Secular Drift Research Articles

Excitation of the Earth's Polar Motion due to Mass Variations in Major Hydrological Reservoirs

Previous studies on the hydrological excitation of the Earth's polar motion have neglected the effect of water mass variations of hydrological reservoirs that have time scales much longer than a month. To remedy this, the present paper calculates the polar motion excitation caused by variations in major natural lakes, the impoundment in artificial reservoirs, and the depletion of a major groundwater aquifer. It is found that (1) the annual water mass variation in natural lakes contributes a significant fraction in the total hydrological excitation of the annual wobble, (2) the hydrological reservoirs have been negligible in the Chandler wobble excitation, and (3) the contribution of hydrological reservoirs to the total secular polar drift has been negligible in this century due to fortuitous cancellation among reservoirs.

Deformation of the Viscoelastic Earth Due to the Secular Change In the Earth's Axis of Rotation

The cause of the secular change in the Earth's rotation axis relative to the surface geography is regarded as the viscoelastic response of the earth to the mass displacement generated by late Pleistocene deglaciation and the sea level changes related to it. On the other hand, the secular drift of the pole will also bring about viscoelastic change in the Earth's shape because the Earth is not a sphere but a spheroid with an equatorial bulge. In the case of polar drift, we estimated the deformation of the Earth's surface and the Earth's core, as well as the change in the Earth's gravity field. We used a compressible, radially stratified, Maxwell viscoelastic earth model for the inverse calculations and also investigated if the viscous flow in the mantle can compensate for the mass redistribution caused by polar drift. As a result of these calculations, the viscous flow in the mantle seems not to be able to compensate for the mass redistribution caused by polar drift if the mantle viscosity is higher than 1022 poise. the agreement or disagreement between the rotation axis of the Earth and the principal axis of inertia determined by satellites can add a new constraint to the viscosity of the Earth's mantle.

A new research for the secular polar motion in this century

A new research for the secular drift of the Earth's pole was made based on nine long sequences of latitude observations and led to the following conclusions. 1.During this century, the Earth's pole has been moving with a mean rate of about 0″.0016/yr along the meridian about 70° (W). This drift rate is much less than the 0″.0035/yr derived from the ILS sequence.2.Relative to the North American continent, the Ukiah station located on the west coast of the U.S. shows a local drift of about 6 cm/yr northward, which coincides well with that determined by new techniques.3.Referring to the Europe-Asia plate, the whole North American continent shows a drift northward with a rate of about 8 cm/yr. The Mediterranian shows a similar drift of about 6 cm/yr. Perhaps these drifts are the consequences of plate motion and/or deflection of local vertical. It is useful for ascertaining the sources of the drifts to intercompare longer sequences observed with different techniques, including classical and new ones.4.Three of five ILS stations, Ukiah, Gaithersburg, and Carloforte, show significant local drifts. Therefore, the Conventional International Origin (CIO), which is defined by the 1903.0 mean latitudes of five ILS stations, is far from fixed on the Earth's surface. It is necessary to re-define an origin of the pole of the Conventional Terrestrial System (CTS).5.The quasi-30-year libration showed by the ILS data is not the real pattern of the Earth's polar motion, but results from both the irregular polar motion over some period and the local motion of Ukiah.

ATTITUDE DRIFT OF TORQUE-FREE FLEXIBLE GYROS USING THE VISCOUS DAMPING MODEL

The obejective of this paper is to analyse the rotational motion of a flexible body. A flexible body is defined in this work to be a body for which any deflections of the body during its motion are so small that only first-order deflection terms need be retained. Other simplifying assumptions are that the flexible body is axisymmetric in its underformed state and that there are no external torques applied to the body. A review of torque-free rigid-body rotational motion is presented as an introduction to flexible-body motion. The flexible-body equations of motion are then formulated using a linearized Tisserand frame. The flexible-body analysis is superior to a rigid-body analysis in that it gives information on the long-term-attitude behaviour of a rotating body. It is shown that the energy loss of the body causes a secular drift of the attitude. This drift is expressed as a function of the vibrational parameters of the body. A simple idealized example is then worked out using the flexible-body assumptions.

