation of long-period polar motion (Hide et al. 1996). There is some evidence that the relative motion between core and mantle contributes to the so-called Markowitz-wobble, which is an oscillation with a period of about 30 yr (Dumberry & Bloxman 2002). ...

This paper focuses on the contribution of inter-annual hydrological mass redistributions to the excitation of polar motion. Variations in hydrological angular momenta are computed from the Land Dynamics Model (LaD) for the period between 1986 January and 2004 May. For validation, the numerical results for the hydrological excitations are compared with respective time-series derived from geodetic observations. In order to provide a comparable reference, the latter are reduced by atmospheric and oceanic effects which are the prominent contributors to polar motion excitation on subdiurnal to decadal timescales. Both the hydrological and the geodetic excitation series are low-pass filtered by means of a Vondrák filter in order to remove the dominant annual oscillations. For the comparison of hydrological and geodetic excitations, wavelet scalograms and cross-scalograms along with the respective normed coherency are computed. Analyses reveal that the hydrological mass redistributions deduced from LaD contribute to polar motion excitation at retrograde periods around 4 yr, although the signal energy is smaller in the hydrological excitations than that in the residual geodetic excitations.

... At the CMB, an SA with i = 1 and j = 0 cannot be generated by the interactions of the field with the toroidal zonal flow acceleration (see equation (14) and Table 1) responsible for the changes in LOD, but can be the result of flow accelerations contributing to changes in pressure at the CMB [e.g., Chulliat and Hulot, 2000]. If these changes in pressure result in torques that are not aligned with the axis of rotation they may contribute to changes in the orientation of the Earth's rotation axis (the Earth orientation parameters, EOP) [Hinderer et al., 1987[Hinderer et al., , 1990Greff-Lefftz and Legros, 1995;Hide et al., 1996;Hulot et al., 1996], although this signal should be small. A 2.5 year periodic signature of this process is, however, not present in the EOP data [see, e.g., Gibert and Le Mouël, 2008], rejecting the above hypothesis. ...

The first time derivative of residual length-of-day observations is
known to contain a distinctive 6 year periodic oscillation. Here we
theorize that through the flow accelerations at the top of the core the
same periodicity should arise in the geomagnetic secular acceleration.
We use the secular acceleration of the CHAOS-3 and CM4 geomagnetic field
models to recover frequency spectra through both a traditional Fourier
analysis and an empirical mode decomposition. We identify the 6 year
periodic signal in the geomagnetic secular acceleration and characterize
its spatial behavior. This signal seems to be closely related to recent
geomagnetic jerks. We also identify a 2.5 year periodic signal in
CHAOS-3 with unknown origin. This signal is strictly axially dipolar and
is absent from other magnetic or geodetic time series.

... It appears that the topographic coupling torques are too large for DLOD if they are suf®cient for polar-motion variations (Jault & Le Moue Èl 1989;Hinderer et al. 1990). Recent investigations show that the topographic coupling is probably too small by a factor 10 (Greff- Lefftz & Legros 1995) or 5 (Hide et al. 1996) to explain the decadal variations of polar motion. Hulot et al. (1996) concluded that the excitation of polar motion by outer-core processes is a combination of several processes. ...

In this paper an explanation of the observed decadal variations of the polar motion of the Earth is presented. Recent investigations show that the contribution of surface processes is too small to excite the observed magnitudes of the decadal variations of polar motion. After removing the known effects of atmospheric variations from the observed polar motion, we obtain significant residuals that obviously can only be explained by processes in the core. In this paper, we investigate the effect of a relative inner-core rotation. In particular, we assume that the orientation of the figure axis of the inner core changes with respect to the outer core and mantle. Due to the flattening of the inner core and the density difference between the inner and outer core, these changes contribute to variations of the Earth's polar motion due to internal mass redistributions. The objective of this study is to determine those changes in the orientation of the figure axis of the inner core that produce mass redistributions necessary to excite the decadal variations of the observed polar motion minus the estimated atmospheric influence.
Using polar motion data and the atmospheric excitation function, it is possible to determine the excitation function of the internal process superimposed on the free wobble of the Earth by linear approximation of the Liouville equation. On the other hand, provided that only the contribution of the mass redistributions is significant, we can express the time function obtained in terms of the orientation of the figure axis of the inner core. The final expression then contains the corresponding orientation angles as unknowns. Using this expression, we calculate the orientation angles from the numerically determined values of the excitation function. The calculation results in a mean tilt of 1°, and a mean eastward drift of 0.7° yr−1 of the figure axis of the inner core and quasi-periodic decadal variations of its orientation angles.
The associated changes of the mass geometry in the core due to these variations of the figure axis of the inner core are then used to estimate their influence on the Earth's outer gravity field. Finally, we compare the magnitude of the resulting gravity field variations with the accuracy of recent and future gravity field models.

... This result was also confirmed by Jault and Le Mouël (1989) (they attached to Hide's method more detailed reasoning by allowing for the role of inertial force on the outer core fluid to complete the angular momentum budget in the core and mantle (see Section 2.1.1)). The calculation of the equatorial topographic torque by Hide's method has also been attempted, which indicates that its typical magnitude is smaller by several factors than that corresponding to the Markowitz wobble (Lefftz and Legros, 1995; Hide et al., 1996; Hulot et al., 1996). The time series of these calculations achieved no significant correlation in phase with the observation. ...

With the prospect of studying the relevance of the topographic core-mantle coupling to the variations of the Earth's rotation and also its applicability to constraining the core surface flow, we investigate the variability of the topographic torque estimated by using core surface flow models accompanied by (a) uncertainty due to the non-uniqueness problem in the flow inversion, and (b) variance originating in that of geomagnetic secular variation models employed in the inversion. Various flow models and their variances are estimated by inverting prescribed geomagnetic models at the epoch 1980. The subsequent topographic torque is then calculated by using a core-mantle boundary topography model obtained by seismic tomography. The calculated axial and equatorial torques are found subject to the variability of order 10 19 and 10 20 Nm, respectively, on which (b) is more effective than (a). The variability of the torque is attributed even to (a) and (b) of the large-scale flows (degrees 2 and 3). Yet, it still seems unlikely for the decadal polar motion with the observed amplitude to be excited exclusively by the equatorial topographic torque associated with any of reasonable core surface flow models. It is also confirmed that, with the topography model adopted here, the axial topographic torque on a rigid annulus in the core (coaxial with the Earth's rotation axis) associated with any of reasonable flow models is larger by two orders of magnitude than the plausible inertial torque on such cylinders. This implies that any core surface flow model consistent with the topographic coupling does not exist, unless the topography model is appropriately modified. Nevertheless, the topographic coupling might provide not only a weak constraint for explaining the decadal LOD variations, but also the possibility to probe the core surface flow and the core dynamics.

... [43] Interactions between the fluid outer core and mantle also appear to be ineffective in exciting decadal polar motion variations. Electromagnetic coupling between the core and mantle appears to be 2 – 3 orders of magnitude too weak [Greff-Lefftz and Legros, 1995] and topographic coupling appears to be too weak by a factor of three to ten [Greff-Lefftz and Legros, 1995; Hide et al., 1996; Hulot et al., 1996]. In addition, the modeled decadal polar motion variations resulting from these studies show little agreement in phase with the observed variations. ...

