Body tides of a convecting, laterally heterogeneous, and aspherical Earth

The variability in the earth's rotation rate not due to known solid body tides is dominated on time scales of about four years and less by variations in global atmospheric angular momentum (M), as derived from the zonal wind distribution. Among features seen in the length of day (Δl.o.d.) record produced by atmospheric forcing are the strong seasonal cycle, quasi-periodic fluctuations around 40–50 days, and an interannual signal forced by a strong Pacific warming event, known as the El Niño. Momentum variations associated with these time scales arise in different latitudinal regions. Furthermore, winds in the stratosphere make a particularly important contribution to seasonal variability.Other related topics discussed here are (i) comparisons of the M series from wind fields produced at different weather centers, (ii) the torques that dynamically link the atmosphere and earth, and (iii) longer-term non-atmospheric effects that can be seen upon removal of the atmospheric signal. An interesting application for climatological purposes is the use of historical earth rotation series as a proxy for atmospheric wind variability prior to the era of upper-air data. Lastly, results pertaining to the role of atmospheric pressure systems in exciting rapid polar motion are presented.

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Viscoelasticity of the lower mantle from forward modeling of normal modes and solid Earth tides

10.5194/egusphere-egu2020-10789 ◽

2020 ◽

Author(s):

Ulrich Faul ◽

Harriet Lau

Keyword(s):

Absorption Band ◽

Solid Earth ◽

Lower Mantle ◽

Normal Modes ◽

Earth Tides ◽

Solid Earth Tides ◽

Anelastic Behavior ◽

Body Tides ◽

Anelastic Deformation ◽

Intrinsic Dissipation

Grain scale diffusive processes are involved in the rheology at convective timescales, but also at the transient timescales of seismic wave propagation, solid Earth tides and post-glacial rebound. Seismic and geodetic data can therefore potentially provide constraints on lower mantle properties such as grain size that are unconstrained otherwise. Current models of the transient viscosity of the lower mantle infer an absorption band of finite width in frequency. Seismic models predict a low frequency end to the absorption band at timescales corresponding to the longest normal modes of about an hour. By contrast, geodetic models infer the onset of an absorption band at these frequencies to cover anelastic deformation at timescales up to 18.6 years. A difficulty in extracting frequency dependence from mode and tide data is its convolution with depth dependence.To circumvent this problem we select a distinct set of seismic normal modes and solid Earth body tides that have similar depth sensitivity in the lower mantle. These processes collectively span a period range from 7 minutes to 18.6 years. This allows the examination of frequency dependent energy dissipation over the lower mantle across 6 orders of magnitude. To forward model the transient creep response of the lower mantle we use a laboratory-based model of intrinsic dissipation that we adapt to the lower mantle mineralogy. This extended Burgers model represents an empirical fit to data principally from olivine, but also MgO and other compounds. The underlying microphysical model envisions a sequence of processes that begin with a broad plateau in dissipation at the highest frequencies after the onset of anelastic behavior, followed by a broad absorption band spanning many decades in frequency. The absorption band transitions seamlessly into viscous behavior. Since dissipation both for the absorption band and for (Newtonian) viscous behavior is due to diffusion along grain boundaries there can be no gap between the end of the absorption band and onset of viscous behavior.Modeling of the planetary response to small strain excitation necessitates consideration of inertia and self gravitation. The phase lag due to solid Earth body tides therefore does not correspond directly to the intrinsic dissipation measured in the laboratory as material property. We have developed a self consistent theory that combines the planetary response with time-dependent anelastic deformation of rocks. Results from a broad range of forward models show that at lower mantle pressures periods of modes fall onto the broad plateau in dissipation at the onset of anelastic behavior. This explains the apparent frequency independence or even negative frequency dependence observed for some normal modes. At longer timescales, solid Earth tides fall on the frequency-dependent absorption band. This reconciles seemingly contradictory results published by seismic and tidal studies. Observations at even longer timescales are needed to constrain the transition from absorption band to viscous behavior.

