We first introduce the basic theory of the third-order gradient tensor of the gravitational potential, which is also called the gravitational curvature tensor(GCT). Second, we provide analytic expressions of the third-order gradient tensor of the gravitational potential caused by the homogenous spheroid. Finally, through theoretical analysis and synthetic model tests, we discuss the sensitivity of the source’s parameters(mass, buried depth, horizontal location and geometric shape) on the zero, first, second and third-order gradient tensors of the gravitational potential. Results show that, among the zero, first, second and third-order gradient tensors of the gravitational potential, the third-order gradient tensor of the gravitational potential decays most quickly as the distance between observation point and source increases. Therefore, the GCT has multiple characteristics, such as, highest sensitivity on the buried depth of the source; the best exploration capacity for shallow mass, and on the contrary the worst capacity for deep mass; and the highest sensitivity of the horizontal location of the source. This ability is weakened as the buried depth of the source increases. The type is also the most diverse, indicating that under the same distribution of points, the three-step tensor can capture more field and field source information, especially the short-wave component of the gravity field and the remaining mass of the shallow part.

This paper makes use of mobile gravity observation data of Guangxi and its neighboring regions from 2014 to 2017, systematically analyzing the change in the regional gravity field, as well as its relationship with the July 15, 2017 M_S4.0 earthquake in Nandan, Guangxi. Combined with GPS observation data and investigation results of seismology and geology, it explores the temporal and spatial distribution characteristics and the mechanism of the change in the regional gravity field. The results show that: (1) before and after M_S4.0 earthquake in Nandan, the abnormal change in the gravity near the earthquake area is closely related to the main fracture in space, which reflects the crustal deformation and tectonic activity along controlling earthquake fracture that caused the change in the earth's surface gravity from 2014 to 2017; (2) the dynamic image of the differential scale gravity field better reflects the gravity variation near the epicenter before and after Nandan M_S4.0 earthquake, and it is a system evolution process from “abnormity of local gravity→ characteristic abnormity of four-quadrant distribution→reverse change earthquake-triggering”; (3) gravity change and horizontal motion reflected from GPS observations suggest that Nandan M_S4.0 earthquake is located in the distribution center of gravity four-quadrant and near the peak of surface compression, and this observational fact further supports that the dynamic changes in gravity field and deformation field have implications for the prediction of locations of moderate-strong earthquakes; (4) the area of Tian'e-Nandan-Huanjiang is the most gravitationally-evolving area and it is also a surface compression transition zone of horizontal deformation. At the same time, it is located in Moho surface and other deep-line intensely changing sections, M_L3.0 earthquake encircling area, and abnormal b value area along main fracture. Combined with the images of seismic activities and the comprehensive analysis of observed anomaly of fixed-point precursors, it is considered that there still exist a danger of moderate-strong earthquakes in this area.

Based on the lock in the shearing force model and seismic dislocation theory, we describe the lock in shearing force of the earthquake as an equivalent dislocation. We build the mathematical relationship between lock in shearing force and the surface gravity. Considering the rough-difference interference, we use robust-Bayesian least squares inversion to obtain the parameters of equivalent dislocation. The inversion results show that the seismogenic type is high dip angle strike-slip, and that the seismogenic energy is close to the Yao’an earthquake moment magnitude provided by USGS. It proves that this method can be applied to predict the future focus characteristics and seismogenic magnitude with the four-quadrant gravity image before an earthquake.

Gravity inversion can be used to determine Moho depths in sea regions where we lack adequate seismic information. In this study, the gravity anomaly is used to calculate the Moho depths of the South China Sea and adjacent regions. After isolating the gravity anomaly of Moho depths from the free-air gravity anomalies, the resulting gravity residual is used to invert the Moho depths based on Parker-Oldenburg inversion algorithm. To eliminate the high-frequency oscillations that occured in the inversion process, a cosine filter for gravity data filtering in wave number domain is applied, where smaller and greater frequency parameters are estimated from the energy spectrum of the residual gravity anomaly. The average difference in Moho depths between this study and the seismic measurement results is 1.59 km, the standard deviation is 1.9 km. The results show that the Moho depths in the study regions show the obvious regional tectonic features.

The classical remove-restore theory is improved. We propose a regional gravity field calibration algorithm considering the gradient feature of terrain using EGM2008 (the satellite gravity field model), surface gravity/GPS joint observation data and ASTER digital terrain model. Based on the layout of the dynamic gravity regional network in China, the calibration range of the gravity field is more reasonable. Compared with the classical application of removal-restoration method in western Sichuan, the new calculation shows that the standard removal-restoration method model can reduce the standard deviation of the gravity field model data in western Sichuan from 65.09 mGal to 61.24 mGal, and combined with the impact of the terrain gradient, it can be further reduced to 59.31 mGal. In this paper, 283 gravimetric data recently published by the International Gravity Bureau are used to calibrate the gravitational field in the eastern Himalayan syntaxis and adjacent areas. Through the Bouguer gravity anomaly map, it is obvious that there is a strong positive correlation between the Bouguer gravity anomaly and the terrain distribution; furthermore, there is a clear area of low value isostatic anomalies in the central and eastern parts of the study area.