1] The contribution of atmospheric wind and surface pressure and oceanic current and bottom pressure variations during 1949–2002 to exciting changes in the Earth's orientation on decadal timescales is investigated using an atmospheric angular momentum series computed from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis project and an oceanic angular momentum series computed from a near-global ocean model that was forced by surface fluxes from the NCEP/NCAR reanalysis project. Not surprisingly, since decadal-scale variations in the length of day are caused mainly by interactions between the mantle and core, the effect of the atmosphere and oceans is found to be only about 14% of that observed. More surprisingly, it is found that the effect of atmospheric and oceanic processes on decadal-scale changes in polar motion is also only about 20% (x component) and 38% (y component) of that observed. Therefore redistribution of mass within the atmosphere and oceans does not appear to be the main cause of the Markowitz wobble. It is also found that on timescales between 10 days and 4 years the atmospheric and oceanic angular momentum series used here have very little skill in explaining Earth orientation variations before the mid to late 1970s. This is attributed to errors in both the Earth orientation observations prior to 1976 when measurements from the accurate space-geodetic techniques became available and to errors in the modeled atmospheric fields prior to 1979 when the satellite era of global weather observing systems began.

... Indeed, the idea that pressure variations at the CMB may entrain polar motion through a combination of a change in the moment of inertia and an equatorial torque on the mantle (by topographic coupling at the CMB) has been investigated by many authors (e.g. Hinderer et al. 1987 Hinderer et al. , 1990 Greff-Lefftz & Legros 1995; Hulot et al. 1996; Hide et al. 1996). The general conclusion of these studies is that the predicted polar motion is too small by approximately a factor 5–10, in the best of cases, to explain the observed decadal variations in polar motion. ...

The temporal variation in the density structure associated with convective motions in the outer core causes a change in the Earth's gravity field. Core flows also lead to a gravity change through the global elastic deformations that accompany changes in the non-hydrostatic pressure at the core–mantle boundary (CMB). In this work, we present predictions of the gravity changes from these two processes during the past century. These predictions are built on the basis of flows at the surface of the core that are reconstructed from the observed geomagnetic secular variation. The pressure-induced gravity variations can be reconstructed directly from surface core flows under the assumption of tangential geostrophy; predicted variations in the Stokes coefficients of degree 2, 3 and 4 are of the order of 10−11, 3 × 10−12 and 10−12, respectively, with a typical timescale of a few decades. These correspond to changes in gravity of 70, 30 and 15 nGal, and to equivalent geoid height variations of 0.15, 0.05 and 0.02 mm, respectively. The density-induced gravity variations cannot be determined solely from surface core flows, though a partial recovery is possible if flows with important axial gradients dominate the dynamics at decadal timescales. If this is the case, the density-induced gravity signal is of similar amplitude and generally anti-correlated with the pressure-induced signal, thus reducing the overall amplitude of the gravity changes. However, because we expect decadal flows to be predominantly axially invariant, the amplitude of the density-induced gravity changes should be much smaller. Our prediction also allows to determine upper bounds in pressure change at the CMB and density change within the core that have taken place during the past 20 yr such that observed gravity variations are not exceeded; for harmonic degree 2, we find a maximum pressure change of approximately 350 Pa and a maximum departure from hydrostatic density of approximately 1 part in 107. Although the predicted gravity changes from core flows are small, they are at the threshold of detectability with high-precision gravity measurements from satellite missions such as GRACE. The most important challenge to identifying a core signal will be the removal of interannual gravity variations caused by surface processes which are an order of magnitude larger and mask the core signal.

... The conclusion of all these studies is that surface processes cannot excite a polar motion of the amplitude and form of the Markowitz wobble. The polar motion resulting from an exchange of angular momentum between the core and the mantle by electromagnetic (Greff-Lefftz & Legros 1995) and topographic coupling (Greff-Lefftz & Legros 1995; Hide et al. 1996; Hulot et al. 1996) at the core–mantle boundary (CMB) is also incapable of explaining the Markowitz wobble. Another possibility is that the Markowitz wobble may be a consequence of forced time-dependent changes in the orientation of the figure axis of the inner core. ...

SUMMARYA decadal polar motion with an amplitude of approximately 25 milliarcsecs (mas) is observed over the last century, a motion known as the Markowitz wobble. The origin of this motion remains unknown. In this paper, we investigate the possibility that a time-dependent axial misalignment between the density structures of the inner core and mantle can explain this signal. The longitudinal displacement of the inner core density structure leads to a change in the global moment of inertia of the Earth. In addition, as a result of the density misalignment, a gravitational equatorial torque leads to a tilt of the oblate geometric figure of the inner core, causing a further change in the global moment of inertia. To conserve angular momentum, an adjustment of the rotation vector must occur, leading to a polar motion. We develop theoretical expressions for the change in the moment of inertia and the gravitational torque in terms of the angle of longitudinal misalignment and the density structure of the mantle. A model to compute the polar motion in response to time-dependent axial inner core rotations is also presented. We show that the polar motion produced by this mechanism can be polarized about a longitudinal axis and is expected to have decadal periodicities, two general characteristics of the Markowitz wobble. The amplitude of the polar motion depends primarily on the Y12 spherical harmonic component of mantle density, on the longitudinal misalignment between the inner core and mantle, and on the bulk viscosity of the inner core. We establish constraints on the first two of these quantities from considerations of the axial component of this gravitational torque and from observed changes in length of day. These constraints suggest that the maximum polar motion from this mechanism is smaller than 1 mas, and too small to explain the Markowitz wobble.

... In this way, the total torque on the fluid core remains small, and so does its angular momentum variation. However, attempts at evaluating the equatorial torque at the CMB suggest that the latter is too small to provide the balance (Greff-Lefftz & Legros 1995; Hide et al. 1996; Hulot et al. 1996). Another possibility is if the torque on the inner core is not from surface stresses but from a gravitational volume force. ...

SUMMARYA tilt of the geometric figure of the inner core with respect to the mantle results in a global internal mass displacement. This comprises two parts: the redistribution of mass from the rigid equatorial rotation of the elliptical inner core; and that from global elastic deformations that occur to maintain the mechanical equilibrium. This global mass reorganization leads to changes in the moment of inertia tensor and, equivalently, to changes in the degree 2 component of the gravitational field. In this work, we compute the predicted changes in both gravity and in the moment of inertia tensor as a function of inner core tilt. We show that the inclusion of elastic deformations increases the amplitude of the gravity change at the surface by a factor 1.97. The Stokes coefficients that are the most affected are C21, S21: a tilt angle of 0.05° leads to a change in these coefficients of ∼4 × 10−11, while leading to changes in other coefficients of degree 2 that are three orders of magnitude smaller. Observed changes in C21, S21 and in polar motion contain decadal variations of undetermined origin; in an effort to determine whether these could be caused by temporal changes in inner core tilt, we compute the changes in C21, S21 based on the observed polar motion and compare this prediction against observed variations as determined by satellite laser ranging (SLR) between 1985 and 2005. We show that observed decadal changes in C21, S21 and in polar motion suggest that both are predominantly driven by variations in the moment of inertia tensor. The source of these variations cannot be unambiguously determined, nor can we confirm whether they are of internal or surficial origin. Changes in inner core tilt are then not necessarily the cause of these variations, though if they are, our results show that motion in the fluid core must not play a significant role in the global angular momentum balance.

