The rotation of the physical Earth is far more complex than the rotation of a biaxial or slightly triaxial rigid body can represent. The linearization of the Liouville equation via the Munk and MacDonal perturbation s...The rotation of the physical Earth is far more complex than the rotation of a biaxial or slightly triaxial rigid body can represent. The linearization of the Liouville equation via the Munk and MacDonal perturbation scheme has oversimplified polar excitation physics. A more conventional linearization of the Liouville equation as the generalized equation of motion for free rotation of the physical Earth reveals: 1) The reference frame is most essential, which needs to be unique and physically located in the Earth;2) Physical angular momentum perturbation arises from motion and mass redistribution to appear as relative angular momentum in a rotating Earth, which excites polar motion and length of day variations;3) At polar excitation, the direction of the rotation axis in space does not change besides nutation and precession around the invariant angular momentum axis, while the principal axes shift responding only to mass redistribution;4) Two inertia changes appear simultaneously at polar excitation;one is due to mass redistribution, and the other arises from the axial near-symmetry of the perturbed Earth;5) The Earth at polar excitation becomes slightly triaxial and axially near-symmetrical even it was originally biaxial;6) At polar excitation, the rotation of a non-rigid Earth becomes unstable;7) The instantaneous figure axis or mean excitation axis around which the rotation axis physically wobbles is not a principal axis;8) In addition to amplitude excitation, the Chandler wobble possesses also multiple frequency-splits and is slow damping;9) Secular polar drift is after the products of inertia and always associated with the Chandler wobble;both belong to polar motion;10) The Earth will reach its stable rotation only after its rotation axis, major principal axis, and instantaneous figure axis or mean excitation axis are all completely aligned with each other to arrive at the minimum energy configuration of the system;11) The observation of the multiple splits of the Chandler frequency is further examined by means of exact-bandwidth filtering and spectral analysis, which confirms the theoretical prediction of the linearized Liouville equation. After the removal of the Gibbs phenomenon from the polar motion spectra, Markowitz wobbles are also observed;12) Error analysis of the ILS data demonstrates that the incoherent noises from the Wars in 1920-1945 are separable from polar motion and removable, so the ILS data are still reliable and useful for the study of the continuation of polar motion.展开更多
We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor...We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor, and then find their zero points. The results show thatthe mean periods of the Chandler (annual) wobble are 430.71+-1.07 (365.24+-0.11) and 432.71+-0.42(365.23+-0.18) mean solar days for the data sets of 1900-2001 and 1940-2001, respectively. Themaximum relative variation of the quasi-instantaneous period to the mean of the Chandler wobble isless than 1.5% during 1900-2001 (3%-5% during 1920-1940), and that of the annual wobble is less than1.6% during 1900-2001. Quasi-instantaneous and mean values of Q are also derived by using theenergy density―period profile of the Chandler wobble. An asymptotic value of Q = 36.7 is obtainedby fitting polynomial of exponential of σ^(-2) to the relationship between Q and σ during1940-2001.展开更多
Measuring Terrestrial Water Transient Storage in its various components of Earth by orbiting sensors on satellites has been a quest for more than 40<span><span><span style="font-family:;" &quo...Measuring Terrestrial Water Transient Storage in its various components of Earth by orbiting sensors on satellites has been a quest for more than 40<span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">years. Not only in the Hydrology community but also Climatology and Meteorology, Geology, Geodesy, Geophysics and Oceanography ha</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ve</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the challenge </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">to</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> attempt to first learn how to measure, then measure and assess the results. The importance is that Earth’s environments are changing and human communities, local and national governing bodies need ability to assess current hazards and to have predictive capabilities for society both local and international. So too the Gravity Recovery and Climate Experiment (GRACE) has joined the ongoing international space-based missions. There will be more after GRACE. For now is an important juncture in the effort to measure Terrestrial Water Transient Storage to ask, “What can GRACE measure and what is GRACE measuring”? Results of this investigation of the GRACE datasets by spectral methods indicate the detection of the Chandler Wobble but the Annual Wobble is aliased and below significance. Therefore, interpretations of Terrestrial Water Transient Storage are failed.</span></span></span>展开更多
The period and quality factor of the Chandler wobble(CW)are useful for constraining the Earth’s internal structure properties,such as the mantle elasticity.It has been shown that the CW is mainly excited by a combina...The period and quality factor of the Chandler wobble(CW)are useful for constraining the Earth’s internal structure properties,such as the mantle elasticity.It has been shown that the CW is mainly excited by a combination of atmospheric and oceanic processes;hence based on a deconvolution method,we can remove them from the excitation sequence of the CW to estimate its period P and quality factor Q.We finally re-estimate P=432.3±0.8 days and Q=85±15 for the CW.Based on those two estimates,we investigate the relationship between the geomagnetic jerks and the excitation sequences of the CW.The geomagnetic jerks or jerk bounds are well consistent with the sudden changes of the excitation sequences of the CW.This demonstrates that the geomagnetic jerks could be a possible excitation source of the CW.It is crucial for understanding the excitation of the CW and for deeper geophysical insights into the geomagnetic jerks.展开更多
