Analysis of GAMIT/GLOBK in high-precision GNSS data processing for crustal deformation

Yu Li

Institute of Geophysics,China Earthquake Administration,Beijing,100081,China

China Earthquake Networks Center,China Earthquake Administration,Beijing,100045,China

Keywords:GAMIT/GLOBK GNSS Crustal deformation Geophysical model

ABSTRACT The advances in satellite navigation and positioning technology and the worldwide establishment of continuoustracking stations have greatly promoted the development and application of the high-precision Global Navigation Satellite System (GNSS).GAMIT/GLOBK,as a popular high-precision GNSS data-processing software,has been widely used in monitoring crustal deformation,tsunami,iceberg,etc.Based on the basic observations and various geophysical models processed by GAMIT/GLOBK,we analyze the influence of the correction of applied geophysical models,and describe the techniques of parameter estimation and accuracy assessment.In addition,taking the present crustal movement in the Chinese mainland and the MW7.8 earthquake in Nepal as examples,we discuss the applications of GAMIT/GLOBK in crustal deformation monitoring and its future prospect.

1.Introduction

Global Navigation Satellite System (GNSS) is a worldwide,allweather,high-precision space positioning technology developed in the 1990s.It is widely used in basic surveying and mapping,aerospace,transportation,and earth science.Since its appearance,numerous countries have started to develop permanent continuous tracking stations in a larger scale,which have gradually formed a broad GNSS tracking network.Meanwhile,their contributions have greatly promoted the technical innovation of GNSS,enabling precise positioning,accurate satellite orbit determination,and relevant geodynamic research.The current GNSS network includes the Global GNSS tracking network built by the International GNSS Service(IGS;http://www.igs.org/network/ne twork.php),the GPS Earth Observation Network(GEONET)built by the Geospatial Information Authority of Japan (GSI;https://www.gsi.g o.jp/),and the Plate Boundary Observation network (PBO;https://www.unavco.org/projects/past-projects/pbo/pbo.html) established by the United States,which relies on the Earth Scope Project and the Crustal Movement Observation Network of China I and II(CMONOC,https://www.cenc.ac.cn) built by China.The network produces abundant GNSS observation data for refined geoscience research and more importantly,provides a new platform for large-scale,quantitative investigations of crustal deformation.

In recent years,the improvement of satellite systems,the progress of signal-receiving technology,the refinement of the geophysical models involved in data processing,and the improvement of the earth reference frame have all contributed to the increase of GNSS positioning accuracy.At present,three types of international,high-precision GNSS data processing software are available:GAMIT/GLOBK,jointly developed by Massachusetts Institute of Technology,Scripps Institute of Oceanography,and Harvard University;the Bernese software developed by University of Bern in Switzerland;and GIPSY developed by NASA Jet Propulsion Laboratory.Given that Bernese is a paid software and GIPSY developed by U.S.Army is not available in China,the open source software,GAMIT/GLOBK,has been widely used.GAMIT/GLOBK consists of three parts.The first is GAMIT,which is a baseline processing software that uses GNSS carrier phase observations for positioning and orbit integration.It originated in the Planetary Ephemeris Program in the 1960s and was further developed in the 1980s.The second part is GLOBK,which was originally developed to process long baseline interferometry(VLBI)data in the 1980s.It was then upgraded to support the GAMIT output files and combine the VLBI and satellite laser ranging data in the 1990s.The third part is track/trackRT,which is used to process kinematic GNSS data (trackRT for real-time processing).After nearly half a century of development,the latest version of GAMIT/GLOBK is 10.71,which can process GPS/GLONASS/BDS/Galileo data separately(Herring et al.,2018).

In this paper,we analyze the influence of the correction of applied geophysical models,and describe the techniques of parameter estimation and accuracy assessment.Finally,we use two examples to illustrate the existing problems and the latest developments of GAMIT/GLOBK.

2.Fundamentals of GAMIT/GLOBK

2.1.Basic observations

GNSS produces carrier beat phase and pseudo-range observations.For carrier beat phase observations,the output from a single phase-tracking channel of a GNSS receiver is primarily used in high-precision geodesy to study crustal deformation,similar to the GAMIT/GLOBK software.This carrier beat phase observation is the difference between the phase of the carrier wave implicit in the signal received from the satellite and the phase of a local oscillator within the receiver.Such phase observations can be used for postioning measurements with a millimeter accuracy or higher.

