Historical eclipses and Earth's rotation

F Richard Stephenson took a long view of Earth's rotation history in the 2002 Harold Jeffreys Lecture in October.     

Variations in the Earth's rotation and crustal deformations

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Secular tidal and nontidal variations in the Earth's rotation

Summary On the basis of the angular momentum balance in the Earth — Moon — Sun system and with the use of the observed secular variation in the Moon's mean motion and the variation in the second zonal geopotential harmonic, the tidal and nontidal variations in the angular velocity of the Earth's rotation are computed and different values describing the field of tidal forces estimated.

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Deceleration in the Earth's rotation due to the Sun

Summary The estimate of the tidal long-term decrease in the angular velocity of the Earth's rotation due to the Sun is given as –(0.8±0.3)×10 ^–22 rad s ^–2. It was computed on the basis of the observed total long-term decrease in , of the observed tidal deceleration of the Moon and the observed decrease in the second-degree zonal Stokes geopotential harmonic term. Adopting the estimate given, the product of the Love number and the tidal phase lag angle due to the Sun (in degrees) comes out as 0.53±0.20.

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Effects of Earth's rotation on convection in magma chambers

The rotation of the Earth is predicted to have a strong influence on the convective motions in basaltic magmas which cool at high and intermediate latitudes on the Earth's surface. Convection in layers greater than 100 m deep is characterised by large Taylor numbers and small Rossby numbers, for which laboratory experiments provide evidence of strong rotationally-induced flows. In the case of convection driven by either thermal or compositional buoyancy fluxes from horizontal top or bottom boundaries Coriolis forces induced by the Earth's rotation are expected to cause the turbulent convective motions to form into intense vortices whose axes tend to be close to the vertical. These vortices should be tall and thin, be very unsteady, and have rapid vertical motion in their cores. Earth's rotation is likely to have little or no effects on convection in very shallow convecting layers ( < 100 m) of basaltic magmas or in chambers of more viscous (granitic) magmas. When convection is driven by horizontal density differences (such as those produced by cooling or crystallization at sloping or vertical walls or by simple lateral variation of layer depth) in basaltic chambers of order 10 km or greater in width the rotation of the Earth may cause relatively rapid horizontal (geostrophic) circulation over the lateral scales of the chamber. These predictions involve some extrapolation of fluid dynamical principles from laboratory to magma chamber conditions. Speculative comments on some possible petrological implications are included.     

On the non-tidal secular acceleration of the Earth's rotation

Summary The secular positive acceleration of the Earth's rotation has been computed on the basis of the observed secular decrease of the second zonal harmonic[5]. It corresponds to the observed secular deceleration of the Earth's rotation which should be greater because of oceanic tides.

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Thermodiffusion and Diffusion Correction Factors of Neutral Gases in the Earth's Atmosphere

Surveys in Geophysics - The Maxwell–Stefan diffusion equations for multicomponent neutral gas mixtures with thermodiffusion ratios and diffusion correction factors in the...     

The Antarctic circumpolar current and its influence on the Earth's rotation

Summary At least in case of semidiurnal tides, theirmotions contain most of their relative angular momentum. There are other periodic currents in the ocean with cycles of months to years which may influence the Earth's rotation within such time scales. These currents are mainly due to seasonal or climatic variations of the wind stress and the water mass distribution in the oceans. The main question is: how much of the oceanic angular momentum is temporarily stored within the oceans and what is the time scale of the transfer to the solid Earth. As an example, we have estimated the phase and the amplitude of the angular momentum which is stored in the Antarctic Circumpolar Current. Its phase resembles the one of the whole observed semiannual discrepancy in the angular momentum budget of the solid Earth plus the atmosphere; the amplitudes are comparable.