文摘The rotation of the physical Earth is far more complex than the rotation of a biaxial or slightly triaxial rigid body can represent. The linearization of the Liouville equation via the Munk and MacDonal perturbation scheme has oversimplified polar excitation physics. A more conventional linearization of the Liouville equation as the generalized equation of motion for free rotation of the physical Earth reveals: 1) The reference frame is most essential, which needs to be unique and physically located in the Earth;2) Physical angular momentum perturbation arises from motion and mass redistribution to appear as relative angular momentum in a rotating Earth, which excites polar motion and length of day variations;3) At polar excitation, the direction of the rotation axis in space does not change besides nutation and precession around the invariant angular momentum axis, while the principal axes shift responding only to mass redistribution;4) Two inertia changes appear simultaneously at polar excitation;one is due to mass redistribution, and the other arises from the axial near-symmetry of the perturbed Earth;5) The Earth at polar excitation becomes slightly triaxial and axially near-symmetrical even it was originally biaxial;6) At polar excitation, the rotation of a non-rigid Earth becomes unstable;7) The instantaneous figure axis or mean excitation axis around which the rotation axis physically wobbles is not a principal axis;8) In addition to amplitude excitation, the Chandler wobble possesses also multiple frequency-splits and is slow damping;9) Secular polar drift is after the products of inertia and always associated with the Chandler wobble;both belong to polar motion;10) The Earth will reach its stable rotation only after its rotation axis, major principal axis, and instantaneous figure axis or mean excitation axis are all completely aligned with each other to arrive at the minimum energy configuration of the system;11) The observation of the multiple splits of the Chandler frequency is further examined by means of exact-bandwidth filtering and spectral analysis, which confirms the theoretical prediction of the linearized Liouville equation. After the removal of the Gibbs phenomenon from the polar motion spectra, Markowitz wobbles are also observed;12) Error analysis of the ILS data demonstrates that the incoherent noises from the Wars in 1920-1945 are separable from polar motion and removable, so the ILS data are still reliable and useful for the study of the continuation of polar motion.
基金Supported by the National Natural Science Foundation of China
文摘We apply complex Morlet wavelet transform to three polar motion data series,and derive quasi-instantaneous periods of the Chandler and annual wobble by differencing the wavelettransform results versus the scale factor, and then find their zero points. The results show thatthe mean periods of the Chandler (annual) wobble are 430.71+-1.07 (365.24+-0.11) and 432.71+-0.42(365.23+-0.18) mean solar days for the data sets of 1900-2001 and 1940-2001, respectively. Themaximum relative variation of the quasi-instantaneous period to the mean of the Chandler wobble isless than 1.5% during 1900-2001 (3%-5% during 1920-1940), and that of the annual wobble is less than1.6% during 1900-2001. Quasi-instantaneous and mean values of Q are also derived by using theenergy density―period profile of the Chandler wobble. An asymptotic value of Q = 36.7 is obtainedby fitting polynomial of exponential of σ^(-2) to the relationship between Q and σ during1940-2001.
文摘Measuring Terrestrial Water Transient Storage in its various components of Earth by orbiting sensors on satellites has been a quest for more than 40<span><span><span style="font-family:;" "=""> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">years. Not only in the Hydrology community but also Climatology and Meteorology, Geology, Geodesy, Geophysics and Oceanography ha</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ve</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the challenge </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">to</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> attempt to first learn how to measure, then measure and assess the results. The importance is that Earth’s environments are changing and human communities, local and national governing bodies need ability to assess current hazards and to have predictive capabilities for society both local and international. So too the Gravity Recovery and Climate Experiment (GRACE) has joined the ongoing international space-based missions. There will be more after GRACE. For now is an important juncture in the effort to measure Terrestrial Water Transient Storage to ask, “What can GRACE measure and what is GRACE measuring”? Results of this investigation of the GRACE datasets by spectral methods indicate the detection of the Chandler Wobble but the Annual Wobble is aliased and below significance. Therefore, interpretations of Terrestrial Water Transient Storage are failed.</span></span></span>
基金supported by the NSFC(grants No.41774024,41721003,41974022)by Educational Commission of Hubei Province of China(grant No.2020CFA109)the Project Supported by the Special Fund of Hubei Luojia Laboratory
文摘The period and quality factor of the Chandler wobble(CW)are useful for constraining the Earth’s internal structure properties,such as the mantle elasticity.It has been shown that the CW is mainly excited by a combination of atmospheric and oceanic processes;hence based on a deconvolution method,we can remove them from the excitation sequence of the CW to estimate its period P and quality factor Q.We finally re-estimate P=432.3±0.8 days and Q=85±15 for the CW.Based on those two estimates,we investigate the relationship between the geomagnetic jerks and the excitation sequences of the CW.The geomagnetic jerks or jerk bounds are well consistent with the sudden changes of the excitation sequences of the CW.This demonstrates that the geomagnetic jerks could be a possible excitation source of the CW.It is crucial for understanding the excitation of the CW and for deeper geophysical insights into the geomagnetic jerks.
