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 mea展开更多
The Chandler wobble excitation function (hereinafter, geodetic excitation) is obtained by removing the seasonal components and low frequency components with periods from several years to decades from the polar motion ...The Chandler wobble excitation function (hereinafter, geodetic excitation) is obtained by removing the seasonal components and low frequency components with periods from several years to decades from the polar motion excitation function derived from SPACE2002 series. The geophysical excitation functions of the individual AAM, OAM, HAM, and two combined excitations of the AAM + OAM and AAM + OAM + HAM at 1d, 5d, 1m and 3m in- tervals are statistically tested for the hypothesis of the nor- mality, and then tested for the hypotheses of identical distri- bution between the geodetic and the geophysical excitations. The results show that, among the total 16 components of the two combined excitation functions at 1d, 5d, 1m and 3m in- tervals,most follow random normal processes, the hy- potheses of identical distribution between the geodetic exci- tation and the two combined excitation are acceptable, while most of the hypotheses of identical distribution between the geodetic excitation and the individual excitations of the AAM, OAM, and HAM are rejectable. These results elucidate from a new point of view, that the excitations from AAM, OAM, and HAM are the main sources of the Chandler wobble, and the Chandler wobble excitation function is of a random normal property.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
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 mea
文摘The Chandler wobble excitation function (hereinafter, geodetic excitation) is obtained by removing the seasonal components and low frequency components with periods from several years to decades from the polar motion excitation function derived from SPACE2002 series. The geophysical excitation functions of the individual AAM, OAM, HAM, and two combined excitations of the AAM + OAM and AAM + OAM + HAM at 1d, 5d, 1m and 3m in- tervals are statistically tested for the hypothesis of the nor- mality, and then tested for the hypotheses of identical distri- bution between the geodetic and the geophysical excitations. The results show that, among the total 16 components of the two combined excitation functions at 1d, 5d, 1m and 3m in- tervals,most follow random normal processes, the hy- potheses of identical distribution between the geodetic exci- tation and the two combined excitation are acceptable, while most of the hypotheses of identical distribution between the geodetic excitation and the individual excitations of the AAM, OAM, and HAM are rejectable. These results elucidate from a new point of view, that the excitations from AAM, OAM, and HAM are the main sources of the Chandler wobble, and the Chandler wobble excitation function is of a random normal property.
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.
