Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

In this paper, an improved weighted least squares （WLS）, together with autoregressive （AR） model, is proposed to improve prediction accuracy of earth rotation parameters（ERP）. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.

Rotation of the Earth as a Triaxial Rigid Body

The Earth is taken as a triaxial rigid body, which rotates freely in the Euclidian space. The starting equations are the Euler dynamic equations, with A smaller than B and B smaller than C. The Euler equations are solved, and the numerical results are provided. In the calculations, the following parameters are used: (C-B)/A=0.003 273 53; (B-A)/C=0.000 021 96; (C-A)/B=0.003 295 49, and the mean angular velocity of the Earth's rotation, ω =0.000 072 921 15 rad/s. Calculations show that, besides the self-rotation of the Earth and the free Euler procession of its rotation, there exists the free nutation: the nutation angle, or the angle between the Earth's momentary rotation axis and the mean axis that periodically change with time. The free nutation is investigated.

Earth Rotation Parameter Estimation by GPS Observations

The methods of Earth rotation parameter (ERP) estimation based on IGS SINEX file of GPS solution are discussed in detail. There are two different ways to estimate ERP: one is the parameter transformation method, and the other is direct adjustment method with restrictive conditions. By comparing the estimated results with independent copyright program to IERS results, the residual systemic error can be found in estimated ERP with GPS observations.

Earth＇s Temporal Principal Moments of Inertia and Variable Rotation

Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth＇s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10^ 8 mas/yr; the third component of the rotational angular velocity, ω3 , has a decrease of 1.0×10^ 22 rad/s^2, which is around 23% of the present observed value. Studies show in detail that both 0 and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.

Research on the relationship between Earth＇s variable rotation and global seismic activity

Based on the time series of observational variations of the length of day (LOD) and seismic data in the world,the relations of the decadal fluctuation and seasonal variation in the Earth's rotation with global seismic activityare studied in this paper. The results suggest that there are overall correlations on temporal scale and regionaldiscrepancy on spatial scale between global seismic activity and the Earth's variable rotation, especially the seismic activity in the Eurasian seismic zone (not including southeast Asia) and the Lower California-Eastern Alaskaseismic zone correlating well with the Earth's variable rotation. According to the relations mentioned above, theobservational data of the Earth'S rotation might provide a referential basis for monitoring global seismic activity.

Anomalies identification of Earth’s rotation rate time series (2012-2017) for possible correlation with strong earthquakes occurrence

The analysis of the Earth’s rotation rate time series,from January 1,2012 till December 31,2017,is performed using two different time series analysis methods,both based on signal decomposition joined with forecasting approach.Anomalies in the time series are detected making the comparison between the raw signal and the forecasting one at the 95% confidence interval.The two methods show consistent results and the best is selected according to the evaluation of the prediction uncertainty.Both methods highlight correlations between detected anomalies in the Earth’s rotation rate time series and the world’s earthquakes occurrence with magnitude≥7 and/or number of events≥150 per day,within a time interval of ±10 days from each earthquake event.This study brings an innovation in the analysis of such time series and helps to better understand the extent of this relationship.

Earth rotation deceleration/acceleration due to semidiurnal oceanic/atmospheric tides:Revisited with new calculation

The global oceanic/atmospheric tides exert decelerating/accelerating secular torques on the Earth rotation. We developed new formulations to accurately calculate amounts of two kinds of secular tidal torques. After Melchior, we found that an additional factor 1+k-l = 1.216, which has been formerly neglected, must be multiplied unto the tidal torque integral. By using our refined formulations and the recent oceanic/atmospheric global tide models, we found that:(i) semidiurnal oceanic lunar/solar tides exert decelerating torques of about-4.462 × 10^(16)/-0.676 × 10^(16) Nm respectively and(ii) atmospheric S_2 tide exerts accelerating torque of 1.55 × 10^(15) Nm. Former estimates of the atmospheric S_2 tidal torque were twice as large as our estimate due to improper consideration of loading effect. We took the load Love number for atmospheric loading effect from Guo et al.(2004). For atmospheric loading of spherical harmonic degree two, the value of k′=-0.6031 is different from that for ocean loading as k′ =-0.3052,while the latter is currently used for both cases-ocean/atmospheric loading-without distinction. We discuss(i) the amount of solid Earth tidal dissipation(which has been left most uncertain) and(ii) secular changes of the dynamical state of the Earth-Moon-Sun system. Our estimate of the solid Earth tidal torque is-4.94×10^(15) Nm.

A possible interrelation between Earth rotation and climatic variability at decadal time-scale

Using multichannel singular spectrum analysis （MSSA） we decomposed climatic time se- ries into principal components, and compared them with Earth rotation parameters. The global warming trends were initially subtracted. Similar quasi 60 and 20 year periodic os- cillations have been found in the global mean Earth temperature anomaly （HadCRUT4） and global mean sea level （GMSL）. Similar cycles were also found in Earth rotation variation. Over the last 160 years multi-decadal change of Earth＇s rotation velocity is correlated with the 60-year temperature anomaly, and Chandler wobble envelope reproduces the form of the 60-year oscillation noticed in GMSL. The quasi 20-year oscillation observed in GMSL is correlated with the Chandler wobble excitation. So, we assume that Earth＇s rotation and climate indexes are connected. Despite of all the clues hinting this connection, no sound conclusion can be done as far as ocean circulation modelling is not able to correctly catch angular momentum of the oscillatory modes.