In general,to eliminate or reduce the effect of some errors,such as offsets of satellites and receiver clocks,satellite-orbit errors,and atmospheric-refraction errors,GAMIT/GLOBK treats double-difference observations and uses the least-squares algorithm to estimate the parameters (Herring et al.,2018).This is also an important feature that differentiates GAMIT/GLOBK from other software.

Although the pseudo-range observations are not sufficiently precise to be directly applied in high-precision geodetic surveys,they are useful for estimating the offsets of receiver clocks,resolving ambiguities,and repairing cycle slips in phase observations.As a result,GAMIT/GLOBK provides several alternative combinations of observations depending on the actual situation.

LC or L3 observations,also called ionosphere-free phase combination,is a linear combination of the L1 and L2 phase measurements of the GPS signal (Bock et al.,1986;Dong and Bock,1989) (Equa.1).LC observations can compensate for almost all effects of the ionospheric delay(the first-order ionospheric delay;the second and third orders are<1 cm most of the time(Hoque et al.,2008)and could be neglected),which is a major source of error in GNSS measurements.LC is expressed as

whereL1 andL2 are the corresponding phase measurements,respectively,andf1andf2are the frequency ofL1 andL2,respectively.

LG orL4 observations,also called geometry-free combination,compensate for all geometrical and other nondispersive delays (e.g.,atmospheric delay),providing a direct measure of the ionospheric variations and signal scattering or multipath.LG(Equa.2) is given by

MW-WL orL6 observations,also called the Melboure–Wubbena wide-lane combination(Melboure,1985;Wubbena,1985),relies on the acquisition of precise (P-code) pseudo-range.The MW-WL (Equa.3)combination ofL1,L2,P1,andP2 is given by

whereP1 andP2 are the pseudo-range of the P-code.L6 observation is free of both ionospheric and geometric effects,and only is related with the integer ambiguities forL1 andL2.

In theory,the MW-WL combination may be used to process GNSS data,and the fixation of the integer ambiguities is independent of baseline length.If the observed values of any two stations form a double difference,the double-difference integer ambiguities can be resolved.However,this process requires empirical corrections for the receiver type and is related to the satellite.Such process forms the differential code biases (DCBs).The IGS data analysis center-CODE (Center for Orbit Determination in Europe,AIUB,Switzerland,http://ftp.aiub.unibe.ch/CODE/) has been providing the DCB services since 2002.Applying DCB correction gives theP1 andP2 pseudo-range,which resolves the integer ambiguities of long baselines,thereby significantly improving the position accuracy (Herring et al.,2006;Steigenberger et al.,2006;Ge et al.,2005b).

2.2.Geophysical models

To accurately determine the three-dimensional location of a GNSS station,the satellites,propagation path,receiver,and antenna must all be considered.Each of these factors can cause positioning errors from centimeters to kilometers (Beutler et al.,1994a,1994b;Kouba,2009;Montenbruck et al.,2015;Schmid et al.,2007;Boehm et al.,2007;Petrie et al.,2010).In GAMIT/GLOBK,most of the errors caused by these factors are corrected by the corresponding geophysical models.

2.2.1.Satellite effects

The basic principle of GNSS positioning is to determine the position of the receiver by measuring the distance between four or more satellites with known positions and determine the position of the GNSS receiver through distance rendezvous.An important aspect of this method is that it requires knowing the motion of each satellite.In general,satellite motion can be described by a set of six initial conditions (Ash,1972)(Cartesian position and velocity,or osculating Keplerian elements)and a model of the forces acting on the satellite over its trajectory.To accurately simulate the motion,we are required to know some essential information,including the acceleration induced by the gravitational attraction of the sun and the moon,the higher-order terms in Earth's static gravity field,and the solid-Earth and ocean tides.In addition,we should account for the non-gravitational forces exerted by direct solar radiation pressure,radiation reflected from Earth,radiation emitted by the spacecraft's radio transmission,and gas emission from the spacecraft's batteries and attitude-control system (Colombo,1986;Beutler et al.,1994b;Zeibart et al.,2002).In the new version of GAMIT/GLOBK 10.71,the parameter number of the radiation pressure model is enlarged from 9 to 13,adding two twice-per-revolution(2/rev)and two 4/rev term.

