Earth: Review Article

Every year on 22 April, we have celebrated Earth Day and the beautiful planet we call home. Earth Day, established in 1970, has been used to highlight our planet’s environmental challenges and raise awareness of the importance of protecting our world for future generations [1]. To provide the protection of our planet, we should explain Earth’s environmental challenges to the best of our knowledge in frames of contemporary Geophysics. This paper gives a short overview of the developed Hypersphere World-Universe Model (WUM) and pay particular attention to the principal role of Dark Matter (DM) in the Earth’s life. In this manuscript, we discuss different aspects of the Earth: a condition of Young Earth before the Beginning of life on It;Internal Structure;“The 660-km Boundary” that we named Geomagma;Random Variations of Earth’s Rotational Speed on a daily basis;Origin of Moon;Expanding Earth;Internal Heating;Faint Young Sun paradox;Geocorona and Planetary Coronas;High-Energy Atmospheric Physics. WUM proposed principally different ways to solve the problems of Internal Heating, Origin of the Moon, and Faint Young Sun paradox based on DM core of the Earth. The Model revealed the fact that the Sun Activity causes the Geomagma Activity and, as a consequence, Random Variations of Earth’s Rotational Speed by the varying Sun’s magnetic field.

A review of the 19th International Symposium on geodynamics and earth tide, Wuhan 2021

Modern geodetic technologies such as high-precision ground gravity measurements,satellite gravity measurements,the global navigation satellite system,remote sensing methods,etc.provide rich observation data for monitoring various geodynamic processes of the global Earth and its surface.The 19th International Symposium on Geodynamics and Earth Tides brought together scientific researchers from 26 countries around the world,shared the application of various measurements in different geoscience issues,covering Earth tidal deformation,oceanic and atmospheric loading effects,earthquake cycle,hydrology,Earth rotation changes,etc.,and provided a precious exchange platform for global peers.

Earthquake, Volcano and Earth Rotation Harmonics

Earthquake prediction is considered impossible for there is no scientific way to find the date and time, the location, and the magnitude of an earthquake. A new idea is introduced in this paper—earth rotation harmonics triggered natural volcano and earthquake. With earth rotation harmonics response model for a location, it could be possible to calculate the earthquake date and time, and the magnitude. Properties of earth rotation harmonics triggered earthquake are discussed and verified with earthquake data from USGS website. Also, both earth tide and ocean tide effects on earthquake are discussed and verified with earthquake data—tides did not trigger the natural earthquake, they only affect the earthquake activities and time.

Remarks about External Forces Acting on Earth’s Rotation Axis

It is well known that a variation in the direction of Earth’s rotation axis is a real astronomical phenomenon, named nutation. It is interesting if a variation of this axis can take place only in intensity, in the simplest theoretical case of only two rigid body dynamics. This paper presents two positions of the Moon during its monthly orbit, where a sudden variation of Earth’s rotation axis in intensity can take place. The duration of this phenomenon is limited in time, maybe an instant or a day, and then a vortex can appear.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

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.

The deforming and rotating Earth——A review of the 18th International Symposium on Geodynamics and Earth Tide,Trieste 2016

The 18th International Symposium on Geodynamics and Earth Tides 2016 covered phenomena that generate temporal variations in geodetic and geophysical observations. In calculating the stress field for Earth tides, the observed geodetic response is used for defining the Earth＇s theology, the Earth internal structure, ＇Earth rotation parameters, and the functioning of the sophisticated instrumentation mounted on Earth and satellites. The instrumentation capable of observing Earth tides, measures changes generated by lithospheric plate movements, as the earthquake cycle and volcanism. Hydrology, tem- perature, and pressure, either of natural or anthropogenic origin, affect the high precision observations, and therefore must be included in this study-realm.

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.

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.

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.

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.

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.

Investigation on variations of apparent stress in the region in and around the rupture volume preceding the occurrence of the 2021 Alaska MW8.2 earthquake

On July 29, 2021, a large earthquake of MW8.2 occurred south of the Alaska Peninsula. To investigate the spatial-temporal changes of crustal stress in the earthquake-stricken area before this event, we selected 159 earthquakes of 4.7 ≤ MW ≤ 6.9 that occurred in the epicentral region and its surroundings between January 1980 and June 2021 to study the temporal variation and spatial distribution of their apparent stress. In addition, we analyzed the correlation between seismic activities and Earth’s rotation and explored the seismogenic process of this earthquake. The crustal stress rose from January 2008 to December 2016. This period was followed by a sub-instability stage from January 2017 until the occurrence of the MW8.2 earthquake. The average rate of apparent stress change in the first five years of the stress increase period was roughly 2.3 times that in the last four years. The lateral distribution of the apparent stress shows that the areas with apparent stress greater than 1.0 MPa exhibited an expanding trend during the seismogenic process. The maximum apparent stress was located at the earthquake epicenter during the last four years. The distribution of the apparent stress in the E-W vertical cross section revealed that an apparent stress gap formed around the hypocenter during the first five years of the stress increase period, surrounded by areas of relatively high apparent stress. After the Alaska earthquake, most parts of this gap were filled in by aftershocks. The seismic activities during the sub-instability stage exhibited a significant correlation with Earth’s rotation.