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Der Antarktische Ringstrom und sein Einfluß auf die Erdrotation

Zusammenfassung Zumindest im Fall der halbtägigen Gezeiten der Ozeane enthalten derenBewegungen den größten Teil ihres variablen Drehimpulses. Andere periodische Meeresströmungen mit Perioden von Monaten bis Jahren könnten die Erdrotation ebenfalls beeinflussen. Solche Strömungen werden vor allem durch jahreszeitliche oder klimatische Veränderungen der Schubspannung des Windes und der Wasserstände verursacht. Die Hauptfrage ist jedenfalls diese: Wieviel Drehimpuls ist in jeder Phase in den Ozeanen gespeichert, und in welcher Zeit wird er mit der festen Erde ausgetauscht. Als Beispiel haben wir Phase und Amplitude des Drehimpulses abgeschätzt, der im Antarktischen Ringstrom enthalten ist. Diese Werte wurden mit den entsprechenden der Diskrepanz verglichen, die in der Bilanz feste Erde plus Atmosphäre offen bleibt. Die Phasen stimmen gut überein, und die Amplituden sind vergleichbar.

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Le courant circumpolaire antarctique et son influence sur la rotation de la terre

Résumé Au moins dans le cas des marées semi-diurnes lesmouvements des océans «contiennent» la plus grande partie de la variabilité de la quantité de moment angulaire de la terre. D'autres courants océaniques périodiques dont la période varie du mois à l'année peuvent aussi avoir une influence sur la rotation de la terre. De tels courants sont avant tout provoqués par des variations saisonnières ou climatiques de la tension superficielle due aux vents et des niveaux d'eau dans les océans. La question principale est en tout cas la suivante: quelle est à chaque phase la quantité de moment angulaire stockée dans les océans et en combien de temps est-elle échangée avec la masse solide de la terre. A titre d'exemple, nous avons évalué la phase et l'amplitude de la quantité de moment angulaire stockée dans le courant circumpolaire antarctique. Ces valeurs furent comparées aux valeurs correspondantes de l'anomalie qui subsiste dans le bilan terre solide plus atmosphère. Les phases sont concordantes et les amplitudes sont comparables.

     

Agreement between Earth's rotation and mass displacement as detected by GRACE

The progress in GRACE data processing should improve the estimation of low degree spherical harmonics which are expected to agree better with Earth's rotation observations. The polar motion and length-of-day excitations determined from the spherical harmonics of the GRGS latest release (RL02) are explored and compared to the previous release (RL01). The RL02 gives best fit of the observed annual variations than RL01 and geophysical models do. However, the observed residual signal obtained after removing annual and semiannual oscillations is still better explained by the geophysical models even if RL02 estimates are improved at these frequencies scales. Linear trends are also estimated over study period (2003–2008). The linear trends of χ₁ based on GRACE RL01/02 and EOP are similar but they are very different for χ₂. Further studies with longer time series of GRACE and future gravimetric missions could help better interpret the long term variations and the effects of ice sheet mass loss or post glacial rebound. Concerning LOD variations, GRACE/LAGEOS mass displacement information brings better agreement with EOP observations, compared to the pressure term estimated by models, however the RL02 has not shown significant improvement.     

Earth's Rotation And High Frequency Equatorial Angular Momentum Budget Of The Atmosphere

The effect of the atmosphere on the Earth's rotation can be computed by twodifferent but fundamentally equivalent approaches. The more commonly used is the so-called angular momentum approach, and the second is the torque approach. Their physicalmeanings are recalled, and numerical results from the two are intercompared, concentrating on the lowest periods of a few days or shorter. The indirect effect of the atmosphereon the Earth rotation due to atmospheric forcing on the ocean is also described based on both static and dynamic oceanic models.Results are discussed for the equatorial components and for the highest frequencies.     

地球重力场恢复中的位旋转效应

分析了地球自转引起的位旋转效应公式中采用近似速度的影响. 对一组GFZ的快速科学轨道、一组TUM的约化动力法轨道以及一组GFZ的事后科学轨道,计算了星历提供的速度与只有地球引力场对卫星产生作用时的卫星速度的差值,其中参考重力场模型分别采用EGM96、EIGEN2和EIGEN_CG01C. 通过比较得出：轨道数据与EIGEN2地球重力场模型的自恰性优于EGM96和EIGEN_CG01C地球重力场模型. 速度差各分量的变化具有很明显的周期性且与卫星轨道的运行周期相吻合. 当要求在卫星轨迹处获得1m2/s2精度的扰动位时,也即要求位旋转效应公式中卫星速度的近似精度小于2mm/s时,GFZ的快速科学轨道、TUM的约化动力法轨道只需要剔除那些速度精度不满足要求的卫星轨迹点;当要求在卫星轨迹处获得0.5m2/s2精度的扰动位时,应当重新估算上述轨道的速度信息,或采用精度更高的GFZ事后科学轨道.     