2.2.2.Phase-center effects

In addition to the orbital motion of a satellite,we need to consider meter-level offsets between the satellite center of mass and the phase center of the transmitting receiving antennas(see Fig.1)(Wang,2009).For example,matched ground antennas in a regional network can essentially eliminate the effects caused by the phase center;however,for longer baselines and/or different antenna types,such effects can contribute several centimeters to the estimated height (Herring et al.,2018).Research has also shown that an error in the phase center of both the satellite transmitting antenna and the station receiving antenna deviates the scale in the GPS solution (Schmid and Rothacher,2003;Zhu et al.,2003;Gendt and Schmid,2005).Zhu et al.(2003)present the basic relationship between the scale deviation Δsof the GPS solution and the error Δbof the satellite antenna radial deviation:Δs≈-7.8Δb.In other words,the 1 m error of radial deviation from the satellite antenna changes the GPS solution by 7.8 ppb of the scale.Therefore,IGS officially launched the absolute antenna phase center model on November 5th,2006(Gendt,2006),which was adopted by GAMIT/GLOBK to model the phase center offsets and phase center variations with elevation and azimuth.The most used ground antennas have been determined by electromechanical measurements(http://gnpcvdb.geopp.de;http://www.ngs.noaa.gov/ANTCAL),and the satellite antennas have been determined by analyzing global tracking data(Schmid et al.,2007).

Fig.1. Radial error between absolute phase center model and relative phase center model of GPS satellite antenna (quoted from Wang,2009).

2.2.3.Tidal effect

Positioning discrepancies induced by the tidal effect must be corrected in high-precision GNSS data processing,mainly including solidtide correction,ocean-tide correction,and polar-tide correction.

The periodic deformation of the solid earth caused by the gravitational force of the sun and the moon is the largest non-tectonic crustal deformation (Wang et al.,2005),which displaces GNSS stations according to the Love number and Shida number.The two numbers are related to the latitude and tidal frequency of a station(Petit and Luzum,2010).GAMIT/GLOBK provides two solid-Earth models:IRES92 and IERS03(from the International Earth Rotation Service).The two numbers of the IERS92 Earth tide model is only associated with the K1 frequency and are independent of other frequencies and of station latitude.In addition,the correlation with K1 is only reflected in a second-order correction of the vertical component(Watson et al.,2006).At the same time,compared with the IERS92 model,the IERS03 model reduces the amplitude of the annual vertical change in the time series of station position.Therefore,the IRES03 model is usually used in high-precision GNSS data processing.

Ocean tidal loading can lead to centimeter-or even decimeter-scale changes in GNSS positioning in some regions and time zones,and its correction depends on the ocean-tide model.GAMIT/GLOBK often uses the FES2004 ocean-tide model(Lyard et al.,2006),which is based on the hydrodynamics method.Satellite altimeters are used for correcting the tidal loading of each measurement station and the change in Earth's center of mass.

Polar tide refers to the elastic response of the crust to the drift(polar shift)of Earth's axis of rotation.The polar shift process the spin axis and defines a rough circle with a diameter of about 20 cm at the North Pole;this process is accompanied by a long-term variation in the rotation axis.In other words,long-term changes and periodic changes occur simultaneously.These variations displace measuring stations on the centimeterlevel(Petit and Luzum,2010),especially in the vertical direction,and are thus required to be investigated in high-precision GNSS positioning.

In general,the position of the instantaneous pole is described in terms of its deviation from an average pole.Namely,the accurate estimate of the average pole is critical for improving the polar-tide correction of the station position.Therefore,GAMIT/GLOBK provides two ways to describe the motion of the average pole.The IERS03 standard uses the average pole observations over the period 1900–2000 to construct a linear average pole model,which produces a deviation in the estimate of the average pole after 2000.The IERS10 standard fits the data for the period 1976–2010(Petit and Luzum,2010) to a third-order polynomial and uses a linear model to extrapolate the average pole after 2010.The correction given by the average pole model means that the polar tide correction of IERS03,which has been followed since 2000,is biased.Thus,the magnitude of this deviation must be accounted for to maintain a high-precision reference frame and correctly analyze regional tectonic movements.

