Micro-Gal level gravity measurements with cold atom interferometry

Developments of the micro-Gal level gravimeter based on atom interferometry are reviewed, and the recent progress and results of our group are also presented. Atom interferometric gravimeters have shown high resolution and accuracy for gravity measurements. This kind of quantum sensor has excited world-wide interest for both practical applications and fundamental research.

Long-term gravity changes in Chinese mainland from GRACE and ground-based gravity measurements

A long-term （9 years） gravity change in Chinese mainland is obtained on the basis of observation of the ground-based national gravity network. The result shows several features that may be related to sore, large-scale groundwater pumping in North China, glacier-water flow and storage in Tianshan region, and pre seismic gravity changes of the 2008 MsS. 0 Wenchuan earthquake, which are spatially similar to co-seismi, changes but reversed in sign. These features are also shown in the result of the satellite-based GRACE obser vation, after a height effect is corrected with GPS data.

A new high-precision gravity solid tidal model for Precision Gravity Measurement Facility

It is significant for establishing gravity datum to construct precise gravity solid tidal model,A simple method with relatively low performance is to interpolate tidal parameters from the global gravity solid tide models.A competitive approach is to determine local gravity solid tidal model by harmonic analysis using long-time serial gravity observations.In this paper a new high-precision gravity solid tidal model for Precision Gravity Measurement Facility is estimated from two co-site gravimeters in the cave laboratory using modern international standard data processing techniques,whose accuracy is evaluated further by comparing with previous publications.The results show that:(1)the determined gravity solid tidal models from two co-site gravimeters are in good agreement with each other,of which the maximum differences for amplitude factors and phase delays don’t exceed 0.01700%and 2.50990°,respectively.(2)the performance of the obtained gravity solid tidal model is 0.00411 for amplitude factors and 0.24120°for phase delays,which is a little better than that of previous publications using superconducting gravity data from Wuhan station.(3)our results and methods are corrective and effective.(4)our model is tiny different from that provided by Wuhan station,which implies that it is necessary to construct a gravity solid tidal model for Precision Gravity Measurement Facility,rather than just adopting existing models at Wuhan station.Our results are helpful in realizing the goal of Precision Gravity Measurement Facility.

Interpretation of Geological and Gravity Data from the Bamiléké Plateau (West-Cameroon): Implication for the Understanding of Its Underground Lithotectonic Geometry

The Bamiléké Plateau represents a key domain in the understanding of the geodynamics associated with the central Cameroon shear. The study aimed to highlight the subsurface architecture of the plateaus basement setting with focus on high potential areas for hydrogeological and mining development projects. To this end, geological field observations were carried out. Since the structures sought were near-surface, a separation approach based on the upward continuation method was applied to the Bouguer anomaly grid. A set of processing techniques, including vertical derivative or DZ, analytical signal or SA and categorization of gravity signatures, was applied to generate the residual map. The synthesis geological model, obtained from analysis and interpretation of the various transformed maps and 2.5D modeling of two gravity profiles P1 and P2 highlights the following features: 1) intrusions of steep-sided granitic batholiths from Dschang to Bandjoun (profile P1), increasing in width from NW (Dschang) to SE (Bandjoun);2) larger volume batholiths with moderate sides located at Bafang and Bangangté (profile P1). These plutonic massifs were weakened by brittle deformation, which favored the emplacement of phonolite or anorthosite dykes within them. The emplacement of these dykes was accompanied by compressional faults with high dip between Dschang and Bandjoun and extensional faults with medium dip between Bafang and Bangangté. These fault zones (trending N85E to N95E) are ideal for hydrogeological investigations in a basement setting, as well as a series of dyke networks that could potentially be preferred zones for the circulation and accumulation of useful substances. The resulting geological sections P1 and P2 highlight the influence of granitic intrusions in the geological system of the study area, as well as the structural control associated with the various dyke intrusions. All the models obtained can serve as fundamental references for hydrogeological and mining exploration project on the Bamiléké Plateau.

Determination of the degree 120 time-variable gravity field in the Sichuan-Yunnan region using Slepian functions and terrestrial measurements

The terrestrial time-variable gravity measurements are characterized by a high signal-to-noise ratio and sensitivity to the sources of mass change in the Earth's crust.These gravity data have many applications,such as surface deformation,groundwater storage changes,and mass migration before and after earthquakes.Based on repeated terrestrial gravity measurements at 198 gravity stations in the Sichuan-Yunnan region(SYR)from 2015 to 2017,we determine a time series of degree 120 gravity fields using the localized spherical harmonic(Slepian)basis functions.Our results show that adopting the first 6 Slepian basis functions is sufficient for effective localized Slepian modeling in the SYR.The differences between two gravity campaigns at the same time of year show an obvious correlation with tectonic features.The degree 120 timevariable gravity models presented in this paper will benefit the study of the regional mass migration inside the crust of the SYR and supplement the existing geophysical models for the China Seismic Experimental Site.