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. （2004. Science in China, Ser. D, 47（12）： 1147-1154） for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth＇s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.

DISTRIBUTION OF ACTIVE EARTH PRESSURE OF RETAINING WALL WITH WALL MOVEMENT OF ROTATION ABOUT TOP

Based on the Coulomb's theory that the earth pressure against the back of a retaining wall is due to the thrust exerted by the sliding wedge of soil from the back of the wall to a plane which passes through the bottom edge of the wall and has an inclination equal to the angle of θ, the theoretical answers to the unit earth pressure, the resultant earth pressure and the point of application of the resultant earth pressure on a retaining wall were obtained for the wall movement mode of rotation about top. The comparisons were made among the formula presented here, the formula for the wall movement mode of translation, the Coulomb's formula and some experimental observations. It is demonstrated that the magnitudes of the resultant earth pressures for the wall movement mode of rotation about top is equal to that determined by the formula for the wall movement mode of translation and the Coulomb's theory. But the distribution of the earth pressure and the points of application of the resultant earth pressures have significant difference.

Co-seismic Earth's rotation caused by the 2012 Sumatra earthquake

Earthquakes heavily deform the crust in the vicinity of the fault, which leads to mass redistribution in the earth interior. Then it will produce the change of the Earth＇s rotation （ polar motion and length of day） due to the change of Earth inertial moment. This paper adopts the elastic dislocation to compute the co-seismic polar motion and variation in length of day （LOD） caused by the 2011 Sumatra earthquake. The Earth＇s rota- tional axis shifted about 1 mas and this earthquake decreased the length of day of 1 p,s, indicating the tendency of earthquakes make the Earth rounder and to pull the mass toward the centre of the Earth. The result of varia- tion in length of day is one order of magnitude smaller than the observed results that are available. We also compared the results of three fault models and find the co-seismic change is depended on the fault model.

Relationship among subtropical anticyclone,drought and earth rotation

The deep reason of severe disaster weather with the relationship among the earth nutation,rotation and atmospheric change is explored based on the effective results about the disaster weather prediction of the long term made by the variation of the earth rotation in near 10 years. It is discussed the relationship between the subtropical anticyclone and subtropical easterlies to aim at the problem of high temperature and drought in the globe,further more,the comparison analysis has been made to the earth nutation and the variation of rotation. The research results show that the reasons of severe disaster weather not only are due to atmosphere itself,but have some variation information of earth movement which could be used for the weather forecast.

A Check on the Variations of Earth's Rotation with an Ancient Solar Eclipse

We address the relation between an ancient total eclipse, which occurred on A.D.1542 August 11 and the variation of Earth's rotation. The total eclipse was recorded in some ancient Chinese books, especially in local chronicles. Some of the documents include useful information for determining the location of the totality zone. The parameters of the eclipse are calculated by using the DE406 Ephemeris. A high-precision value of ΔT which expresses the variation of the Earth's rotation, of about 300 ~ 380 s, is obtained.

Atmospheric acceleration and Earth-expansion deceleration of the Earth rotation

Previous studies suggest that tidal friction gives rise to the secular deceleration of the Earth rotation by a quantity of about 2.25 ms/cy. Here we just consider additional contributions to the secular Earth rotation deceleration. Atmospheric solar semi-diurnal tide has a small amplitude and certain amount of phase lead. This periodic global air-mass excess distribution exerts a quasi-constant torque to accelerate the Earth＇s spin rotation. Using an updated atmospheric tide model, we re-estimate the amounts of this atmospheric acceleration torque and corresponding energy input, of which the associated change rate in LOD（length of day） is-0.1 ms/cy. In another aspect, evidences from space-geodesy and sea level rise observations suggest that Earth expands at a rate of 0.35 mm/yr in recent decades, which gives rise to the increase of LOD at rate of 1.0 ms/cy. Hence, if the previous estimate due to the tidal friction is correct, the secular Earth rotation deceleration due to tidal friction and Earth expansion should be 3.15 ms/cy.

The earth dynamic system: the earth rotation vs mantle convection

The earth dynamic system is one of the key scientific questions on the earth science. The thermodynamic behavior and gravity force of the earth and the rheology nature of the mantle prove that mantle convection is the main power source leading the lithosphere to break and move. Yet the directivity of both the structures in the crust and plate movement reminds of the earth rotation. Here we demonstrate that the mantle convection and inertia force of the earth rotation affect each other, the former being the power source of lithosphere plate break and motion, and the latter determining the direction of the mantle convection and plate motion. The sense of plate motion depends on the mantle upwells, whose trends are controlled by the earth rotation. The geometric shapes of the plate boundaries can adjust the direction of plate movement.

