Terrestrial Tides Research Articles

Accuracy Evaluation of Regional and Global Tidal Models (TPXO9 and Goddard Ocean Tide) at Kabil Tidal Station

Indonesia is an archipelagic country with a total marine area of 5.9 million km², consisting of 3.2 million km² of territorial waters and 2.7 km² of Exclusive Economic Zone waters, not including the continental shelf. With the vast waters in Indonesia, sufficient information about the tides is needed. Limitations of terrestrial tide data amidst the increasing need for marine information can be overcome by using global and regional tide models. This study uses the regional tidal data model released by BIG (Geospatial Information Agency) and the global tide model TPXO9 and GOT (Goddard Ocean Tides). From the two global tidal models, the tidal harmonic constant values are extracted at the tidal observation point in Kabil. Evaluation of global and regional tide models is carried out by comparing the amplitude values of the main harmonic constants of the tide models of global and regional tides with the amplitude values of the harmonic constants of terrestrial tidal measurement data to obtain a comparison of accuracy. The results of this research show the value of main tidal harmonic.

Formation of Oscillations with an 11-Hour Period after the Tohoku Earthquake

Records of 68 identical broadband seismic stations of different world regions were studied after the catastrophic Tohoku earthquake on March 11, 2011. The oscillations with a period of ~11 hours lasted for a week. Their properties are distinct from similar 12-hour oscillations of the terrestrial tides. Stations at distances up to several hundred kilometers from each other provide similar records. The increase in the distance changes their structure. The oscillation phases have opposite and coincident polarity at distances of ~3800 and ~7600 km between stations, respectively. Vertical channels of seismographs react in this period range both to the rate of the ground displacement and to the variation in the force of gravity. The amplitude of these oscillations after the Tohoku earthquakes exceeds the variations of the terrestrial tides. They are probably related to excitation of internal gravitation waves in the atmosphere and ionosphere.

Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = $$-25.97\pm 0.05 ''/$$ cent $$^{2}$$ , da/dt = 38.30 ± 0.08 mm/year, and di/dt = −0.5 ± 0.1 $$\upmu $$ as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives $$\sim $$ $$3\times 10^{-12}$$ /year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = $$(1.50 \pm 0.10)\times 10^{-11}$$ /year. For total dn/dt, there is $$\le $$ 1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is $$-1316 ''$$ /cent $$^{2}$$ or 87.5 s/cent $$^{2}$$ for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 $$\upmu $$ as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.

Strain rates estimated by geodetic observations in the Borborema Province, Brazil

The strain rates for the Borborema Province, located in northeastern Brazil, were estimated in this study. For this purpose, we used GNSS tracking stations with a minimum of two years data. The data were processed using the software GIPSY, version 6.2, provided by the JPL of the California Institute of Technology. The PPP method was used to process the data using the non-fiducial approach. Satellite orbits and clock were supplied by the JPL. Absolute phase center offsets and variations for both the receiver and the satellite antennaes were applied, together with ambiguity resolution; corrections of the first and second order effects of the ionosphere and troposphere models adopting the VMF1 mapping function; 10° elevation mask; FES2004 oceanic load model and terrestrial tide WahrK1 PolTid FreqDepLove OctTid. From a multi annual solution, involving at least 2 years of continuous data, the coordinates and velocities as well as their accuracies were estimated. The strain rates were calculated using the Delaunay triangulation and the Finite Element Method. The results show that the velocity direction is predominantly west and north, with maximum variation of 4.0 ± 1.5 mm/year and 4.1 ± 0.5 mm/year for the x and y components, respectively. The highest strain values of extension and contraction were 0.109552 × 10−6 ± 3.65 × 10−10/year and −0.072838 × 10−6 ± 2.32 × 10−10/year, respectively. In general, the results show that the highest strain and variation of velocity values are located close to the Potiguar Basin, region that concentrates seismic activities of magnitudes of up to 5.2 mb. We conclude that the contraction direction of strain is consistent with the maximum horizontal stress derived from focal mechanism and breakout data. In addition, we conclude that the largest strain rates occur around the Potiguar Basin, an area already recognized as one of the major sites of seismicity in intraplate South America.