The physical properties and their lateral variation in 200–400 km thick regions surrounding Earth's core-mantle boundary and inner core boundary are important to the functioning and evolution of Earth's dynamo. The complexity of structure in the lowermost mantle rivals that near its tectonically active surface, but improvements in its imaging may allow better estimates of heat transport across the core-mantle boundary. Some, but not all, seismic observations suggest the existence of 100–200 km thick stably stratified regions at both the top and bottom of the liquid outer core, both of which may affect magnetic secular variations. Seismically resolvable large-scale topography on the core-mantle and inner core boundaries can affect fluid flow in the outer core, inducing signals in the magnetic field and length of day. Lateral variations in seismic velocities in the lowermost outer core and solid inner core, including variations in the anisotropy of the inner core, may reflect lateral variations in the solidification and melting of the inner core.

The observed Earth's polar motion on decadal time scales has long been conjectured to be excited by the exchange of equatorial angular momentum between the solid mantle and the fluid outer core, via the mechanism of electromagnetic (EM) core-mantle coupling. However, past estimations of the EM coupling torque from surface geomagnetic observations is too weak to account for the observed decadal polar motion. Our recent estimations from numerical geodynamo simulations have shown the opposite. In this paper, we re-examine in detail the EM coupling mechanism and the properties of the magnetic field in the electrically conducting lower mantle (characterized by a thin D″-layer at the base of the mantle). Our simulations find that the toroidal field in the D″-layer from the induction and convection of the toroidal field in the outer core could be potentially much stronger than that from the advection of the poloidal field in the outer core. The former, however, cannot be inferred from geomagnetic observations at the Earth's surface, and is missing in previous EM torque estimated from geomagnetic observations. Our deduction suggests further that this field could make the actual EM coupling torque sufficiently strong, at approximately 5 × 1019 Nm, to excite, and hence explain, the decadal polar motion to magnitude of approximately 10 mas. Keywords: Polar motion, Electromagnetic core-mantle coupling, Geomagnetic field, Geodynamo

Long time geodetic observation records show that the orientation of the Earth's rotation axis with respect to the terrestrial reference frame, or polar motion, changes on a broad range of time scales. Apart from external torques from the luni-solar tides, these changes are excited by interactions among different components of the Earth system. The convective fluid outer core has long been conjectured a likely contributor to the observed polar motion on time scales upwards of decades, such as the ∼30−year Markowitz wobble. We investigated the electromagnetic (EM) coupling scenario across the core-mantle boundary (CMB) via numerical geodynamo simulation for different geodynamo parameters (Rayleigh numbers and magnetic Rossby numbers). Our simulated polar motion varies strongly with the dynamo parameters, while its excitation on decadal time scales appear to converge asymptotically within the adopted range of numerical Rossby numbers. Three strongest asymptotic modes emerge from numerical results, with periods around 30, 40 and 60 years for the prograde excitation, and around 24, 30 and 60 years for the retrograde excitation. Their amplitudes are all larger than 5 × 10−8, or approximately 10 milliarcseconds. The results suggest that the electromagnetic core-mantle coupling could explain a substantial portion, if not all, of the observed decadal polar motion. In particular, the predicted 60-year polar motion deserves special attention for future observations and studies.

The Earth does not rotate uniformly. Not only does its rate of rotation vary, but it wobbles as it rotates. These variations in the Earth's rotation, which occur on all observable timescales from subdaily to decadal and longer, are caused by a wide variety of processes, from external tidal forces to surficial processes involving the atmosphere, oceans, and hydrosphere to internal processes acting both at the core-mantle boundary as well as within the solid body of the Earth. In this chapter, the equations governing small variations in the Earth's rotation are derived, the techniques used to measure the variations are described, and the processes causing the variations are discussed.

The output of a coupled climate system model provides a synthetic climate record with temporal and spatial coverage not attainable with observational data, allowing evaluation of climatic excitation of polar motion on timescales of months to decades. Analysis of the geodetically inferred Chandler excitation power shows that it has fluctuated by up to 90% since 1900 and that it has characteristics representative of a stationary Gaussian process. Our model-predicted climate excitation of the Chandler wobble also exhibits variable power comparable to the observed. Ocean currents and bottom pressure shifts acting together can alone drive the 14-month wobble. The same is true of the excitation generated by the combined effects of barometric pressure and winds. The oceanic and atmospheric contributions are this large because of a relatively high degree of constructive interference between seafloor pressure and currents and between atmospheric pressure and winds. In contrast, excitation by the redistribution of water on land appears largely insignificant. Not surprisingly, the full climate effect is even more capable of driving the wobble than the effects of the oceans or atmosphere alone are. Our match to the observed annual excitation is also improved, by about 17%, over previous estimates made with historical climate data. Efforts to explain the 30-year Markowitz wobble meet with less success. Even so, at periods ranging from months to decades, excitation generated by a model of a coupled climate system makes a close approximation to the amplitude of what is geodetically observed.

The goal of our study is to determine accurate time series of geophysical Earth rotation excitations to learn more about global dynamic processes in the Earth system. For this purpose, we developed an adjustment model which allows to combine precise observations from space geodetic observation systems, such as Satellite Laser Ranging (SLR), Global Navigation Satellite Systems, Very Long Baseline Interferometry, Doppler Orbit determination and Radiopositioning Integrated on Satellite, satellite altimetry and satellite gravimetry in order to separate geophysical excitation mechanisms of Earth rotation. Three polar motion time series are applied to derive the polar motion excitation functions (integral effect). Furthermore we use five time variable gravity field solutions from Gravity Recovery and Climate Experiment to determine not only the integral mass effect but also the oceanic and hydrological mass effects by applying suitable filter techniques and a land–ocean mask. For comparison the integral mass effect is also derived from degree 2 potential coefficients that are estimated from SLR observations. The oceanic mass effect is also determined from sea level anomalies observed by satellite altimetry by reducing the steric sea level anomalies derived from temperature and salinity fields of the oceans. Due to the combination of all geodetic estimated excitations the weaknesses of the individual processing strategies can be reduced and the technique-specific strengths can be accounted for. The formal errors of the adjusted geodetic solutions are smaller than the RMS differences of the geophysical model solutions. The improved excitation time series can be used to improve the geophysical modeling.

A short general explanation of tidal forces and tidal effects is given. The influences of Earth tides and ocean tides on the Earth's rotation vector are presented. Today, the theoretical models for periodic variations in the Earth's rotation and in polar motion can be compared with precise measurements done by modern space techniques. Secular changes of the Earth's rotation due to interactions within the Earth-Moon-system are also discussed.

The output of a coupled climate system model provides a synthetic climate record with temporal and spatial coverage not attainable with observational data, allowing evaluation of climatic excitation of polar motion on timescales of months to decades. Analysis of the geodetically inferred Chandler excitation power shows that it has fluctuated by up to 90% since 1900 and that it has characteristics representative of a stationary Gaussian process. Our model-predicted climate excitation of the Chandler wobble also exhibits variable power comparable to the observed. Ocean currents and bottom pressure shifts acting together can alone drive the 14-month wobble. The same is true of the excitation generated by the combined effects of barometric pressure and winds. The oceanic and atmospheric contributions are this large because of a relatively high degree of constructive interference between seafloor pressure and currents and between atmospheric pressure and winds. In contrast, excitation by the redistribution of water on land appears largely insignificant. Not surprisingly, the full climate effect is even more capable of driving the wobble than the effects of the oceans or atmosphere alone are. Our match to the observed annual excitation is also improved, by about 17%, over previous estimates made with historical climate data. Efforts to explain the 30-year Markowitz wobble meet with less success. Even so, at periods ranging from months to decades, excitation generated by a model of a coupled climate system makes a close approximation to the amplitude of what is geodetically observed.

