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 contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth＇s gravitational field measured from the gravity field and steady-state ocean circulation explorer（GOCE）,up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry（SGG） are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth＇s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth＇s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.

Process Analysis of In-situ Strain during the M_s8.0 Wenchuan Earthquake—Data from the Stress Monitoring Station at Shandan

There were huge life and property losses during the Ms8.0 Wenchuan earthquake on May 12, 2008. Strain fluctuation curves were completely recorded at stress observatory stations in the Qinghai-Tibet plateau and its surroundings in the process of the earthquake. This paper introduces the geological background of the Wenchuan earthquake and the profile of in-situ stress monitoring stations. In particular, data of 174 earthquakes （Ms4.0-Ms8.5） were processed and analyzed with various methods, which were recorded at the Shandan station from August 2007 to December 2008. The results were compared with other seismic data, and further analyses were done for the recoded strain seismic waves, co-seismic strain stepovers, pre-earthquake strain valleys, Earth＇s free oscillations before and after the earthquake and their physical implications. During the Wenchuan earthquake, the strainmeter recorded a huge extensional strain of 70 seconds, which shows that the Wenchuan earthquake is a rupture process predominated by thrusting. Significant precursory strain anomalies were detected 48 hours, 30 hours, 8 hours and 37 minutes before the earthquake. The anomalies are very high and their forms are very similar to that of the main shock. Similar anomalies can also be found in strain curves of other shocks greater than Ms7.0, indicating that such anomalies are prevalent before a great earthquake. In this paper, it is shown that medium aftershocks （Ms5.5- 6.0） can also cause Earth＇s free oscillations. Study of free oscillations is of great significance to understand the internal structure of the Earth and focal mechanisms of earthquakes and to recognize slow shocks, thus providing a scientific basis for the prevention and treatment of geological disasters and the prediction of future earthquakes.

A rapid compensation method for launch data of long-range rockets under influence of the Earth＇s disturbing gravity field

Regarding the rapid compensation of the influence of the Earth＇ s disturbing gravity field upon trajectory calculation,the key point lies in how to derive the analytical solutions to the partial derivatives of the state of burnout point with respect to the launch data.In view of this,this paper mainly expounds on two issues：one is based on the approximate analytical solution to the motion equation for the vacuum flight section of a long-range rocket,deriving the analytical solutions to the partial derivatives of the state of burnout point with respect to the changing rate of the finalstage pitch program;the other is based on the initial positioning and orientation error propagation mechanism,proposing the analytical calculation formula for the partial derivatives of the state of burnout point with respect to the launch azimuth.The calculation results of correction data are simulated and verified under different circumstances.The simulation results are as follows：（1） the accuracy of approximation between the analytical solutions and the results attained via the difference method is higher than 90%,and the ratio of calculation time between them is lower than 0.2%,thus demonstrating the accuracy of calculation of data corrections and advantages in calculation speed;（2） after the analytical solutions are compensated,the longitudinal landing deviation of the rocket is less than 20 m and the lateral landing deviation of the rocket is less than 10 m,demonstrating that the corrected data can meet the requirements for the hit accuracy of a long-range rocket.

Evidences of the expanding Earth from space-geodetic data over solid land and sea level rise in recent two decades

According to the space-geodetic data recorded at globally distributed stations over solid land spanning a period of more than 20-years under the International Terrestrial Reference Frame 2008,our previous estimate of the average-weighted vertical variation of the Earth＇s solid surface suggests that the Earth＇s solid part is expanding at a rate of 0.24 ± 0.05 mm/a in recent two decades.In another aspect,the satellite altimetry observations spanning recent two decades demonstrate the sea level rise（SLR） rate 3.2 ± 0.4 mm/a,of which1.8 ± 0.5 mm/a is contributed by the ice melting over land.This study shows that the oceanic thermal expansion is 1.0 ± 0.1 mm/a due to the temperature increase in recent half century,which coincides with the estimate provided by previous authors.The SLR observation by altimetry is not balanced by the ice melting and thermal expansion,which is an open problem before this study.However,in this study we infer that the oceanic part of the Earth is expanding at a rate about 0.4 mm/a.Combining the expansion rates of land part and oceanic part,we conclude that the Earth is expanding at a rate of 0.35 ± 0.47 mm/a in recent two decades.If the Earth expands at this rate,then the altimetry-observed SLR can be well explained.