Artificial satellites: resonance effects produced by terrestrial tide

Abstract: Effects due to resonances in the orbital motion of artificial satellites disturbed by the terrestrial tide are analyzed. The nodal co-rotation resonance, apsidal co-rotation resonance and the Lidov-Kozai’s mechanism are studied. The effects of the resonances are analyzed through the variations of the metric orbital elements. Libration and circulation motions for high orbits with high eccentricities are verified for the Lidov-Kozai’s mechanism.

Terrestrial tidal variations in the selenopotential coefficients

The variations in the coefficients of the harmonics of second degree of the selenopotential caused by the terrestrial tides have been studied. In the paper we use analytical expressions for the tidal variations in the Stokes coefficients obtained for a model of the elastic celestial body with a concentric distribution of mass using the fundamental elastic parameter k 2 of the Moon. Taking into account the resonant properties of the Moon’s motion, the variations in the selenopotential coefficients are presented in the form of Fourier series in the arguments of the theory of lunar orbital motion: l M, l S, F and D. The variations in the polar moment of inertia of the Moon due to the terrestrial tides lead to marked variations in the Moon’s axial rotation, which also have been determined and tabulated. From the results obtained, it follows that the tide periodic variations in the gravitational coefficients of the Moon are an order larger than the corresponding tide variations in the geopotential coefficients.

On Effect of Terrestrial Tide Waves on the Stress-Strain State of Rock Masses

It is established that impulse manifestations of convergence of walls in development workings are caused by terrestrial tides and geosphere energy transformations dependent on the Moon's and Sun's cycles. The recommendations are made to take into account planetary dynamics of stress-strain state when scheduling and carrying out mining operations.

Polarisation and precise calibration of the LEP beam energy

We report in this article on two issues of precision accelerator physics, performed at the LEP collider, that challenged international collaborations. The first result is an increase of the polarisation degree from an almost vanishing natural level to 50%, opening the way to energy calibration by resonant depolarisation. The second result is a systematic and precise determination of the collider centre-of-mass energy correcting for subtle effects such as the azimuthal variation of the beam energy, the magnets temperature, the effects of parasitic earth currents and terrestrial tides. It resulted in an extremely accurate test of the Standard Model and set significant constraints on the top quark and Higgs masses. To cite this article: J.-P. Koutchouk, M. Placidi, C. R. Physique 3 (2002) 1121–1130.

Use of Geoid for Assessing Trigonometric Height Accuracy and Detecting Vertical Land Motion

An improved geoid model for Taiwan was developed using land and sea gravity anomalies and altimeter-derived geoid gradients by least-squares collocation. The estimated model accuracy ranges from 2 cm in the flat area to 10 cm in the mountainous area. This geoid model, along with GPS ellipsoidal heights, is used to determine the errors of the “orthometric heights” at Taiwan’s first-order triangulation stations, yielding an RMS error of 0.97 m. Yushan, east Asia’s highest peak, is now estimated to be 3,950.50 m above the mean level at Keelung from this geoid model and GPS measurements. With recent measured ellipsoidal heights at 33 benchmarks in eastern Taiwan, an average uplift rate of 4.46 cm/year is found along the Longitudinal Valley, and 3.02 cm/year along the coastal highway. This uplift is the result of the collision between the Philippine Sea plate and the Eurasian plate, and the rates are consistent with those derived from terrestrial measurements and tide gauge records.

Study of the Correlations Between Long-Periodic Terrestrial Tides and Occurrence of Earthquakes in the Vrancea Site

Following studies already performed by various authors concerning specific tectonic faults we analyse statistically the possibility that earthquakes in the very active seismological zone of Vrancea (Roumania) may be triggered by the vertical luni-solar tidal oscillations when retaining only the components other than diurnal and semi-diurnal. Our conclusion is that for three of the four leading tides, with periods 18.6 y, 182.62 d, and 13.66 d, the earthquakes occur preferentially during the ascending part of each of the sine oscillation. This property is especially visible for the leading 13.66 d fortnightly wave, and for the 18.6 y wave, for which results are very similar to that of Kilston and Knopoff (1983), who analyzed data related to the San Andreas fault in Southern California. As a complement, we carried out an analysis of earthquake periodicities w.r.t. the variation rate of each of the tides above, given by the half-period sine oscillation, which also leads to interesting possible correlations.