Anomalous curvature of equipotential surfaces due to variations in the Earth's rotation

Summary The anomalies of the Gaussian curvature of geopotential equipotential surfaces due to variations in the Earth's rotation vector have been derived theoretically.

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Time-dependent density anomalies in a stratified,viscoelastic mantle: Implications for the geoid,Earth's rotation and sea-level fluctuations

The effects on the = 2 geoid component and Earth's rotation due to internal mass anomalies are analyzed for a stratified viscoelastic mantle described by a Maxwell rheology. Our approach is appropriate for a simplified modeling of subduction. Sea-level fluctuations induced by long-term rotational instabilities are also considered. The displacement of the Earth's axis of rotation, called true polar wander (TPW) and the induced eustatic sea-level fluctuations, are extremely sensitive to viscosity and density stratification at the 670 km seismic discontinuity. Phase-change models for the transition zone generally allow for huge amount of TPW, except for large viscosity increases; the dominant contribution in Liouville equations comes from a secular term that reflects the viscous behaviour of the mantle. In chemically stratified models, TPW is drastically reduced due to dynamic compensation of the mass anomalies at the upper-lower mantle interface. When the source is embedded in the upper mantle close to the chemical density jump, transient rotational modes are the leading terms in the linear Liouville equations. Long-term rotation instabilities are valuable contributors to the third order cycles in the eustatic sea-level curves. Rates of sea-level fluctuations of the order of 0.05–0.1 mm/yr are induced by displacements of the Earth's axis of rotation compatible with paleomagnetic data.     

Critical remarks on the use of medieval eclipse records for the determination of long-term changes in the Earth's rotation

The use of some Arabic medieval solar and lunar eclipse records for the determination of secular changes in the Earth's rotation is critically reviewed. The published results derived from these data suggest a non-uniform decrease in the Earth's rotation rate over the last 27 cy. There is, however, up to this day no sound physical explanation for the deduced non-tidal oscillations, with an apparent period of about 1500 yr and a semi-amplitude of some 4 ms in the l.o.d., which overlayed to a constant secular tidal change in the Earth's rotation rate produce a net non-uniform deceleration of the Earth's rotation. In this paper we discuss a set of observations, which were executed by professional Arabic astronomers. We show by our analysis the way in which the non-uniform deceleration of the Earth's rotation was constructed. A correct reading of the Arabic medieval observations shows that they do not contradict a secular constant decrease in the Earth's rotation rate of nearly -4.6 10-22 rad s-2. This value is in accordance with other similar ones derived from ancient eclipse records and from satellite tracking data.     

本州M_W9.1地震前破裂区内地震与地球自转之间的相关现象

强震发生前震源系统可能处于不稳定状态,在这种情况下,震中附近地区的地震活动或许会对微小的应力变化敏感.地球自转会在震源断层面上引起应力,地球自转速率变化也会在震源断层面上引起应力变化.由于地球自转速率变化非常微小,在震源断层面上引起应力变化也非常微弱,如果震源区处于极不稳定状态,这种微弱的应力变化或许会激发一些地震活动.这些被激发的地震活动将会表现出与地球自转速率变化的显著相关性.为了考察2011年3月11日日本本州9.1地震发生前震中附近地区是否存在与地球自转速率变化显著相关的地震活动,选取2000年1月-2011年2月M≥5.0地震集中活动区域为研究区域,根据USGS发布的1991年1月-2011年2月的地震目录,利用舒斯特(Schuster)统计检验方法,研究了地球自转与本州M_W9.1地震前发生的地震活动之间的相关性.检验结果用P值来评估,P值越低表示相关性越显著.结果如下:在研究区内5.4≤M≤6.9地震的P值的时间变化显示本州M_W9.1地震前从2009年6月-2010年1月存在低于0.5%的P值.当P值达最低值时,约82%的5.4≤M≤6.9地震发生在地球自转速率季节性变化的加速期,显示出了地震活动与地球自转速率加速之间的显著相关性.取3°×3°的空间窗,以0.1°的步长沿经度和纬度滑动对P值进行空间扫描,可以得到P值的空间分布.扫描区域远大于研究区,经纬度范围为(33°N-43°N,138°E-147°E).在P值的空间分布图上,可发现在P值处于最低值期间,低于0.5%的P值集中分布在研究区的北部,本州M_W9.1地震震中位于这个低P值区的边缘.因此,本州M_W9.1地震前在其破裂区内存在显著的与地球自转相关的地震活动现象,说明破裂区内存在非常不稳定的地区.     