A new investigation of the secular drift of the Earth's pole

A new investigation of the secular drift of the Earth's pole was made based on nine long series of latitude observations. This led to the following conclusions: 1) During this century, the Earth's pole has been moving approximately along meridian 70 °W at a mean rate of 0.0016″/yr, much less than the 0.0035″/yr derived from the ILS sequence. 2) Relative to the North American Continent, the Ukiah Station located on the western shore of the U.S. shows a local drift of about 6 cm/yr toward north, in good agreement with the result from the new techniques. 3) Relative to the Europe-Asia plate, the whole North American Continent shows a northward drift of about 8 cm/yr. The Mediterranean shows a similar drift of about 6 cm/yr. 4) Three of five ILS stations, Ukiah, Gaithersberg and Carloforte, show significant drifts. Therefore, the Conventional International Origin (CIO), which is defined by the mean latitudes at 1903.0 of the five stations, is far from being fixed on the Earth's surface, and is not suitable as the origin of the Earth Reference System.

Nutation Accretion or Decay Due to Internal Energy Dissipation

In the present paper the secular attitude drift of a torquefree axisymmetric gyro is studied as a function of its attitude. By arguing that the gyro’s energy loss is due to the hystereses of its structural elements, an energy dissipation function is established, which is found to be proportional to an innate dissipativity of the gyro’s body and to the gyro’s attitude angle. It is then shown that deformations of the gyro configuration are required, to facilitate the attitude drift induced by dissipation. The deformed gyro configuration is found to be a function of the (slowly drifting) attitude angle only, thus making it nearly constant. As a consequence the concept of rigidity, so essential for gyrodynamics, need not be abandoned. The available experimental evidence is very sparse, but sufficient to show that typical satellites have innate dissipations in the order of microwatts due to structural hysteresis alone; and more, of course, when equipped with a nutation damper.

Random walk of the Earth's pole related to the Chandler wobble excitation

The equation governing the polar motion shows that the polar secular drift and the Chandler wobble amplitude are related to each other. In particular, a drift of the mean pole position comes out as a consequence of the maintenance of the Chandler wobble by possible step perturbations of the Earth's inertia tensor. The minimum excitation functions necessary to explain the Chandler wobble amplitude variations for the period 1901—84 are derived from the Chandler term, with the hypothesis that the excitations follow a uniform random distribution in time. It is shown that they have the statistical properties of the steps of a two-dimensional random walk. These functions are then used to derive, from a statistical simulation, a lower limit of the secular drift which may result from the excitation of the Chandler wobble. The drift generated by the random walk is of the same order of magnitude as the observed secular drift for the period 1901—84, but their time dependence is different. This indicates that the observed secular drift cannot be explained as the consequence of an excitation of the Chandler wobble by random steps of the Earth's inertia tensor. However, the possible contribution of the Chandler wobble excitation to the polar drift has to be taken into account when other mechanisms, such as lithospheric rebound related to deglaciation, are proposed.

Station coordinates, baselines, and Earth rotation from LAGEOS laser ranging: 1976–1984

Satellite laser range (SLR) measurements to LAGEOS from May 1976 to January 1984 have been used to compute earth rotation parameters and the geocentric positions of 57 laser tracking station sites occupied during this interval. The station position determinations were part of a simultaneous solution which includes LAGEOS orbit elements in 15‐day arcs and earth rotation parameters in 3‐day subarcs using residuals from a 7.7‐year LAGEOS long arc (LLA 8402). Systematic differences between the terrestrial reference frames implied by the University of Texas station coordinate solution (LSC 8402) and by previous solutions computed at the University of Texas (UT) and at Goddard Space Flight Center (GSFC) are reviewed. The new solution resolves a 0.72 m z axis difference between the terrestrial reference system origins inferred from the GSFC solution (SL5) and the previous UT solution (LSC 8112). The implied origins of the LSC 8402 solution and the SL5 solution are consistent to less than 60 mm in all components, and after removing orientation and scale differences, the coordinates for 26 common tracking stations have an rms difference of less than 80 mm. The rms difference in baseline length for 22 station pairs used in the recent Crustal Dynamics Project very long baseline interferometry (VLBI)/SLR intercomparison experiment is 50 mm between the GSFC and UT laser solutions and 40 mm between the UT laser solution and the VLBI solution. The earth rotation parameters computed in 3‐day intervals have an internal precision of 2 marc sec (62 mm at the earth's surface) for xp and yp and 0.15 ms (70 mm at the equator) for UT1. The estimated accuracy of the series, based on dual‐baseline VLBI intercomparisons, is approximately 2 marc sec for xp and yp and 0.2 ms for UT1. The effects of plate motion on the determination of the secular drift in polar motion using the 7.7‐year series is shown to be at the level of 1 marc sec/yr. Finally, baseline changes have been investigated by repeated station coordinate determinations using 60‐day subsets of the 7.7‐year interval of the LAGEOS data set. In each 60‐day solution interval, orbit elements were estimated at 15‐day intervals, and earth rotation parameters were determined at 5‐day intervals. For the 4‐year period beginning in January 1980, baseline length changes inferred by the successive 60‐day solutions were found to be in general agreement with the motions predicted by the AM1‐2 plate motion model of Minster and Jordan.