Fig.2(a) shows the change of the pole trajectory relative to the average pole obtained by IERS03 and IERS10,respectively,suggesting that the differences in the pole trajectory increase with time.The resulting change in polar-tide correction depends on station location and time.Fig.2(b)shows the U components of the polar-tide corrections of the IGS core station ALGO in North America and station LHAS in China,relative to the average poles of IERS03 and IERS10,respectively.The difference between the two corrections is approximately linear in time.The deviation of the average pole of IERS03 leads to a deviation of+0.09 mm/a in the rate of vertical movement of the ALGO station,whereas the deviation at the LHAS station is -0.01 mm/a.Fig.3 shows the impact and magnitude of this deviation on a global scale.

Given the above deviations,it is generally recommended to use the IERS10 specification to correct the pole tide effect in GAMIT/GLOBK.

2.2.4.Effects of atmospheric refraction

The tropospheric and ionospheric refraction also significantly affect high-precision GNSS positioning.In GAMIT/GLOBK,the path delay caused by tropospheric refraction is well handled by using the global mapping function(Boehm et al.,2006) combined with the global meteorological model(GPT or GPT2)(Boehm et al.,2007;Lagler et al.,2013).However,the mapping function used at present assumes a symmetrically stratified atmosphere,which is contrary to fact.Furthermore,previous studies have shown that the index of refraction of the atmosphere in the horizontal direction is nonuniform.Therefore,in high-precision GNSS data processing,in addition to estimating a zenith delay parameter per hour for each station,a horizontal atmospheric gradient parameter in the east-west and south-north directions of each station is also added to explain atmospheric inhomogeneity.

For the path delay caused by ionospheric refraction,GAMIT/GLOBK uses theLC observable to remove the first-order effect.However,secondand third-order terms are not eliminated in theLC observable and can add up to 15 mm of path delay under high-ionospheric conditions.The second-order term is affected by both ionospheric electron content and the geomagnetic field,whereas the third-order term is not affected by the geomagnetic field and is much smaller in magnitude(usually ignored).At present,GAMIT/GLOBK is able to eliminate the second-and third-order terms by applying the magnetic field (usually IGRF12) and the vertical total electron content with a mapping function (using the daily IONEX files from CODE).

Fig.2. Trajectory of polar motion and polar-tide correction of the U component.

Fig.3. Bias of vertical velocity caused by the deviation of average pole of IERS03.The green triangles show the GNSS stations.

3.Parameter estimation and assessment of accuracy

3.1.Parameter estimation

The most important result obtained from GAMIT/GLOBK is the accurate estimate of the position of GNSS stations.Besides,GAMIT/GLOBK also estimates the orbital and Earth-rotation parameters,zenith delays,and phase ambiguities by fitting to doubly differenced phase observations with the incorporation of a weighted least-squares algorithm.Since the functional (mathematical) model that relates observations to parameters is nonlinear,GAMIT produces two solutions:the first provides coordinates within a few decimeters,and the second gives the final estimates.

In current practice,the GAMIT solution is not frequently used to obtain the final estimates of station positions.Instead,we use GAMIT to make estimates and an associated covariance matrix (“quasi-observations”) of station positions as well as orbital and Earth-rotation parameters.These parameters are then input into GLOBK or other similar programs.Therefore,the data are combined with those from other networks and times and thereby estimate positions and velocities (Feigl et al.,1993;Dong et al.,1998).GLOBK uses a Kalman filter(equivalent to a sequential least-squares fit if the solution has no stochastic parameters),which operates on covariance matrices rather than on normal equations.This step requires the user to specify a priori finite constraint for each estimated parameter (Herring et al.,1990,2018).To avoid biasing the combination,GAMIT generates the solution used by GLOBK with loose parameter constraints.However,since phase ambiguities must be resolved(if possible)in phase processing,GAMIT also generates several intermediate solutions with user-defined constraints before loosening the constraints for its final solution.

