scholarly journals A Simple Theory on the Dynamical Effects of a Stratified Fluid Core Upon Nutational Motion of the Earth

1980 ◽  
Vol 78 ◽  
pp. 165-183 ◽  
Author(s):  
Tetsuo Sasao ◽  
Shuhei Okubo ◽  
Masanori Saito
Keyword(s):  
Linear Equations ◽  
Earth Tide ◽  
Outer Core ◽  
Stratified Fluid ◽  
Earth Tides ◽  
Momentum Balance ◽  
Earth Model ◽  
The Earth ◽  
Fluid Core ◽  
Whole Earth

The theory of Molodensky (1961) on dynamical effects of a stratified fluid outer core upon nutations and diurnal Earth tides is reconstructed on a new and probably much simpler ground. A theory equivalent to Molodensky's is well represented on the basis of two linear equations for angular-momentum balance of the whole Earth and the fluid outer core, which differ from the well-known equations of Poincaré (1910) only in the existence of products of inertia due to deformations of the whole Earth and fluid outer core. The products of inertia are characterized by four parameters which are easily computed for every Earth model by the usual Earth tide equations. A reciprocity relation exists between two of the parameters. The Adams-Wiliamson condition is not a necessary premise of the theory. Amplitudes of nutations and tidal gravity factors are computed for three Earth models. A dissipative core-mantle coupling is introduced into the theory qualitatively. The resulting equations are expressed in the same form as those of Sasao, Okamoto and Sakai (1977). Formulae for secular changes in the Earth-Moon system due to the core-mantle friction are derived as evidences of internal consistency of the theory.

Fundamental statistical techniques for the analysis of earth tides

1971 ◽  
Vol 61 (1) ◽  
pp. 203-215
Author(s):  
Cheh Pan
Keyword(s):  
Computer Technology ◽  
Earth Tide ◽  
Power Spectra ◽  
Correlation Coefficients ◽  
Earth Tides ◽  
Statistical Techniques ◽  
The Earth ◽  
Tidal Data ◽  
Instrumental Drift ◽  
Phase Differences

abstract Recent advances in instrumentation, digital computer technology and mathematical theory promote the error analysis of Earth-tide data. Various statistical techniques developed and used in other fields are applicable in the study of Earth tides, and the accuracy of the Earth's rigidity constants determined from the tides will be greatly improved with the help of these techniques. The fundamentals of the statistical techniques of autocorrelation, crosscorrelation, convolution, statistical means, bandpass filtering, correlation coefficients, power spectra, coherency and equalization are described, and their principal applications in the Earth-tide analysis summarized. Examples of effective application of these techniques in the elimination of the errors in the tidal data such as those introduced from instrumental drift, phase differences between the observed and predicted tides, etc. are discussed. This work is an attempt to introduce statistical analysis into the Earth-tide study.

Lumped harmonics of 15th and 30th order in the geopotential, from the resonant orbit of the satellite 1971–54A

1981 ◽  
Vol 375 (1762) ◽  
pp. 327-350 ◽  
Keyword(s):  
Circular Orbit ◽  
Linear Equations ◽  
Earth Model ◽  
Orbital Inclination ◽  
Order Resonance ◽  
Orbital Perturbations ◽  
Resonant Orbit ◽  
The Earth ◽  
The Individual

The satellite 1971–54A entered a near-circular orbit with period 95.9 min and inclination 90.2°. Between 1972 and 1978 the orbit passed slowly through 15th-order resonance, when the track over the Earth repeats after 15 revolutions, and the 15th- and 30th-order harmonics in the geopotential may produce substantial orbital perturbations. The values of orbital inclination and eccentricity from 269 weekly U. S. Navy orbits between November 1972 and January 1978 have been ana­lysed to determine 12 lumped harmonic coefficients of order 15 and 30. The analysis of inclination yields 15th-order coefficients accurate to 1.5 and 2.8%, and 30th-order coefficients accurate to 7 %. The analysis of eccentricity gives two 15th-order coefficients accurate to 3 and 4 %. These lumped harmonic coefficients are used to test the accuracy of the Goddard Earth Model 10B, which is complete to order and degree 36. The agreement with GEM 10B is excellent, for both 15th and 30th order, and shows that GEM 10B is more accurate than was expected. The 12 values of lumped harmonics obtained give 12 linear equations between individual coefficients of order 15 and 30, which will be used in a future solution for the individual coefficients.