The thickness of the continental lithosphere

Two independent sets of geophysical data are shown to be particularly sensitive to the thickness of the continental lithosphere. Both are connected with the response of the planet to the last deglaciation event of the current ice age. The first set of data consists of relative sea level histories in the age range 0–10 kyr B.P. from sites along the eastern seaboard of North America. Such data appear to require a continental lithospheric thickness in excess of 200 km. The second set of data consists of the ILS record of the motion of the rotation pole over the time range 0–75 years B.P., which reveals a secular drift at the rate of 0.95 (±0.15) deg/106 years toward Hudson Bay. When the viscosity profile of the mantle is fixed to that required to explain free air gravity and relative sea level data from within the ice margin and the observed nontidal acceleration of planetary rotation, then these observations also suggest a continental lithospheric thickness of the same order.

Pleistocene deglaciation and the Earth's rotation: a new analysis

Summary. This paper is concerned with an analysis of the effect of the Pleistocene glacial cycle upon the Earth’s rotation. We demonstrate that two important geophysical observables may be explained as aspects of the rotational response to surface mass loading by ice sheets. These are the astronomically observed non-tidal component of the acceleration of planetary rotation and the secular drift of the rotation pole relative to the surface geography which is evident in the ILS pole path. The former observation is shown to provide an unambiguous constraint upon the viscosity of the planetary mantle and requires a depth dependence of this parameter which is the same as that which has previously been inferred in studies of the relative sea-level variations and free air gravity anomalies associated with post-glacial rebound. The observed secular drift of the pole cannot provide an independent estimate of the viscosity of the mantle because it depends jointly upon mantle viscosity and lithospheric thickness. With the viscosity profile fixed by the rebound data, the observed speed of polar wander suggests a continental lithospheric thickness which is in excess of that appropriate for old ocean basins but nevertheless in accord with independent constraints.

Continental lithospheric thickness and deglaciation induced true polar wander

The secular drift of the earth’s rotation pole, which is evident in ILS data, is a memory of the planet of the last deglaciation event of the current ice age. In order to fit the observed rate and direction of drift with an earth model whose viscosity profile is capable of reconciling the free air gravity and relative sea level data of postglacial rebound, requires a lithospheric thickness which is substantially in excess of that which might be considered an appropriate average thickness for the entire planet. This required thickness, which is greater than 250 km, is nevertheless in accord with independent estimates of the thickness of the continental lithosphere.

Polar wandering and the forced responses of a rotating, multilayered, viscoelastic planet

Changes in the earth's rotation produced by the waxing and waning of large mobile ice sheets can be used to infer the viscosity of the mantle from a comparison with the recent secular polar drift as revealed in the International Latitude Service data and also in the estimates of the nontidal acceleration of the length of the day. We have developed by using an analytical approach a physical model of a rotating earth consisting of an elastic lithosphere, a viscoelastic mantle, and an inviscid core. Forcings from the two major ice sheets, Laurentide and Fennoscandia, have been considered. Sensitivity analysis of the parameters governing the external forcings, such as the length and the time of termination of the deglaciation phase, show in general that there exist two families of mean mantle viscosities, 0(1022 P) and 0(1023 P), which can match the data satisfactorily. However, we find it an improvement to incorporate some amount of shrinkage from the Antarctic ice sheet, obtaining simultaneously a better fit with the two rotational data sets to the lower viscosity solutions. Hence forcings from the southern hemisphere may be able to remove the ambiguity associated with the extraction of mantle viscosity from rotational data. We have also solved the initial value problem of the components of instantaneous angular velocity by means of the Laplace transform for applied loads characterizing the continental ice sheets, which since the mid‐Pliocene have periodically expanded and contracted over the northern hemisphere. In consequence of this continual forcing, polar wander of around 5–10 degrees can take place for a mean mantle viscosity 0 (1022 P). Recent reanalysis of paleomagnetic data in conjunction with hot spot tracks have revealed that several degrees of true polar wander could have occurred in the last 5 m.y. These calculations thus provide a physical explanation for the observed movement of the rotation axis. Membrane stresses of 0 (10) bars can develop from this secular polar motion.