Rock magnetism and the Earth's palaeopoles

Summary On the assumption of a constant earth radius the spherical-trigonometric determination of former pole positions depends on the position of the North Pole of today. On the basis of an expanding earth, the determination of the palaeopoles should not be attempted on the present globe. There should rather be used a pole position on a model globe with a reckoning pole which is situated along the present northern direction of the measuring origin and spaced therefrom by its present pole distance. In that way Palaeozoic pole positions formerly determined in the Mid-Pacific shift to northeastern Siberia.

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Zusammenfassung Bei der sphärisch-trigonometrischen Berechnung früherer Pollagen unter Voraussetzung eines konstanten Erddurchmessers spielt die Lage des heutigen Nordpols eine wichtige Rolle. Bei Voraussetzung einer expandierenden Erde darf jedoch die Bestimmung der Paläopole nicht am heutigen Globus erfolgen. Vielmehr ist an einem Modellglobus ein Berechnungspol zu verwenden, der auf der heutigen Nordrichtung des Meßorts in seiner heutigen Poldistanz von ihm entfernt liegt. Auf diese Weise ergeben sich für das Paläozoikum Pollagen in Nordostsibirien an Stelle von Pollagen mitten im Pazifik.

     

The Earth's gravity field

The Earth's gravity field can be determined from gravity measurements made on the surface of the Earth, and through the analysis of the motion of Earth satellites. Gravity data can be used to solve the boundary value problem of gravimetric geodesy in various ways, from the classical formulation using a geoid to the concept of a reference surface interior to the masses of the Earth to a statistical method. We now have gravity information for 1⁰ data blocks over 46% of the Earth's surface and more than several million point measurements available.Satellite observations such as range, range-rate, and optical data have been analyzed to determine potential coefficients used to describe the Earth's gravitational potential field. Coefficients, in a spherical harmonic expansion to degree 12, can be determined from satellite data alone, and to at least degree 20 when the satellite data is combined with surface gravity material. Recent solutions for potential coefficients agree well to degree 4, but with increasing disagreement at higher degrees.     

Shortwave forcing of the Earth's climate: Modern and historical variations in the Sun's irradiance and the Earth's reflectance

Changes in the Earth's radiation budget are driven by changes in the balance between the thermal emission from the top of the atmosphere and the net sunlight absorbed. The shortwave radiation entering the climate system depends on the Sun's irradiance and the Earth's reflectance. Often, studies replace the net sunlight by proxy measures of solar irradiance, which is an oversimplification used in efforts to probe the Sun's role in past climate change. With new helioseismic data and new measures of the Earth's reflectance, we can usefully separate and constrain the relative roles of the net sunlight's two components, while probing the degree of their linkage. First, this is possible because helioseismic data provide the most precise measure ever of the solar cycle, which ultimately yields more profound physical limits on past irradiance variations. Since irradiance variations are apparently minimal, changes in the Earth's climate that seem to be associated with changes in the level of solar activity—the Maunder Minimum and the Little Ice age for example—would then seem to be due to terrestrial responses to more subtle changes in the Sun's spectrum of radiative output. This leads naturally to a linkage with terrestrial reflectance, the second component of the net sunlight, as the carrier of the terrestrial amplification of the Sun's varying output. Much progress has also been made in determining this difficult to measure, and not-so-well-known quantity. We review our understanding of these two closely linked, fundamental drivers of climate.