SummaryA tilted inner core permits exchange of angular momentum between the core and the mantle through gravitational and pressure torques and, as a result, changes in the direction of Earth's axis of rotation with respect to the mantle. We have developed a model to calculate the amplitude of the polar motion that results from an equatorial torque at the inner core boundary which tilts the inner core out of alignment with the mantle. We specifically address the issue of the role of the inner core tilt in the decade polar motion known as the Markowitz wobble. We show that a decade polar motion of the same amplitude as the observed Markowitz wobble requires a torque of 1020 N m which tilts the inner core by 0.07 degrees. This result critically depends on the viscosity of the inner core; for a viscosity less than 5 × 1017 Pa s, larger torques are required. We investigate the possibility that a torque of 1020 N m with decadal periodicity can be produced by electromagnetic coupling between the inner core and torsional oscillations of the flow in the outer core. We demonstrate that a radial magnetic field at the inner core boundary of 3 to 4 mT is required to obtain a torque of such amplitude. The resulting polar motion is eccentric and polarized, in agreement with the observations. Our model suggests that equatorial torques at the inner core boundary might also excite the Chandler wobble, provided there exists a physical mechanism that can generate a large torque at a 14 month period.

The magnetic field of the Earth is by far the best documented magnetic field of all known planets. Considerable progress has
been made in our understanding of its characteristics and properties, thanks to the convergence of many different approaches
and to the remarkable fact that surface rocks have quietly recorded much of its history. The usefulness of magnetic field
charts for navigation and the dedication of a few individuals have also led to the patient construction of some of the longest
series of quantitative observations in the history of science. More recently even more systematic observations have been made
possible from space, leading to the possibility of observing the Earth’s magnetic field in much more details than was previously
possible. The progressive increase in computer power was also crucial, leading to advanced ways of handling and analyzing
this considerable corpus of data. This possibility, together with the recent development of numerical simulations, has led
to the development of a very active field in Earth science. In this paper, we make an attempt to provide an overview of where
the scientific community currently stands in terms of observing, interpreting and understanding the past and present behavior
of the so-called main magnetic field produced within the Earth’s core. The various types of data are introduced and their
specific properties explained. The way those data can be used to derive the time evolution of the core field, when this is
possible, or statistical information, when no other option is available, is next described. Special care is taken to explain
how information derived from each type of data can be patched together into a consistent description of how the core field
has been behaving in the past. Interpretations of this behavior, from the shortest (1yr) to the longest (virtually the age
of the Earth) time scales are finally reviewed, underlining the respective roles of the magnetohydodynamics at work in the
core, and of the slow dynamic evolution of the planet as a whole.
KeywordsEarth-Geomagnetism-Archeomagnetism-Paleomagnetism-Magnetic observations-Archeomagnetic records-Paleomagnetic records-Spherical harmonic magnetic field models-Statistical magnetic field models-Geomagnetic secular variation-Geomagnetic reversals-Core magnetohydrodynamics-Numerical dynamo simulation-Geodynamo-Earth’s planetary evolution

Very long baseline interferometry (VLBI) observations of compact extragalactic radio sources collected in North America and Europe between July 1980-December 1984 are analyzed. The nutations derived from VLBI data are compared with the nutations in the Wahr series (1981). Good correlation of the data is observed; however, it is detected that a correction of -1.80 + or - 0.18-i(0.42 + or - 0.18) is required for the amplitude of the retrograde annual nutation in the Wahr series. The change in free core nutation resonance frequency is calculated to explain the derivation in the retrograde annual nutation. It is concluded that VLBI earth nutation measurements have sufficient accuracy to be sensitive to core-mantle boundary properties.

The core-mantle boundary (CMB) is the most significant internal boundary within our planet, buried at remote depths and probably forever hidden from direct observation; yet this region is very important to our understanding of the dynamic Earth system. The thermal and chemical processes operating near the CMB have intimate relationships to fundamental events in Earth history, such as core formation, and continue to play a major role in the planet's evolution, influencing the magnetic field behavior, chemical cycling in the mantle, irregularities in the rotation and gravitation of the planet, and the mode of thermal convection of the Earth. This overview highlights the progress and future directions in geophysical investigations of the CMB region. -from Authors

The torque exerted on the mantle is examined with emphasis on purely mechanical topographic or pressure core-mantle coupling. Pressure perturbations accompanying tangentially geostrophic, frozen-flux core flow acting on core-mantle boundary topography can exert an "enormous' torque on the mantle if thermal core-mantle interactions drive such flow. Conditions for growing or changing a dipole and correlating its fluctuations with those in the length of the day are analyzed. -Author

The terrestrial field is traced here to the existence of thermoelectric currents in the metallic interior of the earth. The currents owe their existence to inhomogeneities continually created by turbulent convective motions. In order to obtain a nonvanishing resultant angular momentum of the currents around the earth's axis, the current system must exhibit a particular asymmetry. The latter is shown to originate through the preponderant influence of the Coriolis force upon the convective motions. In Part I the well-known proof, based on potential theory, of the fact that the currents must flow inside and not outside the earth, is briefly reproduced. In Part II an analysis of the formal expression for the current density is given. By means of a development in spherical harmonics the conditions for a nonvanishing current momentum can be formulated. It appears that temperature fluctuations in an otherwise homogeneous medium always yield a zero momentum, therefore the existence of inhomogeneities in the material is also required. In Part III it is pointed out that geophysicists have previously obtained evidence of the existence of a metallic core of the earth in which the viscosity is extremely low as compared to the viscosity of the rocks. Radioactive impurities which are very small compared to the total radioactivity of the earth are sufficient to maintain thermally driven convective motions in the metallic core. An estimate of the various terms in the hydrodynamic equations shows that the Coriolis force is much larger than all other dynamical effects. In Part IV we discuss the effect of the Coriolis force in producing that particular asymmetry which leads to a resultant angular momentum of the currents. It is shown that the inhomogeneities in material required according to the analysis of Part II can be accounted for by phase transformations of the material induced by the pressure changes which are connected with the vertical component of the motions. In Part V an attempt is made to estimate numerically the current density, basing the estimate on some general results of the theory of conductivity. For temperature variations of the order of 10° the calculated value of the current is in satisfactory agreement with the observed magnitude of the earth's magnetic moment. At the end, the bearing of these ideas upon the magnetism of sunspots is briefly discussed.

Astronomically-determined irregular fluctuations in the Earth's rotation
vector on decadal time scales can be used to estimate the fluctuating
torque on the lower surface of the Earth's mantle produced by
magnetohydrodynamic flow in the underlying liquid metallic core. A
method has been proposed for testing the hypothesis that the torque is
due primarily to fluctuating dynamic pressure forces acting on irregular
topographic features of the core-mantle boundary and also on the
equatorial bulge. The method exploits (a) geostrophically-constrained
models of fluid motions in the upper reaches of the core based on
geomagnetic secular variation data, and (b) patterns of the topography
of the CMB based on the mantle flow models constrained by data from
seismic tomography, determinations of long wave-length anomalies of the
Earth's gravitational field and other geophysical and geodetic data.
According to the present study, the magnitude of the axial component of
the torque implied by determinations of irregular changes in the length
of the day is compatible with models of the Earth's deep interior
characterized by the presence of irregular CMB topography of effective
"height" no more than about 0.5 km (about 6% of the equatorial bulge)
and strong horizontal variations in the properties of the D″ layer
at the base of the mantle. The investigation is now being extended to
cover a wider range of epochs and also the case of polar motion on
decadal time scales produced by fluctuations in the equatorial
components of the torque.

