Secular Variations of the Zonal Harmonics and Polar Motion as Geophysical Constraints

Author(s):  
R. S. Nerem ◽  
S. M. Klosko
1975 ◽  
Vol 26 ◽  
pp. 409-413
Author(s):  
P. Melchior

The ideas I shall try to develop are probably not original but I hope they reflect a general opinion of those who have looked into the problem of the Earth’s rotation.We must examine here related points:1. The polar motion and the variation of UT1.2. The system of reference with respect to which these periodic or secular variations are described.


2005 ◽  
Vol 14 (12) ◽  
pp. 1989-2023 ◽  
Author(s):  
DAVID M. LUCCHESI

This work has been motivated by the criticisms raised on the error budget contribution — on a recently performed measurement of the Lense–Thirring effect — from the uncertainties of the secular variations of the Earth's even zonal harmonics. The relativistic secular precession has been observed from the analysis of 11 years of LAGEOS and LAGEOS II laser ranging data. In the analysis, the recent EIGEN–GRACE02S gravity field model (derived from GRACE data only) was used during the orbit determination process using the NASA Goddard software package GEODYN II. In particular, the measurement has been derived combining the nodes only of the two LAGEOS satellites in order to cancel the larger error source, due to the uncertainty of the first even zonal harmonic, and solved for the Lense–Thirring effect predicted by Einstein's general relativity. The authors of the relativistic measurement claimed an error of about 1% of the relativistic effect as due to the temporal variation of the even zonal harmonics. The main criticism is that on a much larger error estimate, about 11% of the relativistic effect on the analyzed time span of the two LAGEOS satellites orbital data should be considered. Moreover, the authors of the relativistic measurement emphasized that whatever the value they chose for the secular variations, in particular of the effective value for [Formula: see text], they always obtained the same discrepancy of about 1% between the observed and predicted effect, without however providing a detailed explanation. In the present work we address all the cited aspects. In particular, we explain the physical reason for the results obtained by the authors of the relativistic measurement in all their simulations. As we will see, two additional errors (linear in time) must be considered in the satellites orbit analysis if we want to correctly explain the experimental results. The first is a time-dependent error related with the mismodeling of the secular variations of the even zonal harmonics. The inclusion of this error in the error analysis explains why the same discrepancy between the observed and predicted effect has been always obtained independently of the assumed value for [Formula: see text], i.e. for the errors in the time variations of the even zonal harmonics. The second is a time-independent error related to the non-coincidence between the reference epoch of the gravity field, i.e. the middle epoch of the time span during which the gravity field has been determined by the GRACE mission, and the reference epoch fixed in the orbit analysis program. The inclusion of this error in the error analysis explains the 1% value for the discrepancy between the prediction and the observations. In order to validate our results we fitted for an effective [Formula: see text] from the combined nodes of the LAGEOS satellites with the EIGEN2S gravity field model obtained from the CHAMP mission. From our fit, we consistently confirmed our previous statements. In particular, we prove a very interesting and new approach in order to compute the effective values of the time variations of the even zonal harmonics from the estimate of the time-independent error previously cited.


1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.


1972 ◽  
Vol 1 ◽  
pp. 93-101 ◽  
Author(s):  
S. Yumi

ABSTRACTAnalysing the residual latitude of the station, local trend in latitude variation other than by the polar motion was found.Residual latitude was calculated for each of 26 stations which gave the continuous records of observation during 6 years comprising — 1962 — 1967 as a difference between observed variation of latitude and – normal variation calculated by the polar coordinates Iderived from all the results of 26 stations.As far as the results during these six years are concerned, local trend at any station it seemed to be expressed in terms of 3λ.Assumed effect of local trend on the coordinates values of the instantaneous pole is also discussed.


1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.


1975 ◽  
Vol 26 ◽  
pp. 341-380 ◽  
Author(s):  
R. J. Anderle ◽  
M. C. Tanenbaum

AbstractObservations of artificial earth satellites provide a means of establishing an.origin, orientation, scale and control points for a coordinate system. Neither existing data nor future data are likely to provide significant information on the .001 angle between the axis of angular momentum and axis of rotation. Existing data have provided data to about .01 accuracy on the pole position and to possibly a meter on the origin of the system and for control points. The longitude origin is essentially arbitrary. While these accuracies permit acquisition of useful data on tides and polar motion through dynamio analyses, they are inadequate for determination of crustal motion or significant improvement in polar motion. The limitations arise from gravity, drag and radiation forces on the satellites as well as from instrument errors. Improvements in laser equipment and the launch of the dense LAGEOS satellite in an orbit high enough to suppress significant gravity and drag errors will permit determination of crustal motion and more accurate, higher frequency, polar motion. However, the reference frame for the results is likely to be an average reference frame defined by the observing stations, resulting in significant corrections to be determined for effects of changes in station configuration and data losses.


1976 ◽  
Vol 32 ◽  
pp. 613-622
Author(s):  
I.A. Aslanov ◽  
Yu.S. Rustamov

SummaryMeasurements of the radial velocities and magnetic field strength of β CrB were carried out. It is shown that there is a variability with the rotation period different for various elements. The curve of the magnetic field variation measured from lines of 5 different elements: FeI, CrI, CrII, TiII, ScII and CaI has a complex shape specific for each element. This may be due to the presence of magnetic spots on the stellar surface. A comparison with the radial velocity curves suggests the presence of a least 4 spots of Ti and Cr coinciding with magnetic spots. A change of the magnetic field with optical depth is shown. The curve of the Heffvariation with the rotation period is given. A possibility of secular variations of the magnetic field is shown.


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