In using the GRACE filtering process, the traditional de-correlation filtering method presents difficulties in perfectly preserving the real signal and weakening the stripe error at the same time. In order to solve this problem, the paper makes a certain improvement on the filtering method and combined EOF filtering method with de-correlation filtering method. Several experiments are used to filter real GRACE data and simulated data, respectively. The results show that the improved filtering method inherits the advantages of the EOF filtering method and the de-correlation filtering method. The method weakens the influence of the north-south stripe error as much as possible,while preserving the most realistic signal.

Using August 2002 to December 2016 GRACE data, TWS variations are derived after deducting the leakage affect, and temporal spatial variation and change trend are analyzed. Results show that the growth of TWS is 0.13±0.12 cm/a. Areas where TWS significantly changed have more leakage influence. For example, after correction, in the Three Gorges Reservoir TWS increased from about 10 to 15-20 mm/a, presenting a greater spatial heterogeneity. In addition, the Yangtze River basin water cycle changes are closely studied using a variety of meteorological data thorough angles of weather impact and human activity. Precipitation and TWS have high correlation, TWS delaying 1 to 2 months. Whereas in the upstream source, temperature is the dominant factor, increasing trends of which have been accelerating melting glaciers, leading to an increasing trend of TWS. The Three Gorges project increased TWS. ENSO phenomena are another significant factor influencing TWS in the Yangtze River basin.

We are concerned with the difficulty of constant temperature measurement in the assembly site, which has a great influence on distance measurement. In this paper, a correction method for laser tracker segmented integral distance measurement is advanced, and the correction model of segmented integral distance measurement is established. Through the single line temperature ranging correction experiment, based on radian laser tracker, the experimental results show that the method can effectively reduce the influence of temperature gradient, provide theoretical support for the temperature gradient correction of the assembly site, and help to improve the accuracy of aircraft and other assembly and manufacturing.

In this paper, the recent progress of lunar laser ranging (LLR) is introduced briefly, including the establishment of facility, lunar orbit, and lunar exploration with multiple data sources. The observable of LLR is the round-trip travel time of laser pulses between stations on the earth and passive reflectors on the moon. LLR can help us fully understand the earth-moon system and has many applications. The next generation of retro-reflector will improve the accuracy of LLR measurements and improve the science by one to two orders of magnitude. Yunnan observatory of CAS has successfully received laser photons returned recently, becoming the first laser station with the capacity of lunar laser ranging in China. The accuracy of the lunar orbit can benefit from the increasing number of LLR stations. The technology of lunar exploration is increasing. The combination of multiple data will result in a better and more comprehensive understanding of the moon.

We study the influence of pseudo-stochastic pulse in the absorption of low earth orbit (LEO) satellites and the unmodeled perturbation forces of four navigation systems. We also analyze the influence of accuracy on fitting orbit. The results show that pseudo-stochastic pulse can effectively absorb the unmodeled perturbation forces of LEO and GNSS satellites. For LEO satellites, pseudo-stochastic pulse can simulate the influence of atmospheric resistance on orbit, and achieve millimeter level fitting precision. For GNSS satellites, pseudo-stochastic pulse can only absorb sun light pressure perturbation to some extent; however, combined with the ECOM sun light model it can fully absorb perturbation forces unabsorbed by the ECOM model and achieve millimeter level fitting precision, requiring setting up a set of pseudo-stochastic pulse parameters every day.

In this paper, based on kinematic method and reduced-dynamic method, using on-board GPS observation data, the precise orbits of SWARM are implemented. The orbit accuracy is assessed using the post-scientific orbit released by ESA. The results show that the seven-day average RMS values of radial, along-track and cross-track directions of kinematic orbits are all less than 3 cm, and the accuracy of orbit determination reaches the centimeter level. The radial RMS of reduced-dynamic orbits is about 0.65 cm and the along-track and cross-track directions are about 1.3 cm, which are better than expected. In addition, the fast orbital precision of SWARM, based on fast ephemeris released by IGS, is approximately equal to that of precise orbit determination. However, in the near real-time orbit determination of SWARM satellite, the 3D-RMS of kinematic orbit determined by ultra-fast ephemeris is 9.68 cm, and the 3D-RMS of reduced-dynamic orbit is 3.61 cm. The accuracy of the orbit is lower than the fast ephemeris results.

As the service capabilities of the GPS system has improved steadily, and with the increasing demand for real-time positioning service, real-time satellite clock products are gaining more attention by experts and scholars in relevant fields. In this paper, we implement real-time GPS satellite clock offset estimation based on a modified mixed-differenced algorithm. The realization of this method consists of four steps, which can generate final real-time satellite clock offset products for users. The real-time clock product of GPS satellites is solved using real-time stream data from 68 globally distributed stations. For the generated real-time GPS satellite clock products from Jan 14 to Jan 19, 2018, two ways are used to evaluate the products: first, comparing with the IGS rapid clock offset products; and second, applying the products in real-time kinematic PPP. We verify that the real-time clock product based on the modified mixed-differenced algorithm can reach accuracy of about STD 0.15 ns, RMS 0.63 ns. It can provide real-time centimeter-level positioning service.