Coseismic gravity and displacement changes of Japan Tohoku earthquake(Mw 9.0)

The greatest earthquake in the modern history of Japan and probably the fourth greatest in the last 100 years in the world occurred on March 11, 2011 off the Pacific coast of Tohoku.Large tsunami and ground motions caused severe damage in wide areas, particularly many towns along the Pacific coast. So far, gravity change caused by such a great earthquake has been reported for the 1964 Alaska and the 2010 Maule events. However, the spatial-temporal resolution of the gravity data for these cases is insufficient to depict a co-seismic gravity field variation in a spatial scale of a plate subduction zone. Here, we report an unequivocal co-seismic gravity change over the Japanese Island, obtained from a hybrid gravity observation（combined absolute and relative gravity measurements）. The time interval of the observation before and after the earthquake is within 1 year at almost all the observed sites, including 13 absolute and 16 relative measurement sites, which deduced tectonic and environmental contributions to the gravity change. The observed gravity agrees well with the result calculated by a dislocation theory based on a self-gravitating and layered spherical earth model. In this computation, a co-seismic slip distribution is determined by an inversion of Global Positioning System（GPS） data. Of particular interest is that the observed gravity change in some area is negative where a remarkable subsidence is observed by GPS, which can not be explained by simple vertical movement of the crust. This indicated that the mass redistribution in the underground affects the gravity change. This result supports the result that Gravity Recovery and Climate Experiment（GRACE） satellites detected a crustal dilatation due to the 2004 Sumatra earthquake by the terrestrial observation with a higher spatial and temporal resolution.

PRECISE LEVELING OF THE VERY LONG QINLING MOUNTAIN TUNNEL

The Qinling tunnel with length of 18. 488km is located on the railway line from Xi’ an (Shanxi Province) to Ankan (Sichuan Province) in the middle of Qinling moun- tain. It is the longest double track railway tunnel in China and takes the third place in the world. According to the design, the break-through error in vertical direction caused by the al- timetric control surveying is limited to 18mm for the case of one piercing face. Because the leveling route reaches over 120km in length and must go over two mountains in 2 800m height, the first-order precise leveling and precise gravity measurement should be carried out in the construction stage. In this paper the field leveling approach, the application of new technology,some experience as well as the office calculation with final results analysis are in- troduced. By meticulous planning, organization and observation, the final accuracy of vertical difference between two tunnel end points is only 8mm, and it provides reliable surveying guarantee for this great tunnel engineering. Finally it is pointed out that this vertical differ- ence distinguishes obviously from the primary measurement result as high as 114mm. It means that the primary result is not accurate enough.

A new ellipse fitting method of the minimum differential-mode noise in the atom interference gravimeter

Ellipse fitting is a useful tool to obtain the differential signal of two atom interference gravimeters. The quality standard of ellipse fitting should be the deviation between the true phase and the fitting phase of the interference fringe. In this paper, we present a new algorithm to fit the ellipse. The algorithm is to minimize the differential noise of two interference gravimeters and obtain a more accurate value of the gravity gradient. We have theoretically derived the expression of the differential-mode noise and implemented the ellipse fitting in the program. This new algorithm is also compared with the classical methods.

Improve the performance of interferometer with ultra-cold atoms

Ultra-cold atoms provide ideal platforms for interferometry.The macroscopic matter-wave property of ultra-cold atoms leads to large coherent length and long coherent time,which enable high accuracy and sensitivity to measurement.Here,we review our efforts to improve the performance of the interferometer.We demonstrate a shortcut method for manipulating ultra-cold atoms in an optical lattice.Compared with traditional ones,this shortcut method can reduce the manipulation time by up to three orders of magnitude.We construct a matter-wave Ramsey interferometer for trapped motional quantum states and significantly increase its coherence time by one order of magnitude with an echo technique based on this method.Efforts have also been made to enhance the resolution by multimode scheme.Application of a noise-resilient multi-component interferometer shows that increasing the number of paths could sharpen the peaks in the time-domain interference fringes,which leads to a resolution nearly twice compared with that of a conventional double-path two-mode interferometer.With the shortcut method mentioned above,improvement of the momentum resolution could also be fulfilled,which leads to atomic momentum patterns less than 0.6hkL. To identify and remove systematic noises,we introduce the methods based on the principal component analysis (PCA) that reduce the noise in detection close to the 1/√2 of the photon-shot noise and separate and identify or even eliminate noises.Furthermore,we give a proposal to measure precisely the local gravity acceleration within a few centimeters based on our study of ultracold atoms in precision measurements.