Uncertainty analysis of atmospheric friction torque on the solid Earth

The wind stress acquired from European Centre for Medium-Range Weather Forecasts （ECMWF）, National Centers for Environmental Prediction （NCEP） climate models and QSCAT satellite observations are analyzed by using frequency-wavenumber spectrum method. The spectrum of two climate models, i.e., ECMWF and NCEP, is similar for both 10 m wind data and model output wind stress data, which indicates that both the climate models capture the key feature of wind stress. While the QSCAT wind stress data shows the similar characteristics with the two climate models in both spectrum domain and the spatial distribution, but with a factor of approximately 1.25 times larger than that of climate models in energy. These differences show the uncertainty in the different wind stress products, which inevitably cause the atmospheric faction torque uncertainties on solid Earth with a 60% departure in annual amplitude, and furtherly affect the precise estimation of the Earth＇s rotation.

Anomalous Nuclear Reaction in Earth’s Interior:a New Field in Physics Science?

Tritium （3^H） in excess of the atmospheric values was found at volcanic Lakes Pavin （France）, Laacher （Germany） and Nemrut （Turkey）, as well as Kilauea Volcano at Hawaii （USA） and other volcanoes. Because 3^H has a short half-life of 12.3 years, the tritium and the resulting 3^He must have formed recently in the Earth. The result suggests that nuclear reactions may generate a significant amount of tritium in the interior of the Earth, although we have not yet learned what the reaction mechanism may be responsible. The nuclear reaction that can be responsible for tritium production in the Earth is probably a new research field in physics science. Nuclear reactions that generate tritium might be a source of ＂missing＂ energy （heat） in the interior of the Earth. Finding in-situ 3^H in the mantle may exhibit an alternative explanation of 3^He origin in the deep Earth.

Spheroidal oscillations of the Earth stimulated by the Sumatra-Andaman earthquake with CDSN data

The 0S2-0S54 spheroidal modes of Earth＇s free oscillations, triggered by the great Sumatra-Andaman earthquake of 26 December 2004 are retrieved from VHZ data recorded by seven upgraded stations of China Digital Seismograph Network （CDSN）. We compare these spheroidal modes with theoretical free oscillation spectra calculated from the Preliminary Reference Earth Model （PREM） and find a coincidence between their periods. Spectral splitting phenomenon is observed obviously in 0S2, 0S3, 0S4, 2S1 and 1S2 free oscillation modes. What is most noticeable is that the oscillation mode 2S1 is reported for the second time （the first time by Rosat et al） without any data stacking. We simulated the split singlet of 0S2 mode on seven CDSN stations based on general focal mechanism and seismic moment of the earthquake. The result shows that seismic moment of the earthquake can reach 10^23 N.m. We also find that the recording of Earth＇s free oscillations carries abundant information of source mechanism and earthquake location, which is applicable to the detailed study of source rupture parameters.

The principal moments of inertia calculated with the hydrostatic equilibrium figure of the Earth

As an indication of the Earth＇s mass distribution, the principal moments of inertia （PMOI, i.e., A, B, C） of the Earth are the basic parameters in studies of the global dynamics of the earth, like earth nutation, and the geophysics. From the aspect of observation, the PMOI can be calculated from the spherical coefficients of observed gravity field. In this paper, the PMOI are calculated directly according to its definition with the figures of the Earth＇s interior derived by a generalized theory of the hydrostatic equilibrium figure of the Earth. We obtain that the angle between the principal axis of the maximum moment of PMOI and the rotational axis is 0.184~, which means that the other two principal axes are very closely in the equatorial plane. Meanwhile, B-A is 1.60 x 10-5 MR2, and the global dynamical flattening （H） is calculated to be 3.29587 ~ 10-3, which is 0.67% different from the latest observation derived value Hobs（3.273795 × 10 ^-3） （Petit and Luzum, 2010）, and this is a significant improvement from the 1.1% difference between the value of H derived from traditional theories of the figure of the Earth and the value of Hobs. It shows that we can calculate the PMOI and H with an appropriate accuracy by a gener- alized theory of the hydrostatic equilibrium figure of the Earth.