Effects of terrestrial tides on the LEP beam energy

The circular e +e − collider LEP located near Geneva is used to investigate the properties of the Z boson. The measurements of the Z boson mass and resonance width are of fundamental importance for the standard model of the electroweak interactions. They require a knowledge of the LEP beam energy with a precision of ∼ 20 ppm, which is provided by a measurement of the electron spin precession frequency. To extrapolate beam energy calibrations over a longer period of time, effects causing energy changes have to be taken into account. Among these are the terrestrial tides due to the sun and moon which move the Earth surface up and down. The lateral components of this motion modify the 26.7 km LEP circumference by about 1 mm. This change in length results in variations of the beam energy up to 120 ppm. We present results of measurements on the influence of terrestrial tides on the LEP beam energy that have been performed in 1992 and 1993.

Spin tune shifts in storage rings

Energy calibration by resonant depolarization is used practically in all colliders (HERA-e, LEP, VEPP-4, VEPP-2M, TRISTAN, CESR, BEPC). It is necessary to estimate the contribution of systematic errors to this method. There are different reasons for these errors: spin tune shift due to real collider optics, energy shifts causing nonlinearity of the guide magnetic field and optics imperfections, RF-cavity misalignments, electrical fields of vacuum pumps, and even terrestrial tides due to the sun and moon. The spin tune shifts which are produced by different reasons can be calculated in code SPINLIE. Some of these sources of errors will be discussed in this report and analytical estimations will be obtained.

Global tidal parameters

Global tidal parameters are shown to have recently increased in accuracy, after more than twenty years of LLR and a decade of superconducting gravimetry, whereas the numerical values for the Earth have not changed substantially. Numerical values of Love numbers for terrestrial planets and the moon are also given for degrees higher than four as load numbers are basically linear combinations of Love numbers, at least for spherical non-rotation approximations. Numerical values for planetary moons, as far as they are known, have also been included in the paper. The static and dynamic behaviour of long-period and pole tide is discussed. Inner solid and outer fluid core effects are critically reviewed, also in view of a century of terrestrial tide observations of the classical type. The separation of long-period tides from secular effects (on a rotating Earth) such as Jn (n<5), is considered.

Lunar and terrestrial tidal effects on the Moon's rotational motion

An accurate model of the rotation of the Moon, constructed by numerical integration, has been presented in a previous paper. All direct perturbations capable of producing at least 10−4 seconds of arc on the Moon's rotational motion have been included, and the physical librations resulting from planetary effects and Earth-Moon figure-figure interactions have been presented. The present study deals with the Moon's physical librations resulting from the non-rigidities of the Moon and the Earth. The effects of the Moon's elasticity and of a lunar phase lag are analyzed. Physical librations due to lunar tides and those due to terrestrial tides are presented and described.

Lorentz Invariance as a Dynamic Symmetry

If all the forces of nature can be reduced to those which follow from a linear combination of a scalar and vector potential, as in electrodynamics, Lorentz invariance can be derived as a dynamic symmetry. All that has to be done is to assume that there is an all pervading substratum or ether, transmitting those forces through space, and that all physical bodies actually observed are held together by those forces. Under this assumption bodies in absolute motion through the substratum suffer a true contraction equal to the Lorentz contraction, and as a result of this contraction clocks in absolute motion go slower by the same amount. The velocity of light appears then to be equal in all inertial reference systems, if Einstein’s clock synchronization convention by reflected light signals is used and which presupposes this result. The Lorentz contraction and time dilation measured on an object at rest relative to an observer who gained a velocity by an accelerated motion is there explained as an illusion caused by a true Lorentz contraction and time dilation of the observer. Both the special relativistic kinematic interpretation and this alternative dynamic interpretation give identical results only in the adiabatic limit where the accelerations are small, because if the Lorentz contraction is a real physical effect, it must take a finite time. However, to break the peculiar interaction symmetry with the ether, and which in the dynamic interpretation is the cause for the Lorentz invariance, the accelerated motions must involve rotation. Only then can non-adiabatic relativity-violating effects be observed and which would establish a preferred reference system at rest with the ether. Under most circumstances relativity-violating effects resulting from such a dynamic interpretation of special relativity would be very small and difficult to observe, a likely reason why they have evaded their detection in the past. For the rotating earth a residual sideral tide has been observed with a superconducting gravimeter, and which could be explained by an “ether wind” of about 300 km /sec at rest with the cosmic microwave background radiation. However, because of the observational uncertainties in measuring the terrestrial tides no definite conclusion can be drawn. A number of new experiments are therefore needed to decide the question regarding a possible weak violation of special relativity.