The paper analyzes the noise characteristics of GNSS short baseline time series for 5 years, finds the long periodic noise components(random walk noise), selects the optimal noise model and evaluates the effect of the different noise models on estimation of periodic amplitude and linear velocity. The results show that short baseline time series in colored noise should consider the flicker noise and random walk noise. Furthermore, the random walk noise component may be related to the real motion measurement of the station. It is assumed that there is a 0.4-0.6 mm/a deviation between the velocity estimation obtained from white noise and the velocity estimation obtained under the optimal noise model, while the effect on periodic amplitude can be ignored.

Tropospheric delay is one of the main errors in space geodetic techniques, and it must be correctly mitigated. In this paper, the radiosonde data are used to analyze the applicability of the grid tropospheric models GPT2w, IGGtrop, and GTPs in China. The results show that the GPT2w model and the IGGtrop model have accuracy of about 4.0-4.2 cm near the ground. The models’ performance in the western region is better than that in the eastern region, and the worst accuracy is found in the southeast. The accuracy in summer is obviously lower than that in winter. The GPT2w model version with lower spatial resolution may produce abnormal deviations in the middle and western regions. The GPT2w model clearly has systematic deviations, positive in the middle and western parts and negative in the southeast part. The accuracy of IGGtrop model is much higher than GPT2w model at heights above 3 km and remains stable with the increasing height. In addition, IGGtrop model is recommended to correct ZTD errors in aircraft positioning navigation. The temporal resolution of GTPs model is higher than empirical models, which results in higher accuracy, especially for the southeast region with variable humidity. However, it is unable to apply GTPs model in some areas due to insufficient GNSS data, which are used to update GTPs model. By analyzing the accuracy of different tropospheric models in China, this study provides a reference for users in China region.

In this paper we aim to solve the problem that the traditional iterative closet point algorithm is not robust. Using the iterative closet point registration residuals law, the M-estimators and selecting weight iteration, an improved iterative closet point registration algorithm based on the weight of the point cloud is provided. In order to achieve protection against gross errors, using the residuals for each point on the registration calculation to calculate the corresponding initial weight, we use iteration method with variable weights to calculate suitable weight on the basis of additional points of weights. The experimental results indicate that proposed iteration method is capable of improving the effect of registration, and the improved algorithm is suitable for the registration of point cloud with gross errors.

On March 11,2011, an earthquake of magnitude of 9.0 occurred at Japan. Earth’s free oscillation and teleseismic surface waves caused by this earthquake are recorded by both tiltermeters and seismometers in Yunnan province, China. Some low-frequency signals, which are out of the seismometer’s pass-band, appear in seismic data and cannot be easily interpreted by classic seismological theory. By assuming the trigger signals as translation motion and tilt motion individually, the records of seismometer are simulated by a mathematic seismometer model. We argue that the signal out of the seismometer’s pass-band recorded at Eryuan station, of which the period is 390 s(6.5 min), is the response of seismometer to tilt motion, not to translating motion.

This study makes full use of the surface wave and the primary wave information from the shallow reflection seismic data. We use the method of MASW to obtain the shallow shear wave velocity structure, and use first break travel-time tomography technology to obtain the P-wave velocity structure. Then, we get the velocity ratio and the poisson ratio data. Combined with the reflection wave stack section and the cross-fault borehole profile, the shallow strata are comprehensively interpreted. To some extent, our method compensates for the missing shallow reflection information, and plays a very important role for determining location and nature of the shallow faults.

The paper analyses the principle of tilt sensor’s zero compensation and sensitivity adjustment according to adjusting procedures of the CG-5 gravimeter tilt sensor parameters. An experiment is performed to verify the principle. The results show that the principle analyzed in this paper is correct. Then, a basis for adjusting tolerance of the tilt sensor parameters is proposed. The principle analysis will be helpful for mastering the CG-5 gravimeter. Furthermore, it is useful for optimizing the instrument and secondary development.

By analyzing the relationship between gravity measurement accuracy and the tilt angle of the levitation system and the height of the supporting leg, and by considering the heavy weight of the supporting leg and the high precision of the displacement adjustment, we adopt a design of high precision electric cylinder driven by the AC servo motor servicing as support leg. By producing the support leg leveling system and doing a leveling experiment, the tilt measurement accuracy is 0.002°, the minimum displacement adjustment is as small as 2.5 μm, the smallest tilt angle position is found, the gravimeter leveling function is realized, and the relationship between gravity accuracy and tilt angle is verified. The experimental results provide a reference for the leveling work and high-precision gravity measurement of SG.