Motions at the top of the core which generate the observed Secular Variation (S.V.) field are computed. To reduce the well known ambiguity of the solution, two constraints are added: the flow is a large scale one and is geostrophic. The computed flow then has a very simple geometry; its poloïdal part is roughly axisymmetrical with respect to an equatorial diameter. This geometry is almost unchanged from 1970 to 1980 while the intensity of the velocity is nearly doubled.

It is noted that the time-scale of the secular variation of the geomagnetic field is rather short compared with the electromagnetic diffusion times appropriate to the earth's core. It is therefore suggested that the secular variation is primarily due to the rearrangement of pre-existing lines of force emanating from the core, and not due to the creation of new (or destruction of old) flux tubes by electromagnetic diffusion. The theoretical consequences of this idea are fully examined. © 1965, Society of Geomagnetism and Earth, Planetary and Space Sciences. All rights reserved.

We discuss the analysis of 798 very long baseline interferometry (VLBI) experiments carried out between July 1980 and February 1989, and the determination from this analysis of corrections to selected coefficients in the International Astronomical Union (IAU) 1980 theory of the nutations of the Earth. Our analysis confirms earlier VLBI results and indicates that most of these corrections can be explained by carefully accounting for (1) corrections to the IAU 1980 rigid-Earth nutation series, (2) the presence of the Earth's inner core, (3) the difference between the dynamic flattening of the Earth inferred from the precession constant and that inferred from seismic models of the internal density structure of the Earth, and (4) the effects of mantle anelasticity and ocean tides. The standard deviations of the corrections to the coefficients are 0.04 milliarcseconds (mas) for terms with periods under 430 days, and 1.0 mas for the terms with a period of 18.6 years. The unresolved issues raised by our analysis are the origins of corrections to the out-of-phase retrograde annual (0.39 mas) and the in-phase prograde 13.66 day (-0.25 mas) nutations. Our analysis also yields a correction to the IAU 1976 value for the luni-solar precession constant of -0.32+/-0.13 arc sec/century (cy). ©1991 American Geophysical Union

The mechanisms responsible for fluctuations in the earth's rotation are investigated in a review of recent theoretical and observational studies. The basic terminology is defined, and consideration is given to tidal terms, long-term nontidal changes, and decade fluctuations in the length of the day and to long-period and Chandler-wobble geographical motion of the rotation pole. It is shown that space observation techniques such as Lageos laser ranging and improved meteorological and geodynamic measurements have led to a better understanding of short-term processes (such as the effects of mantle anelasticity and core-mantle coupling) and can provide the basis for studying the zonal-tide-driven 18.6-yr length-of-day changes, polar wander, and the 30-yr Markowitz wobble in the coming decades. Better seismological data are required to investigate seismic excitation of the Chandler wobble or the topographic coupling of the core and mantle.

The paper deals with the electromagnetic effect of motions in the earth's core, considered as a fluid metallic sphere. On the basis of simple estimates the electric conductivity of the core is assumed of the same order of magnitude as that of common metals. The mathematical treatment follows Hansen and Stratton: three independent vector solutions of the vectorial wave equation are introduced; two of these have vanishing divergence, and they are designated as toroidal and poloidal vector fields. The vector potential and electric field are toroidal, whereas the magnetic field is poloidal. These vectors, expressed in terms of spherical harmonics and Bessel functions, possess some notable properties of orthogonality which are briefly discussed. The theory of the free, exponentially decaying current modes is then given, leading to decay periods of the order of some tens of thousands of years. Next, the field equations in the presence of mechanical motions of the conducting fluid are set up. The field is developed in a series of the fundamental, orthogonal vectors, and the field equations are transformed into a system of ordinary differential equations for the coefficients of this development. The behavior of the solutions depends on the symmetry of the "coupling matrix" that arises from the term of the field equations expressing the induction effects. In order to evaluate this matrix the velocity field is developed into a series of the fundamental vectors similar to the series for the electromagnetic field. It is then shown that when the velocity is a toroidal vector field the coupling matrix is antisymmetrical. When the velocity field is poloidal, the coupling matrix is neither purely symmetrical nor purely antisymmetrical. For stationary fluid motion the linear differential equations can be integrated in closed form by a transformation to new normal modes, whenever the matrix of the system is either symmetrical or antisymmetrical. In the latter case the eigenvalues are purely imaginary and the coefficients of the new normal modes are harmonic functions of time, representing oscillatory changes in amplitude of the field components. For a symmetrical matrix the eigenvalues are real and the time factors of the new normal modes are real exponentials representing amplification or de-amplification as the case may be, depending on the sign of the velocity. For a matrix without specific symmetry, normal modes do not, as a rule, exist but similar, somewhat less stringent results can be derived in special cases. In the case of toroidal flow, in particular, the oscillatory changes of the field components are superposed upon the slow exponential decay characteristic of the free modes.

It can be shown that the currents in the earth's core which give rise to the externally observable magnetic field do not form a complete set of solutions of the field equations. There exists a second set of solutions composed of the modes of the electric type which produce a magnetic field inside the metallic sphere, but appear at the outside only through an electric field too weak to be measured. For reasons of symmetry the most important terms among the electric modes are the quadrupoles. The theory of inductive coupling by fluid motion, developed previously, is here applied to the interaction of the magnetic and electric modes. The system again is non-conservative, and work is done on the field by the fluid, or vice versa. It is shown that the interaction between the magnetic dipole and electric quadrupole modes constitutes a basic amplifier mechanism which amplifies the quadrupole mode until the magneto-mechanical forces exerted by the field upon the fluid begin to slow down the motion, thus prohibiting further increase of the field. This internal quadrupole field is likely to be much larger than the ordinary magnetic dipole field. Further analysis leads one to interpret the couplings between the magnetic and electric modes as a feed-back amplifier whereby the field can be maintained through the power delivered to it by the fluid motion. A survey of possible sources of power for this process indicates that the power for the maintenance of the field is provided from the rotational energy lost by the earth as it is slowed down through the action of the lunar tide.

Since the time Roberts & Scott (1965) first expressed the key ‘frozen flux’ hypothesis relating the secular variation of the geomagnetic field (SV) to the flow at the core surface, a large number of studies have been devoted to building maps of the flow and inferring its fundamental properties from magnetic observations at the Earth's surface. There are some well-known difficulties in carrying out these studies, such as the one linked to the non-uniqueness of the flow solution [if no additional constraint is imposed on the flow (Backus 1968)] which has been thoroughly investigated. In contrast little investigation has been made up to now to estimate the exact importance of other difficulties, although the different authors are usually well aware of their existence. In this paper we intend to make as systematic as possible a study of the limitations linked to the use of truncated spherical harmonic expansions in the computation of the flow. Our approach does not rely on other assumptions than the frozen flux, the insulating mantle and the large-scale flow assumptions along with some simple statistical assumptions concerning the flow and the Main Field. Our conclusions therefore apply to any (toroidal, steady or tangentially geostrophic) of the flow models that have already been produced; they can be summarized in the following way: first, because of the unavoidable truncation of the spherical harmonic expansion of the Main Field to degree 13, no information will ever be derived for the components of the flow with degree larger than 12; second, one may truncate the spherical harmonic expansion of the flow to degree 12 with only a small impact on the first degrees of the flow. Third, with the data available at the present day, the components of the flow with degree less than 5 are fairly well known whereas those with degree greater than 8 are absolutely unconstrained.