Solar Related Waves in the Venusian Atmosphere from the Cloud Tops to 100 km

A quasi-linear diagnostic model using observed solar-related temperatures and a specified solar mean circulation and surface structure to find the solar-related circulation above the clouds of Venus is presented. Despite the greater dependence of model-derived, solar-related circulation on the mean flow than is the case for terrestrial tides, as well as the uncertainty concerning this mean flow, significant conclusions are drawn for the solar-related circulation and thermal structure of Venus. An anomalously large response is found in the polar regions, due to the model's requirement of a process such as dissipation which will act as a major sink for momentum. Dissipation is specified in the model as Rayleigh friction with an unknown free parameter coefficient. In view of this, dissipation is either very efficient by terrestrial standards and accompanied by small solar-related circulation, or similar to that of earth and possessed of a circulation large enough to have an impact on the mean circulation.

Ocean tides, part I: Global ocean tidal equations

A detailed derivation of improved ocean tidal equations in continuous (COTEs) and discrete (DOTEs) forms is presented. These equations feature the Boussinesq linear eddy dissipation law with a novel eddy viscosity that depends on the lateral mesh area, i.e., on mesh size and ocean depth. Analogously, the linear law of bottom friction is used with a new bottom friction coefficient depending on the bottom mesh area. The primary astronomical tide‐generating potential is modified by secondary effects due to the oceanic and terrestrial tides. The fully linearized equations are defined in a single‐layer ocean basin of realistic bathymetry varying from 50 m to 7,000 m. The DOTEs are set up on a 1o by 1o spherically graded grid system, using central finite differences in connection with Richardson's staggered computation scheme. Mixed single‐step finite differences in time are introduced, which enhance decay, dispersion, and stability properties of the DOTEs and facilitate—in Part II of this paper—a unique hydrodynamical interpolation of empirical tide data. The purely hydrodynamical modeling is completed by imposing boundary conditions consisting of no‐flow across and free‐slip along the mathematical ocean shorelines. Shortcomings of the constructed preliminary M2 ocean tide charts are briefly discussed. Needed improvements of the model are left to Part II.

Notes concerning tidal oscillations upon a rotating globe

Speculations on tidal questions are much hampered by our ignorance of the peculiar influence of the earth’s rotation in any but the simplest cases. The importance of this element was first appreciated by Laplace, and he succeeded in obtaining solutions of various problems relating to a globe completely covered with water to a depth either uniform throughout, or at any rate variable only with latitude. His work has been extended by Kelvin, G. Darwin, and Hough. For an excellent summary, reference may be made to Lamb’s ‘Hydrodynamics,’ which includes also important original additions to the theory. But it must not be overlooked that a theory which supposes the globe to be completely covered with water has very little relation to our actual tides. Indeed, in practice, tidal prediction borrows nothing from Laplace’s theory, unless it be to look for tidal periods corresponding with those of the generating forces. And this correspondence, although perhaps first brought into prominence in connection with Laplace’s theory, is a general mechanical principle, not limited to hydrodynamics. If the theory of terrestrial tides is to advance, it can only be by discarding the imaginary globe completely covered with water and considering examples more nearly related to the facts, as was done in some degree by Young and Airy in their treatment of tides in canals. It is true that we are unlikely to obtain in this way more than very rough indications, but even such are at present lacking. I am told that opinions differ on so fundamental a question as whether the Atlantic tides are generated in the Atlantic or are derived from the Southern Ocean. Probably both sources contribute; but a better judgment, based on some sort of discussion on a priori principles, does not appear hopeless. In this connection, it is interesting to observe that a comparison of spring and neap tides shows that the moon is more effective relatively to the sun than would be expected from the ratio of the generating forces. This indicates some approach to synchronism with a natural free oscillation. That the approach is closest in the case of the moon indicates that free period is longer than those of the actual lunar and solar tides.