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Some Geodetic Aspects of the Plate Tectonics Hypothesis

International Astronomical Union Colloquium ◽

10.1017/s0252921100081136 ◽

1980 ◽

Vol 56 ◽

pp. 87-101

Author(s):

Kurt Lambeck

Keyword(s):

Plate Tectonics ◽

Geodetic Data ◽

Geophysical Data ◽

Plate Boundaries ◽

Frequency Range ◽

Crustal Motion ◽

Intraplate Tectonics ◽

The Earth ◽

Seismic Frequencies ◽

Body Tides

AbstractGeodetic observations of gravity, body tides, the Earth’s rotation and crustal motion and deformation potentially provide important constraints in the general inversion of geophysical data for determining the structure and evolution of the Earth. More specifically, the geodetic data provide constraints on the rheology of the planet in the frequency range intermediate between geological and seismic frequencies, on the geologically instantaneous kinematics of the Earth and on the mechanisms responsible for the motions within the Earth, results that are intimately related to the plate tectonics hypothesis. The discussion is limited here to only a few aspects of these “geodetic” aspects of this hypothesis, including deformation along plate boundaries, intraplate tectonics and vertical motions.

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Magnitudes and Spectra of Important Dynamical Phenomena

International Astronomical Union Colloquium ◽

10.1017/s0252921100050922 ◽

1975 ◽

Vol 26 ◽

pp. 63-77

Author(s):

E. P. Fedotov

Keyword(s):

Polar Motion ◽

Continental Drift ◽

Earth’S Rotation ◽

Reference Systems ◽

Coordinate Systems ◽

Gravitation Field ◽

Earth's Rotation ◽

The Earth ◽

Rigid Attachment ◽

Body Tides

AbstractThe axes of coordinate systems used in geodynamics are believed to be attached to a number of physical points on the surface of the Earth. This is true when measurements of the distances (ranging) are dealt with. On the other hand, the axes of reference systems used by the BIH and IFMS are attached not to the points themselves but to a pencil of plumb lines at these points. For the case of observations with radio interferometers being used for the study of Earth’s rotation, the rotating frame of reference could be attached in some prescribed way toihebaselines of the interferometers.But in no case is rigid attachment possible, because both the above points and lines move relative to each other. We should search for another way to define the reference systems for geodynamics. With that end in view, a knowledge of magnitudes of pertinent dynamical phenomena becomes vital.This paper considers the effects of some dynamical phenomena upon the distances between the points on. the Earth’s surface and upon the angles between plumb lines and, possibly, also between baselines of radio interferometers. In particular, this paper discusses body tides, continental drift, internal motion within crustal blocks, redistribution of mass which can affect the directions of plumb lines, etc. Polar motion and variations in the rate of Earth’s rotation will be also touched upon as far as these phenomena contribute to deformation of the Earth and its gravitation field.The results are summarised in diagrams showing how the variations of the above distances and angles depend upon both time and positions on the Earth. In other words, the power spectrum of the variation will be presented as a function of time and distance expressed either in kilometers or in degrees of arc on the Earth’s surface.

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Viscous flow in a deformable rotating container

Journal of Fluid Mechanics ◽

10.1017/s0022112071003069 ◽

1971 ◽

Vol 45 (1) ◽

pp. 189-201 ◽

Cited By ~ 19

Author(s):

Steven T. Suess

Keyword(s):

Forced Oscillation ◽

Rotation Axis ◽

Direct Consequence ◽

Present Theory ◽

Rotational Frequency ◽

Linear Boundary ◽

Steady State Flow ◽

The Core ◽

The Earth ◽

Body Tides

The steady-state flow in a rotating container is examined when the container is deformed into an ellipsoidal figure which is fixed in inertial space. The analysis is carried out for a fluid of small viscosity, and to the second order in Rossby number. Results show a vortex existing along the rotation axis, this being an interior manifestation of non-linear boundary-layer effects. These effects are a direct consequence of the forced oscillation being at twice the rotational frequency. The configuration is chosen to suggest the effects of gravitational body tides on the dynamics of the core of the earth. This problem is related to the similar problem of a precessing spheroid, and an experiment is described which tests the present theory and confirms previous experimental data from precessing spheroids.

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