Identification of the Earth Tide’s Influences and its Main Influencing-Components on Groundwater Level in an Unconfined-Aquifer

2020 ◽  
Author(s):  
Jian Guo ◽  
Mo Xu ◽  
Haoxin Shi ◽  
Jianhong Ge
Keyword(s):  
Groundwater Level ◽  
Cross Correlation ◽  
Earth Tide ◽  
Unconfined Aquifer ◽  
Earth Tides ◽  
Groundwater Levels ◽  
Monitoring Well ◽  
The Earth ◽  
Cross Correlation Analysis ◽  
Periodic Changes

<p>It is well known that various kinds of factors are causing the fluctuation of the groundwater level. The influence of earth tide on groundwater is first observed in confined-aquifer, while in unconfined-aquifer, understanding the influence of earth tide on the micro-fluctuation of the water level is crucial for obtaining key geo-hydrological parameters of the aquifer. In this study, the groundwater level of a monitoring well in Kualiangzi Village, Zhongjiang County, Deyang, as well as the data of local earth tides and rainfall were collected. And then the identification of the earth tide’s influences and its main influencing-components on groundwater level were studied by means of spectral analysis, cross-correlation analysis and harmonic analysis. The results show that the local groundwater levels are featured periodic changes of 1-day, 1/2 day and 1/3 day, which are corresponded to the earth tide. Moreover, the amplitude of the groundwater levels are negatively correlated with the earth tide, and there is no obvious hysteresis between them. The main influencing-components of earth tide are K1 diurnal wave and S2 semidiurnal wave.</p>

scholarly journals Solved and unsolved questions in the non-rigid Earth nutation study

2007 ◽  
Vol 3 (S248) ◽  
pp. 374-378
Author(s):  
C. L. Huang
Keyword(s):  
Inner Core ◽  
Outer Core ◽  
Earth Model ◽  
Future Studies ◽  
Atmospheric Loading ◽  
The Earth ◽  
Core Boundary ◽  
Oceanic Tides ◽  
Rigid Earth ◽  
Electro Magnetic

AbstractAt the IAU 26th GA held in Prague in 2006, a new precession model (P03) was recommended and adopted to replace the old one, IAU1976 precession model. This new P03 model is to match the IAU2000 nutation model that is for anelastic Earth model and was adopted in 2003 to replace the previous IAU1980 model. However, this IAU2000 nutation model is also not a perfect one for our complex Earth, as stated in the resolution of IAU nutation working group. The Earth models in the current nutation theories are idealized and too simple, far from the real one. They suffer from several geophysical factors: the an-elasticity of the mantle, the atmospheric loading and wind, the oceanic loading and current, the atmospheric and oceanic tides, the (lateral) heterogeneity of the mantle, the differential rotation between the inner core and the mantle, and various couplings between the fluid outer core and its neighboring solids (mantle and inner core). In this paper, first we give a very brief review of the current theoretical studies of non-rigid Earth nutation, and then focus on the couplings near the core-mantle boundary and the inner core-outer core boundary, including the electro-magnetic, viscous, topographic, and gravitational couplings. Finally, we outline some interesting future studies.

scholarly journals Rotational Velocity of an Earth Model with a Liquid Core

1979 ◽  
Vol 82 ◽  
pp. 313-314
Author(s):  
S. Takagi
Keyword(s):  
Rotational Motion ◽  
Velocity Vector ◽  
Inner Core ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Liquid Core ◽  
Outer Core ◽  
Earth Model ◽  
The Earth ◽  
Rotation Of The Earth

There have been many papers discussing the rotation of the Earth (Jeffreys and Vicente, 1957; Molodenskij, 1961; Rochester, 1973; Smith, 1974; Shen and Mansinha, 1976). This report summarizes the application of the perturbation method of celestial mechanics to calculate the rotation of the Earth (Takagi, 1978). In this solution the Earth is assumed to consist of three components: a mantle, liquid outer core, and a solid inner core, each having a separate rotational velocity vector. Hamiltonian equations of motion were constructed to solve the rotational motion of the Earth.

scholarly journals GRACE—Gravity Data for Understanding the Deep Earth’s Interior

2020 ◽  
Vol 12 (24) ◽  
pp. 4186
Author(s):  
Mioara Mandea ◽  
Véronique Dehant ◽  
Anny Cazenave
Keyword(s):  
Gravity Data ◽  
Outer Core ◽  
Space Mission ◽  
Last Deglaciation ◽  
Mantle Boundary ◽  
Core Mantle Boundary ◽  
The Core ◽  
Isostatic Adjustment ◽  
The Earth ◽  
Fluid Core

While the main causes of the temporal gravity variations observed by the Gravity Recovery and Climate Experiment (GRACE) space mission result from water mass redistributions occurring at the surface of the Earth in response to climatic and anthropogenic forces (e.g., changes in land hydrology, ocean mass, and mass of glaciers and ice sheets), solid Earth’s mass redistributions were also recorded by these observations. This is the case, in particular, for the glacial isostatic adjustment (GIA) or the viscous response of the mantle to the last deglaciation. However, it has only recently been shown that the gravity data also contain the signature of flows inside the outer core and their effects on the core–mantle boundary (CMB). Detecting deep Earth’s processes in GRACE observations offers an exciting opportunity to provide additional insight into the dynamics of the core–mantle interface. Here, we present one aspect of the GRACEFUL (GRavimetry, mAgnetism and CorE Flow) project, i.e., the possibility to use gravity field data for understanding the dynamic processes inside the fluid core and core–mantle boundary of the Earth, beside that offered by the geomagnetic field variations.