Effect of different inter-satellite range on measurement precision of Earth’s gravitational field from GRACE

The precision of Earth＇s gravitational field from GRACE up to degree and order 120 was studied for different inter-satellite ranges using the improved energy conservation principle. Our simulated result shows that： For long wavelength （L≤20） at degree 20, the cumulative geoid-height error gradually decreased with increasing range, from 0. 052 cm for 110 km to 1. 156 times and 1. 209 times as large for 220 km and 330 kin, respectively. For medium-wavelength （ 100 ≤ L ≤ 120） at degree 120, the cumulative geoid-height error de- creased from 13. 052 cm for 110 km, to 1. 327 times and 1. 970 times as large for the ranges of 220 km and 330 km, respectively; By adopting an optimal range of 220 ± 50 km, we can suppress considerably the loss of precision in the measurement of the Earth＇ s long-wavelength and medium-wavelength gravitational field.

Construction of Earth's gravitational field model from CHAMP,GRACE and GOCE data

The basic principle of spectral combination method is discussed,and the general expressions of the spectral weight and spectral combination of the united-processing of various types of gravimetric data are shown.What＇s more,based on degree error RMS of potential coefficients,the detailed expressions of spectral combination formulae and the corresponding spectral weights in the Earth＇s gravitational field model（EGM） determination using GOCE ＋ GRACE and CHAMP ＋ GRACE ＋ GOCE are derived.The fundamental situation that ulux-champ2013 s,tongji-GRACE01,go-cons-gcf-2-tim-r5 constructed respectively by CHAMP,GRACE,GOCE data and go-cons-gcf-2-dir-r5 constructed by syncretic processing of GRACE,GOCE and LAGEOS data are explained briefly,the degree error RMS,cumulative geoid height error and cumulative gravity anomaly error of these models are calculated.A syncretic model constructed from CHAMP,GRACE and GOCE data,which is expressed by champ ＋ grace ＋ goce,is obtained based on spectral combination method.Experimentation results show that the precision of CHAMP data model is the lowest in satellite-only models,so it is not needed in the determination of syncretic models.The GRACE data model can improve the GOCE data model in medium-long wavelength,so the overall precision of syncretic model can be improved.Consequently,as many types of gravimetric data as possible should be combined together in the data processing in order to strengthen the quality and reliability with widening scope and improve the precision and spatial resolution of the computational results.

Calculation of passive earth pressure of cohesive soil based on Culmann's method

Based on the sliding plane hypothesis of Coulumb earth pressure theory, a new method for calculation of the passive earth pressure of cohesive soil was constructed with Culmann＇s graphical construction. The influences of the cohesive force, adhesive force, and the fill surface form were considered in this method. In order to obtain the passive earth pressure and sliding plane angle, a program based on the sliding surface assumption was developed with the VB.NET programming language. The calculated results from this method were basically the same as those from the Rankine theory and Coulumb theory formulas. This method is conceptually clear, and the corresponding formulas given in this paper are simple and convenient for application when the fill surface form is complex.