We demonstrate that earth nutation measurements made with very long baseline interferometry are of sufficient accuracy to be sensitive to the properties of the core-mantle boundary. The retrograde nutation with annual frequency is particularly sensitive, since this frequency is closest to that of the free core nutation, a nutational normal mode which produces relative motion of the core and mantle. Our nutation measurements imply a deviation of the amplitude of the retrograde annual nutation from its value as calculated by Wahr and by Sasao et al. If this deviation is interpreted as the effect of a departure of the core-mantle boundary from its hydrostatic figure, then the observed amplitude is consistent with a core-mantle boundary that has a second zonal harmonic deviation from the hydrostatic equilibrium figure, with the peak-to-valley deviation being 490±110 m. The part of the retrograde annual nutation out of phase with the driving torques yields an upper limit on the kinematic viscosity at the surface of the fluid core of 0.54 m2/s (99.5% confidence limit).

Standard time series analysis tech- niques have been applied to the homogeneous polar motion data recently published by the ILS-IPMS (Yumi and Yokoyama, 1980) in order to study some of the more controversial features apparently possessed by the older ILS data. The magnitude and direction of the secular trend unbiased by the presence of harmonics in the data were deter- mined, yielding a rate of polar wander 43.52x10 -3 arc sec/yr (which extrapolates to 40.98 ø/m.y.) in direction 80.1øW longitude. The long-period Markowitz wobble, which dominates the retrograde power spectrum of the data, has a signal to noise ratio in that spectrum of 21:1; its period is well-determined as 31 years. Variations with time of the annual wobble and Chandler wobble were investigated using complex demodulation; the annual wobble was found to undergo relatively in- significant variations in amplitude and phase, in contrast to some analyses of the older ILS data, while the amplitude modulation and 19'25-1940 phase change of the Chandler wobble were re- confirmed.

As arguments in favour of the notion that very slow convection in the highly viscous mantle is confined to the upper 700 km gradually weakened over the past 20 years, so geophysicists have increased their willingness to entertain the idea that significant horizontal variations in temperature and other structural parameters occur at all levels in the lower mantle. Concomitant density variations, including those caused by distortions in the shape of the core--mantle interface, would contribute substantially to long-wavelength features of the Earth's gravity field and also affect seismic travel times. The implied departures from axial symmetry in the thermal and mechanical boundary conditions thus imposed by deep mantle convection on the underlying low-viscosity liquid metallic core would affect not only spatial variations in the long-wavelength features of the main geomagnetic field (which is generated by dynamo action involving comparatively rapid chaotic magnetohydrodynamic flow in the core) but also temporal variations on all relevant timescales, from decades and centuries characteristic of the geomagnetic secular variation to tens of millions of years characteristic of changes in the frequency of polarity reversals. Core motions should influence the rotation of the `solid' Earth (mantle, crust and cryosphere), and in the absence of any quantitatively reasonable alternative line of attack, geophysicists have long supposed that irregular `decade' fluctuations in the length of the day of about 5 × 10-3 s must be manifestations of angular momentum exchange between the core and mantle produced by time-varying torques at the core--mantle interface. The stresses responsible for these torques comprise (a) tangential stresses produced by viscous forces in the thin Ekman--Hartmann boundary layer just below the interface and also by Lorentz forces associated with the interaction of electric currents in the weakly conducting lower mantle with the magnetic field there, and (b) normal stresses produced largely by dynamical pressure forces acting on irregular interface topography (i.e. departures in shape from axial symmetry). The hypothesis that topographic stresses might provide the main contribution to the torque was introduced by the author in the 1960s and the present paper gives details of his recently proposed method for using Earth rotation and other geophysical data in a new test of the hypothesis. The method provides a scheme for investigating the consistency of the hypothesis with various combinations of `models' of (a) motions in the outer reaches of the core based on geomagnetic secular variation data, and (b) core--mantle interface topography based on gravity and seismic data, thereby elucidating the validity of underlying assumptions about the dynamics and structure of the Earth's deep interior upon which the various `models' are based. The scheme is now being applied in a complementary study carried out in collaboration with R. W. Clayton, B. H. Hager, M. A. Spieth and C. V. Voorhies.

The earth's core may be assumed to consist of fluid metal surrounding a solid inner core which probably contains a source of heat to drive convection, but it is not possible at present to select between various possible types of convective motion in the fluid core. Types considered are characterized by some sort of radial flow streams and a tendency for the fluid to rotate on the average more rapidly near the axis to conserve angular momentum during the circulation. Though the actual flow may be quite complicated, proposed mechanisms for generating a terrestrial magnetic field are considered for some oversimplified flow patterns in an attempt to indicate what features of the flow may provide the most important possibilities for field generation. It is suggested that, without a field to absorb the energy, the flow would be accelerated indefinitely and would evolve through a succession of flow patterns, some of which would be expected to have the properties to generate a field capable of preventing further acceleration and prolonging the status quo, thus making it likely that the earth should have a field.

In the last few years seismologists have proposed core-mantle topographies. At the same time much effort has been devoted by geomagneticians to calculate the fluid flow (and the related pressure field) at the top of the core, based on the observation of the secular variation of the geomagnetic field. A ''topographic torque'', which results from the action of the pressure field at the core surface, has long been invoked to allow for exchanges of angular momentum between the core and the mantle. In this paper, we show that this torque can be computed if forces at the top of the core are in geostrophic balance. The deep nature of this topographic torque can be understood only if one goes beyond the case of a pseudo-static equilibrium and considers explicitly the acceleration term in the equation of motion. We show that the pressure field acts in such a way as to accelerate a zonal flow consisting of cylindrical annuli. These annuli rotate like rigid bodies, with an angular velocity which depends on the distance to the rotation axis. Furthermore, we show that a gravity torque may also act on these same cylinders.

It is shown that in a liquid of infinite conductivity hydrodynamic motion may result in an indefinite increase of the strength
of the internal magnetic field ; but that the external field is severely limited in the case when the volume occupied by the
liquid is simply connected. These limitations disappear when the volume is multiply connected. The case of finite conductivity
is then briefly discussed.

Astronomers have long noted that the Earth does not rotate uniformly about an axis fixed in the planet, that both the length-of-day and the direction of the rotation axis vary periodically and irregularly by small amounts. These variations are an immediate consequence of the Earth not being a rigid body. In this book Professor Lambeck discusses the irregular nature of this motion and the geophysical mechanisms responsible for it. A complete analysis of these causes requires a discussion of solid Earth physics, magnetohydrodynamics, oceanography and meteorology. The study of the Earth's rotation is therefore of interest not only to astronomers who wish to explain their observations, but also to many geophysicists who use the astronomers' observations to understand better the Earth's response to a variety of applied forces. The author emphasizes the important contributions made over the last 15 years, this progress being in part a consequence of the overall progress in geophysics and planetary physics and of the developments in space science and technology, which not only require that the Earth's motion be precisely known but which also have provided new and precise methods for monitoring this motion. This book is suitable for geophysicists, astronomers and geodesists who are actively engaged in research as well as for graduate students.