Estimability analysis of geodetic, astrometric and geodynamical quantities in very long baseline interferometry

Within the framework of Newtonian kinematics VLBI observations are analysed with respect to estimability of geodetic and astrometric quantities. An Earth model of either rigid or deformable type is designed; instrumental clock offsets and clock drifts are included. Observational patterns are studied in all detail reviewed in seven tables. Appendix A is an introduction to the set-up of the observational model for a deformable Earth both in terms of coordinate-free and coordinate-related geometry. Appendix B is a study of the invariance characteristics of VLBI observations. Interrelations of three fundamental quantities, length unit, time unit and velocity of light are discussed. An overall result of an Earth model of deformable type is the need of simultaneous observations to more than one source; VLBI time delay observations cannot distinguish between secular changes of network size (expansion or shrinking) and a common secular drift (deceleration or acceleration) of clocks used.

Keplerian Representation of a Non-Keplerian Orbit

The properties of a mean reference orbit are developed through the introduction of an augmented radial potential proportional to c/r2. The arbitrary constant c is chosen to satisfy the perturbed energy level over an oblate Earth. This produces a mean orbit with not only the correct first order anomalistic period, but one which is also functionally identical to a Kepler orbit. Explicit formulas are obtained for the mean elements in terms of the osculating initial values. A comparison of the solution with a numerically integrated 12 h highly eccentric orbit shows that most of the error in the mean orbit is contained within the neglected periodic terms. HE fundamental problem in Keplerian representations of real orbits is the failure to account for the correct energy in the orbit. This leads to secular in-track errors (or equivalently timing errors) of the form, 5M=(nk—n)t, where nk is the Kepler mean motion and n the real mean motion. As a consequence of 6M, perturbations with respect to a reference orbit are not uniformly valid over long intervals of time. A classical approach in perturbation theory is to in- corporate as much as possible of the perturbative influence into a reference orbit that is still expressible in closed form. Garfinkel,1 Sterne,2 and Aksnes3 employ an augmented reference potential that is a function of both radius and latitude. Vinti4 utilizes oblate-spheroidal coordinates that lead to an exact solution for J2 and part of J4. Unfortunately, these solutions introduce elliptic functions and integrals and are somewhat more complicated than pure Kepler motion. If the augmented potential is restricted to a term proportional to c/r2 (where c is a constant) then the solution retains the character of the Kepler motion. By suitable choice of this constant, we bring the orbit to nearly the correct energy level and remove the objectionable secular in-track drift. The use of the energy integral for in-track stabilization is not new. Both Nacozy5 and Baumgarte6 have considered these ideas from the viewpoint of time transformations that incorporate the energy integral. Nacozy7 outlines a method which constrains the numerical solution of a system of dif- ferential equations to remain on an integral surface by ap- plying corrections at each integration step. This procedure is shown to reduce the errors in a two body numerical in- tegration by several orders of magnitude. There are a series of papers on this topic by Baumgarte and Nacozy that generally treat the numerical aspects of stabilization of dynamical systems. The intent here is to present a simple closed form incorporation of the energy integral within the structure of Keplerian mechanics. This solution should prove to be of great utility in orbit transfer and targeting problems.

Decametric radio measurement of Jupiter's rotation period

A total of 26 measurements of Jupiter's 12-year average rotation period were made at frequencies of 18, 20, and 22.2 MHz at observatories in Florida and Chile. An improved method was employed in which histograms of occurrence probability vs central meridian longitude obtained at the same frequency and observatory during apparitions about 12 years (one Jovian year) apart were cross correlated. The longitude shift giving maximum cross correlation was used to correct the initially assumed rotation period value. The mean of the measurements is 9 hr 55 min 29.689 sec, with a standard deviation of the mean of 0.005 sec. This is about 0.02 sec, or 4 standard deviations, less than the System III (1965) value. The measurements indicate that the rotation period was not changing (linearly) at a rate in excess of 0.03 sec/yr. If the synoptic monitoring program is continued through the next maximum of the jovicentric declination of the Earth ( D E), we will probably be able to detect a rate of change in rotation period as small as 0.002 sec/yr. This accuracy might be sufficient to reveal a secular drift in Jupiter's magnetic field.