scholarly journals Influence of the principle of minimum potential energy on the distribution of density and gravitational energy of the Earth for the reference model PREM

2021 ◽  
Vol 43 (1) ◽  
pp. 194-210
Author(s):  
М.М. Fys ◽  
А.L. Tserklevych
Keyword(s):  
Potential Energy ◽  
Internal Structure ◽  
Reference Model ◽  
Minimum Principle ◽  
Functional Condition ◽  
Outer Core ◽  
Gravitational Energy ◽  
Earth Model ◽  
The Earth ◽  
Prem Model

From the point of view of modeling the internal structure of the Earth, its figure and evolution play an important role, which to one degree or another are associated with gravitational energy and the principle of its minimization. The realization of the minimum principle of potential for models of the distribution of the Earth’s density is the key in studies on the detection of inhomogeneous mass distribution. Achieving the minimum gravitational energy of the Earth is equivalent to the approximation of the internal structure to the hydrostatic state, and this condition is achieved due to variations in density. Therefore, for correct geophysical interpretation of gravimetric data, it is necessary to align the PREM (Preliminary Reference Earth Model) with harmonic coefficients of geopotential and minimum functional condition that determines gravitational energy, and only on this basis to estimate variations in density and tectonosphere. An algorithm for representing a piecewise continuous density distribution function in a spherical PREM model by Legendre polynomials is proposed in the paper to calculate the density, potential and energy distribution in an ellipsoidal planet using an additional condition — the minimum of gravitational energy. The use of such an algorithm made it possible to transform the spherically symmetric PREM model to a hydrostatically balanced state. It turned out that in the model obtained, the excess potential energy is concentrated in the inner and outer core of the Earth, and also insignificantly in the planet’s crust. The total energy E for the PREM reference model, which is subdivided into ellipsoidal layers, is 2.3364∙1024 erg, and in the modified PREM model after its correction for the hydrostatic component, it is 2.2828∙1024 erg. Estimation of density redistribution and identification of areas of their greatest change provide a mechanism for explaining the dynamic processes in the middle of the Earth.

scholarly journals The Period of the Chandler Wobble

1980 ◽  
Vol 78 ◽  
pp. 187-193
Author(s):  
F. A. Dahlen
Keyword(s):  
Angular Momentum ◽  
Inner Core ◽  
Center Of Mass ◽  
Angular Frequency ◽  
Chandler Wobble ◽  
Earth Model ◽  
The Earth ◽  
Fluid Core ◽  
Relative Angular Momentum ◽  
The Mean

Realistic models of the Earth are known to possess a solid anelastic inner core, mantle and crust, and a fluid core and oceans. How might we go about calculating the theoretical free period of the Chandler wobble of such an Earth model? Let xi be a set of Cartesian axes with an origin at the center of mass, and let ωi be the instantaneous angular velocity of rotation of these axes with respect to inertial space. The net angular momentum is then Cijωj + hi, where Cij is the inertia tensor, and hi is the relative angular momentum. Let us affix the axes xi in the mantle and crust by stipulating that the relative angular momentum is that of the core and oceans alone, i.e., hi (mantle and crust) = 0; hi = hi (core and oceans). For an infinitesimal free oscillation of angular frequency σ, we can write ωi = Ω(δi3 + mi eiσt), Cij = A(δilδjl + δi2δj2) + Cδi3δj3 + cij eiσt, and hi = hi eiσt, where Ω is the mean rate of rotation and A and C are the mean equatorial and polar moments of inertia.

Tidal excitation of hydromagnetic waves and their damping in the Earth

1994 ◽  
Vol 274 ◽  
pp. 219-241 ◽  
Author(s):  
R. R. Kerswell
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Outer Core ◽  
Decay Rates ◽  
Wave Disturbance ◽  
Instability Mechanism ◽  
The Earth ◽  
Elliptical Instability ◽  
Hydromagnetic Waves

We examine the possibility that the Earth's outer core, as a tidally distorted fluid-filled rotating spheroid, may be the seat of an elliptical instability. The instability mechanism is described within the framework of a simple Earth-like model. The preferred forms of wave disturbance are explored and a likely growth rate supremum deduced. Estimates are made of the Ohmic and viscous decay rates of such hydromagnetic waves in the outer core. Rather than a conclusive disparity of scales, we find that typical elliptical growth rates, Ohmic decay rates and viscous decay rates all have the same order for plausible core fields and core-to-mantle conductivities. This study is all the more timely considering the recent realization that the Earth's precession may also drive similar instabilities at comparable strengths in the outer core.

Sign in / Sign up

Export Citation Format

Share Document