A three dimensional constant viscosity model for the mantle motions
which are caused by viscous shear at the core mantle interface and by
large scale buoyant forces is developed. The model utilizes geomagnetic
data and magnetohydrodynamic theory to define an outermost core free
stream velocity distribution. The resulting free stream velocity field
is used in conjunction with the viscous boundary layer equations to find
the corresponding stress field that the core exerts on the mantle. The
resulting stress field acting on the inner mantle along with various
passive outer boundary conditions are used to find the corresponding
three dimensional velocity field of the mantle. To account for large
scale buoyant forces, the model uses a currently available three
dimensional seismic velocity anomaly distribution for the mantle along
with simple linear models relating seismic velocity anomaly to density
perturbation.

The reality of the decadal fluctuations in the position of the Earth's
rotation pole with respect to the Earth's crust as exhibited in
solutions for the pole path determined using the ILS latitude
observations has been questioned in the past due to concerns about the
contaminating influence of systematic effects at the individual ILS
stations. A new solution for the pole path is recovered in this study by
a technique designed to account for any systematic effects that might be
occurring at individual stations.

Topics related to the study of the differential rotation of the earth
are discussed. Consideration is given to the main hydrodynamic and
electrodynamic equations governing differential rotation, with emphasis
on the 'inverse' problem of inferring motions in the fluid core from
observations of secular changes in the terrestrial magnetic field. The
contribution of GARP data to recent improvements in the measurement of
differential rotation is also considered.

We address the possibility for the core flows that generate the geomagnetic field to contribute significantly to the decade variations of the mean pole position (generally called the Markowitz wobble). This assumption is made plausible by the observation that the flow at the surface of the core-estimated from the geomagnetic secular variation models-experiences important changes on this time scale. We discard the viscous and electromagnetic core-mantle couplings and consider only the pressure torque γpf resulting from the fluid flow overpressure acting on the non-spherical core-mantle boundary (CMB) at the bottom of the mantle, and the gravity torque γgf due to the density heterogeneity driving the core flow. We show that forces within the core balance each other on the time scale considered and, using global integrals over the core, the mantle and the whole Earth, we write Euler's equation for the mantle in terms of two more useful torques γPgeo and γ. The “geostrophic torque”, γPgeo incorporates γpf and part of γgf, while γ is another fraction of γgf. We recall how the geostrophic pressure pgeo, and thus γPgeo for a given topography, can be derived from the flow at the CMB and compute the motion of the mean pole from 1900 to 1990, assuming in a first approach that the unknown γ can be neglected. The amplitude of the computed pole motion is three to ten times less than the observed one and out of the phase with it. In order to estimate the possible contribution of γ we then use a second approach and consider the case in which the reference state for the Earth is assumed to be the classical axisymmetric ellipsoidal figure with an almost constant ellipticity within the core. We show that (γPgeo + γ) is then equal to a pseudo-electromagnetic torque γL3, the torque exerted on the core by the component of the Lorentz force along the axis of rotation (this torque exists even though the mantle is assumed insulating). This proves that, at least in this case and probably in the more general case of a bumpy CMB, γ is not negligible compared with γPgeo. Eventually, we estimate the order of magnitude of γL3, show that it is likely to be small and conclude with further possibilities for the Markowitz wobble to be excited from within the core.

The motions in the Earth's electrically conducting fluid core which are the probable cause of the geomagnetic secular variations have time scales of the order of a few centuries or less. Seismic bounds on the kinematic molecular viscosity of the core and order-of-magnitude arguments about the eddy viscosity make plausible the hypothesis that at such short periods the core motion consists of a boundary layer of Ekman-Hartmann type close to the core mantle boundary, and an interior free-stream motion where the viscosity and resistivity can be set equal to zero. This boundary-layer approximation requires that the unknown vertical length scale of the poloidal geomagnetic field deep in the core be at least as long as the 600 km horizontal length scales inferred at the surface of the core from observations above the mantle. For periods shorter than a century the Ekman and magnetic boundary layers are probably thinner than 120 km. If magnetic flux diffusion is neglected (i.e. if electrical conductivity is considered infinite) in the free stream in the core then the external geomagnetic field is completely determined by the fluid motion at the top of the free stream. Therefore the hypothesis of negligible flux diffusion in the free stream has implications for the geomagnetic secular variation, and these implications can be used as a test of whether there is any motion of a perfectly conducting core which will produce the observed secular variation. If the observed secular variation passes this test, we can write down explicitly all `eligible' velocity fields, i.e. all velocity fields at the top of the free stream in the core which are capable of producing exactly the observed secular variation. The different eligible velocity fields are obtained by different choices of an arbitrary stream function on the surface of the core. We describe a method of selecting from among all eligible velocity fields those which are of particular geophysical interest, such as the one which is most nearly a rigid rotation (westward drift) or the one which is most nearly a latitude dependent westward drift with m degrees of freedom.

In the last few years, models of the flow at the top of the Earth's core and of the related pressure field have been calculated from the secular variation of the geomagnetic field, and core-mantle topographies have been computed by seismologists. A pressure torque results from the action of the pressure field on the core topography which can theoretically be computed from models of both the pressure field and the core-mantle interface. Small-scale features of the flow and of the topography are shown to be capable of contributing strongly to the pressure torque; it is thus impossible to calculate the exact value of the torque from the knowledge of only the long-wavelength components of the models. But the interaction between the large-scale components generates by itself torques two orders of magnitude larger than the torques inferred from the irregularities of the length of the day. It is nevertheless possible to reconcile the topographic coupling mechanism with the length of the day observations, keeping the amplitude of the core topography proposed by seismologists, if an orthogonality relation between the geometry of the fluid upwellings and downwellings at the top of the core and the topography is satisfied. It is shown how to compute such a topography, for a given flow, and close to an original topography provided by seismic tomography. Some consequences of the so-inferred link between the fluid flow at the top of the core and the core-mantle boundary topography are discussed.

Most realistic Earth models published as yet have been given in tabulated form, with the noticeable exception of three simple
parametric Earth models derived by Dziewonski et al. (1975). Simple interpolation in these tables may lead to inconsistencies,
when we consider certain effects which depend crucially on detailed density structure. We establish algorithmic formulae,
which may be used to compute all the mechanical properties of a model in an entirely consistent way, once the density as well
asP— andS— wave velocities are known. We then use this formulation to integrate Clairaut’s equation in a very efficient way, and thus
obtain the hydrostatic flattening to the first order in smallness at any point inside the model. For most geodynamic purposes,
we may suffice with this approximation. Finally, we show the results of some calculations of hydrostatic flattening to the
first and second order, using an iterative technique of solving the integral figure equations, for an Earth model consistent
with all geophysical data available at present. We find that the hydrostatic flattening at the surface should be about 1/298.8,
instead of 1/296.961 as quoted by Nakiboglu (1979) for essentially the same model. Moreover, from our results, we estimate
the actual flattening of the coremantle boundary to be about 1/390.3.

The emergence of greatly improved data sets over the past decade has heightened awareness of the close relationship between changes in the axial component of the angular momentum of the atmosphere and that of the solid Earth, the latter being reflected in small, though detectable, changes in the planet's rate of rotation. Changes in the large-scale wind field, and hence in atmospheric angular momentum, on intraseasonal through interannual time scales can be associated with a number of identifiable meteorological phenomena, whose further study has been given new impetus by the discovery of their signals in Earth's rotation. Future advances in the subject are apt to occur in connection with new data sets that will help address questions remaining about rapid changes in Earth rotation and the torques responsible for the momentum changes. Also in the coming decade, both new data and modeling approaches should help clarify the role of the oceanic portion of Earth's fluid envelope in the planetary momentum balance.