Earth rotation parameter and variation during 2005—2010 solved with LAGEOS SLR data

Time series of Earth rotation parameters were estimated from range data measured by the satellite laser ranging technique to the Laser Geodynamics Satellites（LAGEOS）-1/2 through 2005 to 2010 using the dynamic method. Compared with Earth orientation parameter（EOP）C04, released by the International Earth Rotation and Reference Systems Service, the root mean square errors for the measured X and Y of polar motion（PM） and length of day（LOD）were 0.24 and 0.25 milliarcseconds（mas）, and 0.068 milliseconds（ms）, respectively.Compared with ILRSA EOP, the X and Y of PM and LOD were 0.27 and 0.30 mas, and 0.054 ms, respectively. The time series were analyzed using the wavelet transformation and least squares methods. Wavelet analysis showed obvious seasonal and interannual variations of LOD, and both annual and Chandler variations of PM; however, the annual variation could not be distinguished from the Chandler variation because the two frequencies were very close. The trends and periodic variations of LOD and PM were obtained in the least squares sense, and PM showed semi-annual, annual, and Chandler periods.Semi-annual, annual, and quasi-biennial cycles for LOD were also detected. The trend rates of PM in the X and Y directions were 3.17 and 1.60 mas per year, respectively, and the North Pole moved to 26.8E relative to the crust during 2005—2010. The trend rate of the LOD change was 0.028 ms per year.

Relationships between Earth’s Rotation or Revolution and Geographical Extent of the Global Surface Monsoons

Monsoon seasons, occasionally also known as wet seasons or trade-wind littoral seasons, are found in the regions where there is a complete seasonal reversal of the prevailing surface winds. Accompanying these shifts in the prevailing surface winds are modulations in rainfall activity. Given the fact that our knowledge of the monsoons is mainly based on the interpretation of the mean values of precipitation, cloudiness and winds;relationships between earth’s rotation or revolution and geographical extent of the global surface monsoons deserve to be highlighted. In the abundant literary and audiovisual production devoted to monsoons worldwide and despite the fact that everyone agrees with physical law which shows that Coriolis force acts to the right in the northern hemisphere (to the left in the southern hemisphere), there is no reference to the relationship between Coriolis force (due to earth’s rotation) effects on troposphere general circulation and geographical extent of the global surface monsoons. Furthermore knowing that the ITCZ oscillations on either side of the equators (due to earth’s revolution) determine the seasons (mainly winter and summer), it is clear that earth’s revolution also plays a crucial role in the seasonal reversal of the prevailing surface winds observed in the regions where monsoons are found. Our main objective is to provide a rational answer to the question: what is a monsoon?

Relationship between Earth’s Rotation and Several Strong Earthquakes and Moderate-small Earthquakes Occurring around the Epicenter Regions Prior to Strong Earthquakes

The relationships between Earth＇s rotation and the 1975 Haicheng, Liaoning Ms7.3 earthquake, 2008 Wenchuan, Sichuan Ms8.0 earthquake and the 2004 Sumatra Msg. 0 earthquake, as well as moderate-small earthquakes occurring around the epicenter regions prior to them are investigated in this study. The obtained results could benefit the further understanding of the relationship between the Earth＇s rotation and earthquakes.

Variations of the Earth＇s rotation rate and cyclic processes in geodynamics

The authors analyzed the relationship between variations of the Earth＇s rotation rate and the geodynamic processes within the Earth＇s body, including seismic activity, The rotation rate of a planet determines its uniaxial compression along the axis of rotation and the areas of various surface elements of the body. The Earth＇s ellipticity variations, caused naturally by the rotation rate variations, are manifested in vertical components of precise GPS measurements. Comparative analysis of these variations is considered in view of modern theoretical ideas concerning the Earth＇s figure. The results justify further research that is of interest for improvement of space svstems and technologiesi.

Earth’s rotation-triggered earthquakes before the 2018 M_S5.7 Xingwen earthquake

For earthquakes(ML≥2.0) that occurred from January 2006 to October 2018 around the Ms5.7 Xingwen earthquake occurred on 16 December 2018 in Xingwen,Sichuan province,China,we statistically investigated the correlation between the phase of Earth's rotation and the occurrence of earthquakes via Schuster's test to determine the signals that triggered earthquakes before the Ms5.7 Xingwen event.The results were evaluated based on the P-value where a smaller P-value corresponded to a higher correlation between the occurrence of an earthquake and Earth's rotation.We investigated the spatial distribution of Pvalues in the region around the epicenter of the Ms5.7 Xingwen event,and obtained a result exhibiting a extremely low-P-value region.The松5.7 event occurred inside near the northern boundary of this region.Furthermore,we analyzed the temporal evolution of P-values for earthquakes that occurred within the extremely low-P-value region and found that some extremely low P-values(less that 0.1%),i.e.,significant correlation,were calculated for earthquakes that occurred before the胚5.7 Xingwen earthquake.Among sixty・one earthquakes with the lowest P-value,occurred from May 2014 to April 2018,a vast majority of them occurred during the acceleration of Earth's rotation.The lower P-value obtained in this study reveals that the Xingwen source body probably was extremely unstable prior to the occurrence of the Ms5.7 Xingwen earthquake.