Discovering Crustal Deformation Bands by Processing Regional Gravity Field

Objectives： This article presents a new computational procedure to discover scratches buried in the earth＇s crust. We also validate this new interdisciplinary analysis method with regional gravity data located in a well-known Dabie orogenic zone for test. Methods： Based on the scratch analysis method evolved with mathematical morphology of surfaces, we present a procedure that extracts information of the crustal scratches from regional gravity data. Because the crustal scratches are positively and highly correlated to crustal deformation bands, it can be used for delineation of the crustal deformation belts. The scratches can be quantitatively characterized by calculation of the ridge coefficient function, whose high value traces delineate the deformation bands hidden in the regional gravity field. In addition, because the degree of crustal deformation is an important indicator of tectonic unit divisions, so the crust can be further divided according to the degree of crustal deformation into some tectonic units by using the ridge coefficient data, providing an objective base map for earth scientists to build tectonic models with quantitative evidence. Results： After the ridge coefficients are calculated, we can further enhance the boundary of high ridge-coefficient blocks, resulting in the so-called ridge-edge coefficient function. The high-value ridge-edge coefficients are well correlated with the edge faults of tectonic units underlay, providing accurate positioning of the base map for compilation of regional tectonic maps. In order to validate this new interdisciplinary analysis method, we select the Dabie orogenic zone as a pilot area for test, where rock outcrops are well exposed on the surface and detailed geological and geophysical surveys have been carried out. Tests show that the deformation bands and the tectonic units, which are conformed by tectonic scientists based on surface observations, are clearly displayed on the ridge and ridge-edge coefficient images obtained in this article. Moreover, these computer-generated images provide more accurate locations and geometric details. Conclusions： This work demonstrates that application of modern mathematical tools can promote the quantitative degree in research of modern geosciences, helping to open a door to develop a new branch of mathematical tectonics.

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

Development and calibration of the Moon-based EUV camera for Chang'e-3

The process of development and calibration for the first Moon-based ex- treme ultraviolet （EUV） camera to observe Earth＇s plasmasphere is introduced and the design, test and calibration results are presented. The EUV camera is composed of a multilayer film mirror, a thin film filter, a photon-counting imaging detector, a mech- anism that can adjust the direction in two dimensions, a protective cover, an electronic unit and a thermal control unit. The center wavelength of the EUV camera is 30.2 nm with a bandwidth of 4.6nm. The field of view is 14.7° with an angular resolution of 0.08°, and the sensitivity of the camera is 0.11 count s-1 Rayleigh-1. The geomet- ric calibration, the absolute photometric calibration and the relative photometric cal- ibration are carried out under different temperatures before launch to obtain a matrix that can correct geometric distortion and a matrix for relative photometric correction, which are used for in-orbit correction of the images to ensure their accuracy.

Retrieval of Outgoing Longwave Radiation from COMS Narrowband Infrared Imagery

Hourly outgoing longwave radiation （OLR） from the geostationary satellite Communication Oceanography Meteorological Satellite （COMS） has been retrieved since June 2010.The COMS OLR retrieval algorithms are based on regression analyses of radiative transfer simulations for spectral functions of COMS infrared channels.This study documents the accuracies of OLRs for future climate applications by making an intercomparison of four OLRs from one single-channel algorithm （OLR12.0 using the 12.0 μm channel） and three multiple-channel algorithms （OLR10.8＋12.0 using the 10.8 and 12.0 pm channels; OLR6.7＋10.8 using the 6.7 and 10.8 μm channels; and OLRAll using the 6.7,10.8,and 12.0 μm channels）.The COMS OLRs from these algorithms were validated with direct measurements of OLR from a broadband radiometer of the Clouds and Earth＇s Radiant Energy System （CERES） over the full COMS field of view [roughly （50°S-50°N,70°-170°E）] during April 2011.Validation results show that the root-mean-square errors of COMS OLRs are 5-7 W m-2,which indicates good agreement with CERES OLR over the vast domain.OLR6.7＋10.8 and OLRAll have much smaller errors （～ 6 W m-2） than OLR12.0 and OLR10.8＋12.0 （～ 8 W m-2）.Moreover,the small errors of OLR6.7＋10.8 and OLRAll are systematic and can be readily reduced through additional mean bias correction and/or radiance calibration.These results indicate a noteworthy role of the 6.7 μm water vapor absorption channel in improving the accuracy of the OLRs.The dependence of the accuracy of COMS OLRs on various surface,atmospheric,and observational conditions is also discussed.