Ethnic Patterns of Urbanization in Peninsular Malaysia, 1947-1970

AbstractNotwithstanding the popular nostalgia for the good life in small towns and rural villages, there is a sound rational base for the secular drift from country to town during the last century throughout the world, in countries large and small, rich and poor. In almost every situation, it is clear that those in urban areas have greater access to educational institutions, are exposed to more diverse employment opportunities, and receive higher incomes than rural residents. These differences in economic opportunities and rewards are generally apparent to all. And so inherent in the process of urbanization and the consequent widening of rural-urban disparities is the potential for increased tension with the prevailing distribution system. Rural people, traditionally distrustful of cities, often interpret the growing socioeconomic gap as exploitative in character and pressure political and economic institutions for redress. Yet, most urbanites do not feel advantaged as they compare their plight to more successful urban residents, not to the disadvantaged rural population. In spite of these tensions rural-urban divisions only rarely become the dominant political groupings in a society. Rural to urban migration provides an individual alternative to collective political organization, and governments are often successful in using symbolic politics to allay rural discontent. Yet when rural-urban inequities reinforce other societal divisions such as ethnic groups, the potential for public protest and governmental initiatives is heightened. Such is the case in the plural society of Peninsular Malaysia where the largely rural Malay community is disadvantaged relative to the more urbanized Chinese and Indian minorities. And since the political base of the government is heavily dependent upon rural Malay support, recent public policies are intended to minimize socioeconomic disparities across ethnic communities. One strategy is to increase the proportional representation of Malays in towns and cities. In this paper we review the empirical trends in ethnic patterns of urbanization from 1947 to 1970, prior to advent of explicit public policies to eliminate ethnic inequalities in residence and in socioeconomic rewards.' These trends are interpreted in light of the intent of current government policies.

Analysis of secular polar motion and continental drift

The secular latitude variations of the five ILS stations of Mizusawa, Kitab, Carloforte, Gaithersburg and Ukiah were analyzed taking into account the recent continental drift theory. Using Le Pichon's 1968 reconstruction, the rate of rotation was computed from the astronomical data, fixing the pole of rotation by Le Pichon's determination. The most reasonable solution was obtained considering Mizusawa, Kitab and Carloforte lying on the Eurasia plate, the two American stations as one on the American plate (Gaithersburg) and the other on the North—East Pacific plate (Ukiah). The resulting relative rate between the Euro-American plates is found to be 0".0028/year and between the American—Pacific plates 0".0032/ years, or about 1°,3/106 years and in excellent agreement with the plate tectonic theory.

Does λ2,2vary?

An attempt has been made to find a secular drift in λ2,2 or the phase of the low-order and low-degree part of the geogravity field. This part may be associated with mass anomalies near the core-mantle boundary. On the basis of the geomagnetic evidence, such anomalies might have westward drifts of the order of 0.5°/yr. Tracking data on eight synchronous satellites over a period of 6 years were examined for residual accelerations that might be explained by a drift of the λ2,2 gravity phase angle. No conclusive movement of λ2,2 was detected. But a measured upper bound on the drift of <0.05°/yr is still compatible with possible slow-moving irregularities in the region of the core-mantle boundary.

On Variations in the Chandler Frequency

This paper suggests that some of the reported changes in the Chandler frequency are associated with inelastic changes in the Earth. There has been controversy as to how much of the apparent secular polar drift is due to actual motion of the axis of rotation within the Earth, and how much it is merely the reflection of movements by certain observatories. Therefore, when more southern data are available it will be interesting to see whether similar results are obtained.

A tensioned-wire strain seismometer

A 10 m span, tensioned-wire strain seismometer is described which has successfully recorded solid-tidal strains in Britain. Secular drift is within a few parts in 108 per week and sensitivity exceeds 1 part in 1010. Needing only two-point support it can be installed in a few hours for immediate use. The cost is comparable to that of conventional seismometers and is considerably less than current types of strain meters; it can therefore be used on an extensive scale for geophysics research.