Earth orientation parameters from VLBI determined with a Kalman filter

This paper introduces the reader to our Kalman filter developed for geodetic VLBI（very long baseline interferometry） data analysis. The focus lies on the EOP（Earth Orientation Parameter） determination based on the Continuous VLBI Campaign 2014（CONT14） data, but also earlier CONT campaigns are analyzed. For validation and comparison purposes we use EOP determined with the classical LSM（least squares method） estimated from the same VLBI data set as the Kalman solution with a daily resolution. To gain higher resolved EOP from LSM we run solutions which yield hourly estimates for polar motion and dUTl = Universal Time（UT1）-Coordinated Universal Time（UTC）. As an external validation data set we use a GPS（Global Positioning System） solution providing hourly polar motion results.Further, we describe our approach for determining the noise driving the Kalman filter. It has to be chosen carefully, since it can lead to a significant degradation of the results. We illustrate this issue in context with the de-correlation of polar motion and nutation.Finally, we find that the agreement with respect to GPS can be improved by up to 50% using our filter compared to the LSM approach, reaching a similar precision than the GPS solution. Especially the power of erroneous high-frequency signals can be reduced dramatically, opening up new possibilities for highfrequency EOP studies and investigations of the models involved in VLBI data analysis.We prove that the Kalman filter is more than on par with the classical least squares method and that it is a valuable alternative, especially on the advent of the VLBI2010 Global Observing System and within the GGOS frame work.

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.

Effects of the Earth’s triaxiality on the polar motion excitations

This study aims to evaluate the significance of the Earth＇ s triaxiality to the polar motion theory. First of all, we compare the polar motion theories for both the triaxial and rotationally-symmetric Earth models, which is established on the basis of the EGM2008 global gravity model and the MHB2000 Earth model. Then, we use the atmospheric and oceanic data （the NCEP/NCAR reanalyses and the ECCO assimulation products） to quantify the triaxiality effect on polar motion excitations. Numerical results imply that triaxiality only cause a small correction （ about 0. 1 - 0. 2 mas） to the geophysical excitations for the rotationally-symmetric case. The triaxiality correction is much smaller than the errors in the atmospheric and oceanic data, and thus can be neglected for recent studies on polar motion excitations.

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.

A new method for resolving phase ambiguity in radio interferometry using Earth rotation synthesis

As a key technique in deep space navigation, radio interferometry can be used to determine the accurate location of a spacecraft in the plane-of-sky by measuring its signal propagation time delay between two remote stations. To improve the measurement accuracy, differential phase delay without phase ambiguity is usually desired. Aiming at the difficulties of resolving phase ambiguity with few stations and narrowband downlink signals, a new method is proposed in this work by taking advantage of the Earth rotation. The high accurate differential phase delay between the spacecraft and a calibrator can be achieved not only in the in-beam observation mode but also in the out-of-beam observation mode. In this paper we firstly built the model of phase ambiguity resolution. Then, main measurement errors of the model are analyzed, which is followed by tests and validations of the model and method using the tracking data of the Cassini mission and Chang'E-3 mission. The results show that the phase ambiguities can be correctly resolved to generate a 10-picosecond level accuracy differential phase delay. Angular measurement accuracy of the Cassini reaches the milli-arc-second level, and the relative position accuracy between the Chang'E-3 rover and lander reaches the meter level.

Contribution of CRUST2. 0 components to the tri-axiality of the Earth and equatorial flattening of the core

Equatorial flattening of the core were previously estimated to be 5 × 10^-4 by using seismically derived density anomaly, and 1. 7748280× 10^-5 by assuming that the ratio of polar flattening to equatorial flattening of the core is the same as that of the whole Earth. In this study, we attempted to explain the difference by applying a density-contrast stripping process to the crust in the second method. We use the CRUST2. 0 model to estimate the inertia-moment contribution resulted from the density-contrast structure in the crust to a tri-axial Earth. The contribution of the density contrast in the crust was removed layer by layer. The layers include topography, bathymetry, ice, soft sediment, hard sediment, upper crust, middle crust, lower crust and the reference crust. For the boundaries of the topography and bathymetry layers, we used ETOPO5 values with a resolution of 5＇. For boundaries of other layers, we used values from the CRUST2. 0 model with a resolution of 2~. After the contribution of density contrast is stripped, the equatorial flattening of the core was found to be 6. 544× 10 ^-5, which is still one order of magnitude smaller than the result given by the first method. This suggests that at least one of the methods is not correct. The influence of the uncertainty in the equatorial flattening of the core on the Free Core Nutation frequency is small, but its effect on the gravitational torque acting on the tri-axial inner core cannot be ignored. So an accurate determination of the equatorial flattening of the core is still necessary.