On all-propulsion design of integrated orbit and attitude control for inner-formation gravity field measurement satellite

The inner-formation gravity field measurement satellite （IFS） is a novel pure gravitational orbiter. It aims to measure the Earth＇s gravity field with unprecedented accuracy and spatial resolution by means of precise orbit determination （POD） and relative state measurement. One of the key factors determining the measurement level is the outer-satellite control used for keeping the inner-satellite flying in a pure gravitational orbit stably. In this paper the integrated orbit and attitude control of IFS during steady-state phase was investigated using only thrusters. A six degree-of-freedom translational and rotational dynamics model was constructed considering nonlinearity resulted from quaternion expression and coupling induced by community thrusters. A feasible quadratic optimization model was established for the integrated orbit and attitude control using con- strained nonlinear model predictive control （CNMPC） techniques. Simulation experiment demonstrated that the presented CNMPC aigorithm can achieve rapid calculation and overcome the non-convexity of partial constraints. The thruster layout is rational with low thrust consumption, and the mission requirements of IFS are fully satisfied.

Modeling, measurement and simulation of the disturbance torque generated via solar array drive assembly

The disturbance torque generated via solar array drive assembly(SADA) can significantly degrade the key performance of satellite.The discussed SADA is composed of a two-phase hybrid stepping motor and a set of two-stage straight gear reducer. Firstly, the vibration equation of the two-phase hybrid stepping motor is established via simplifying and linearizing the electromagnetic torque.Secondly, based on the vibration equation established, the disturbance torque model of SADA is created via force analysis and force system simplification. Thirdly, for precisely ground measuring the disturbance torque aroused by SADA, a measurement system,including a strain micro-vibrations measurement platform(SMMP) and a set of gravity unloading device(GUD), is designed.Fourthly, the proposed disturbance torque model is validated by measuring and simulating the disturbance torque produced via SADA driving rigid load through GUD. The results indicate that, the proposed disturbance torque model holds the ability to describe the disturbance torque caused by SADA with high precision. Finally, the disturbance torque emitted by SADA driving a flexible load, designed to simulate solar array, is modeled and simulated via using fixed-interface mode synthesis method(FIMSM). All the conclusions drawn from this article do have a meaningful help for studying the disturbance torque produced by SADA driving solar array on orbit.

Terrestrial water variations in the North China Plain revealed by the GRACE mission

Using eight years of time-variant gravity measurements from the GRACE gravity satellite mission, we estimate monthly terrestrial water storage variations in the North China Plain between August 2002 and August 2010. We find that during this period, the water storage is not constant but accelerate at a rate of -1.1 cm/yr over time. The study confirms that the relatively long-term trend of water storage in the North China Plain (by 13-point moving average) is consistent well with that by linear fitting. Two hydrological models, CPC and GLDAS, are adopted in calculating surface water variations, with results indicating that they agree with those of GRACE. Furthermore, rates of -0.6 cm/yr for surface water variations and -0.5 cm/yr for groundwater variations are found in the North China Plain during the study period. Decrease of rainfall and the groundwater over-exploitation are possibly the main causes for groundwater depletion in the North China Plain. The results will be helpful for better understanding climatic changes and provide reference for the management of water resources and the establishment of policies on preventing and alleviating natural hazards.

The deep-space multi-object orbit determination system and its application to Hayabusa2’s asteroid proximity operations

The deep-space multi-object orbit determination system(DMOODS)and its application in the asteroid proximity operation of the Hayabusa2 mission are described.DMOODS was developed by the Japan Aerospace Exploration Agency(JAXA)for the primary purpose of determining the trajectory of deep-space spacecraft for JAXA’s planetary missions.The weighted least-squares batch filter is used for the orbit estimator of DMOODS.The orbit estimator supports more than 10 data types,some of which are used for relative trajectory measurements between multiple space objects including natural satellites and small bodies.This system consists of a set of computer programs running on Linux-based consumer PCs on the ground,which are used for orbit determination and the generation of radiometric tracking data,such as delta differential one-way ranging and doppler tracking data.During the asteroid proximity phase of Hayabusa2,this system played an essential role in operations that had very strict navigation requirements or operations in which few optical data were obtained owing to special constraints on the spacecraft attitude or distance from the asteroid.One example is orbit determination during the solar conjunction phase,in which the navigation accuracy is degraded by the effect of the solar corona.The large range bias caused by the solar corona was accurately estimated with DMOODS by combining light detection and ranging(LIDAR)and ranging measurements in the superior solar conjunction phase of Hayabusa2.For the orbiting operations of target markers and the MINERVA-II2 rover,the simultaneous estimation of six trajectories of four artificial objects and a natural object was made by DMOODS.This type of simultaneous orbit determination of multi-artificial objects in deep-space has never been accomplished before.