We present a method for determining the large-scale component of a tangentially geostrophic flow beneath the core-mantle boundary compatible with magnetic secular variation observations. We use a tangentially geostrophic basis to ensure the geostrophy of the motion. The fit of the secular variation (SV) generated by the motion to the observed SV (in fact SV models) is adequate, taking into account the existing error level. As in any horizontal geostrophic motion, the flow is expressed as a sum of two independent tangentially geostrophic flows: a zonal component, which is toroidal, and a non-zonal component, which is directly linked with the motions deeper in core. The flow derived for the recent epoch (1970–1985) presents interesting symmetry properties: the non-zonal velocities are the same at two antipodal points, while the zonal velocities are the same at two points symmetrical about the Equator. The non-zonal component of the flow is more vigorous than the zonal one; the consoidal ingredient, though weaker than the toroidal ingredient, is essential and indicates strong vertical motion at depth in low-latitude areas. The SV is actually compatible with a geostrophic motion at the core-mantle boundary and appears to be mainly due to the action of the non-zonal component of the flow.

We present the general expression for the topographic and electromagnetic torques acting at the core-mantle boundary (CMB) as a function of the outer core flow. Invoking angular momentum conservation of the Earth and of the core, we compute the perturbations in the rotation of the Earth, at the decade time-scale, resulting from this fluid motion, since 1900. Electromagnetic coupling is too weak to excite polar motion by two or three orders of magnitude. Although the pressure torque on a CMB topography computed by the authors involves some correlations between the temporal variation of the computed ω2-component of the polar motion and that observed, its amplitude is too weak by a factor of 10 and we have to conclude that it does not seem to be responsible for the decade variations of the polar motion.

Motions at the top of the core are known to be responsible for the secular variation of the Earth's magnetic field. If this flow is supposed geostrophic, the associated pressure field can have an appropriate geometry to exert a pressure torque upon the elliptical core-mantle boundary and, besides, to alter the elastic products of inertia in such a way as to excite the Earth's and core wobbles. We consider some schematic excitation functions and the resulting amplitudes of the Earth's and core rotational motions. The proposed mechanism is shown to be efficient for exciting the long-period Markowitz wobble of the rotation axis and also the Chandler wobble if the variations in the pressure field have the right time scales, as indeed suggested by the available secular variation data.

The interaction of the fluid pressure over the topography of the core mantle boundary generates a torque that leads to perturbations in the Earth's rotation. A general formulation of this topographic torque is proposed with the help of a development in spherical harmonics of the pressure and shape. Various implications of this coupling mechanism are discussed according to the symmetry properties of the dynamic pressure field at the core surface and the distribution of the topographical deviations (bumps) of the core mantle boundary inferred from seismology. Specifically, it is shown that different interaction terms contribute to the equatorial torque; although their sum cannot be precisely quantified using present knowledge, it could be sufficient to excite the Earth's wobble. The axial torque contribution seems to be too large to explain the decade fluctuations of the Earth's rotation rate, suggesting the existence of a mechanism which reduces the axial resulting torque without altering the equatorial one.

Changes in the motions inside the Earth's molten core are associated with changes in the core's angular momentum and, as a consequence, in the mantle's angular momentum. These motions can be estimated because they are responsible for both the maintenance of the geomagnetic field through dynamo action and the high frequency variations of the field. It can be shown that they do not play an important part in the excitation of the Chandler wobble. On the other hand changes in the angular momentum carried by cylindrical annuli rigidly rotating about the rotation axis balance changes in the mantle's angular momentum inferred from length of the day observations. In this paper, torques acting between the core and the mantle are discussed. It proves helpful to consider these mechanisms on a broad range of timescales from 1 day (damping of the free core nutation) to 105 years (equilibration of the Earth's dynamo).

The details of the method used to obtain a polar motion data set are
presented. The recently re-reduced International Latitude Service (ILS)
latitude observations to obtain the amplitudes of the largest forced
nutation terms was used. However, the errors in the recovered nutation
amplitudes are too large to allow us to discriminate between the current
theoretical results. After removing the observed results from the ILS
latitude values the position of the pole along with station corrections
by a novel damped least squares technique were obtained. The observed
trends in the station corrections cannot be caused by continental drift.
The popular motion time series has its data points spaced at intervals
of 19 days. By removing the mean, the trend and the annual term a time
series was obtained that was used to study the Chandler Wobble. The
trend in the polar motion time series is interpreted as a secular draft
of the pole at an average rate of 3.9 milliarc seconds per year in the
direction of -70 E longitude.

HORIZONTAL stresses at the interface where the liquid core of the Earth meets the surrounding solid mantle prevent these two major regions of the Earth from moving independently of one another. Speculations as to the physical nature of these stresses have been made in connexion (a) with the investigation of whether the precessional motion of the mantle is significant as a possible cause of the fluid motions in the core that produce the Earth's magnetic field, and (b) with the interpretation of certain tiny, irregular secular changes in the direction and magnitude of the angular velocity of the mantle as being manifestations of fluctuations in core motions. (The books by Munk and Macdonald1 and Marsden and Cameron2 give extensive lists of pertinent references.)

In studies of the temporal variations of the main internal geomagnetic field (the secular variation or SV), it is usual to consider separately the variations of the dipolar and non-dipolar parts which appear to have different time constants. The mechanism that is generally invoked to explain the generation of SV is the advection of the lines of force of the main field by the highly conducting fluid at the top of the core. Such a mechanism involves the main field as a whole and it is not clear a priori why its two parts should behave separately. I show here that the Coriolis force will probably dominate the force budget at the top of the core and that, in such a case, the motion of the fluid involves the two parts of the field in a different way; in particular, the existing axial dipolar component is not re-engaged in the process which builds up the SV.

This study compares observed polar motion for the period 1900-1985 with meteorologic and hydrologic data for the world over the same period, in an effort to determine whether water storage, in combination with air mass redistribution, can account for the observed variance of polar motion. Monthly time series of estimated continental water storage and air mass excitation functions have been compared at the annual frequency and at the Chandler frequency using power, coherence, multiple coherence, and phase spectra. There is a discrepancy in accounting for more than half the variance of polar motion across a broad range of frequencies. Similar results have been obtained in recent studies of polar motion at frequencies above 1 cycle per year using modem space geodetic determinations of polar motion. The persistence of the discrepancey at the annual frequency and its broadband nature suggest a source of polar motion excitation due to air and water motion which has either not been correctly estimated or not yet identified.

General expressions (with potential applications in several areas of geophysical fluid dynamics) are derived for all three components of the contribution made by the geostrophic part of the pressure field associated with flow in a rotating gravitating fluid to the topographic torque exerted by the fluid on a rigid impermeable bounding surface of any shape. When applied to the Earth's liquid metallic core, which is bounded by nearly spherical surfaces and can be divided into two main regions, the "torosphere" and "polosphere," the expressions reduce to formulae given previously by the author, thereby providing further support for his work and that of others on the role of topographic coupling at the core-mantle boundary in the excitation by core motions of Earth rotation fluctuations on decadal time scales. They also show that recent criticisms of that work are vitiated by mathematical and physical errors. Contrary to these criticisms, the author's scheme for exploiting Earth rotation and other geophysical data (either real or simulated in computer models) in quantitative studies of the topography of the core-mantle boundary (CMB) by intercomparing various models of (a) motions in the core based on geomagnetic secular variation data and (b) CMB topography based on seismological and gravity data has a sound theoretical basis. The practical scope of the scheme is of course limited by the accuracy of real data, but this is a matter for investigation, not a priori assessment.