Multichannel singular spectrum analysis of the axial atmospheric angular momentum

Earth＇s variable rotation is mainly produced by the variability of the AAM（atmospheric angular momentum）. In particular, the axial AAM component X_3, which undergoes especially strong variations,induces changes in the Earth＇s rotation rate. In this study we analysed maps of regional input into the effective axial AAM from 1948 through 2011 from NCEP/NCAR reanalysis. Global zonal circulation patterns related to the LOD（length of day） were described. We applied MSSA（Multichannel Singular Spectrum Analysis） jointly to the mass and motion components of AAM, which allowed us to extract annual, semiannual, 4-mo nth, quasi-biennial, 5-year, and low-frequency oscillations. PCs（Principal components） strongly related to ENSO（El Nino southern oscillation） were released. They can be used to study ENSO-induced changes in pressure and wind fields and their coupling to LOD. The PCs describing the trends have captured slow atmospheric circulation changes possibly related to climate variability.

Atmospheric and Oceanic Excitations to LOD Change on Quasi-biennial Tune Scales

We use wavelet transform to study the time series of the Earth＇s rotation rate （length-of-day, LOD）, the axial components of atmospheric angular momentum （AAM） and oceanic angular momentum （OAM） in the period 1962-2005, and discuss the quasi-biennial oscillations （QBO） of LOD change. The results show that the QBO of LOD change varies remarkably in amplitude and phase. It was weak before 1978, then became much stronger and reached maximum values during the strong El Nino events in around 1983 and 1997. Results from analyzing the axial AAM indicate that the QBO signals in axial AAM are extremely consistent with the QBOs of LOD change. During 1963-2003, the QBO variance in the axial AAM can explain about 99.0% of that of the LOD, in other words, all QBO signals of LOD change are almost excited by the axial AAM, while the weak QBO signals of the axial OAM are quite different from those of the LOD and the axial AAM in both time-dependent characteristics and magnitudes. The combined effects of the axial AAM and OAM can explain about 99.1% of the variance of QBO in LOD change during this period.

Synthetic tidal parameters for gravity over China and its neighbor area

The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are constructed with Earth＇s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model as well as tidal data over China seas. The comparison between synthetic parameters and ones observed by spring gravimeters at some seismic network stations and Hong Kong station and one observed by super-conducting gravimeter at Wuhan station shows that the average differences in amplitude factors and phases are smaller than 0.005 and 0.5° respectively; and that the discrepancies between observational and synthetic parameters are dependent on gravimetric technique in that the synthetic parameters are in well agreement with the superconducting gravimetric observations. This also indicates that the synthetic result is a good estimation for tidal gravity, and the numerical results in the present paper not only can provide ground and space gravimetry such as absolute gravimetry with correction model of tidal gravity, but also provide effective tidal parameters over areas where no observation is carried out.

Dust acoustic shock waves in magnetized dusty plasma

We have presented a theoretical study of the dust acoustic （DA） shock structures in a magnetized, electron depleted dusty plasma in the presence of two temperature superthermal ions. By deriving a Korteweg-de Vries-Burgers equation and studying its shock solution, we aim to highlight the effects of magnetic field and obliqueness on various properties of the DA shock structures in the presence of kappa-distributed two temperature ion population. The present model is motivated by the observations of Geotail spacecraft in the Earth＇s magnetotail and it is seen that the different physical parameters such as superthermality of the cold and hot ions, the cold to hot ion temperature ratio, the magnetic field strength, obliqueness and the dust kinematic viscosity greatly influence the dynamics of the shock structures so formed. The results suggest that the variation of superthermalities of the cold and hot ions have contrasting effects on both positive and negative polarity shock structures. Moreover, it is noted that the presence of the ambient magnetic field affects the dispersive properties of the medium and tends to make the shock structures less wide and more abrupt. The findings of present investigation may be useful in understanding the dynamics of shock waves in dusty plasma environments containing two temperature ions where the electrons are significantly depleted.