3.2.Accuracy assessment

GAMIT/GLOBK has two levels of accuracy assessment:(1) are the data adequate to perform a reasonable estimate?and(2) do the data fit the model to their noise level? The primary indicator that the first criterion is satisfied is the magnitude of the uncertainties of the baseline components.If the uncertainties are larger than the priori constraints previously given by station coordinates and orbital parameters,the user has to check the Q-file or autcln.sum file.Usually,you would find that large quantities of data have been discarded by autcln.For the second level,the primary indicator is the nrms (normalized rms) and wrms(weight rms)of the solution.The former is the ratio of the square root of χ2to freedom,which measures the noise level of the baseline solution.If the data are randomly distributed and thea prioriweights are set correctly,the nrms is nearly consistent and is typically near 0.2.

The wrms,also known as repeatability accuracy,can be divided into short-and long-term types based on the length of the observation time span.The short-term wrms is the root mean square of the weighted mean value observed in multi-session field operation,which reflects the data affected by orbital error,atmospheric delay error,multipath effect,etc.Under multi-session observation conditions,the short-term wrms better reflects the advantages and disadvantages of the station positioning in the short term.The short-term wrms(Equa.4)is obtained by the formula(Larson and Agnew,1991):

whereciis the daily solution,σiis the standard deviation ofci,nis the number ofci,andc(Equa.5)is the weighted average value ofci:

For the long-term wrms,the optimal linear fitting is applied to the positioning results of each period under the condition of multiple periods of observation,and the weighted root mean square error is calculated on this basis.The long-term wrms(Equa.6)reflects the degree of dispersion in the long-term positioning of a station due to environmental influences(such as atmospheric seasonal changes,non-tectonic movement of the monument,orbital long-period error).Specifically,it is given as

whereliand σiare the daily solution and its standard deviation,respectively,nis the number ofli,andis the optimal linear fitting value.

Fig.4 shows the distribution of GNSS stations of CMONOC,and Fig.5 displays the statistical histogram of the long-term wrms of the continuous GNSS stations of CMONOC.It is obvious that the mean values of the wrms in the N–S,E-W,and vertical directions are 2.0 mm,2.4 mm,and 6.6 mm,respectively(see Fig.5).

4.Application of GAMIT/GLOBK in earth science

GAMIT/GLOBK is a high-precision GNSS data processing software that is widely applied in earth science.For example,it has been used to monitor global plate motion or regional crustal movement(Avouac and Tapponnier,1993;Altamimi et al.,2012,2016;Wang,2020)to analyze the dynamics of plate boundaries and interior (Zhang et al.,2005;Bettinelli et al.,2006;Bilham et al.,1997).In addition,it is often combined with the distribution of seismic faults to study the process of earthquake preparation,occurrence,and healing of crustal deformation (He et al.,2018;Jiang et al.,2014;Ryder et al.,2011).The intermediate data produced by the process in GAMIT/GLOBK,such as tropospheric delay,can be used for research atmospheric water vapor content and weather forecasting (Wulfmeyer et al.,2015;Jones et al.,2020;Liang et al.,2020).Another example is the ionospheric total electron content,which can be used to monitor the activities of cosmic particles,and forecast electromagnetic phenomena such as geomagnetic storms(Ciraolo et al.,2007;Zakharenkova et al.,2008).

4.1.Monitoring the crustal movement

The monitoring of large-scale quantitative plate motions or crustal movements benefits from the rapid development of GNSS observation technology,the establishment of widely distributed GNSS tracking stations,and the refinement of data processing methods and models.Fig.6 shows the horizontal vectors of China mainland and surrounding areas with respect to Eurasian plate as indicated by GNSS stations.It is prominent that the overall tectonic deformation of continental China is mainly associated with the collision between Indian and Eurasian plates,and the clockwise and anti-clockwise rotation at East and West Himalayan tectonic junction.It should be noted that when you use GAMIT/GLOBK to process the GNSS data to obtain the crustal movement:(1)Select relatively wide data sets,including good site distribution and data duration(greater than 2 years is best).(2)The co-seismic effect should be taken into account within a certain range of large earthquakes,by data fitting or co-seismic rupture model correction.Besides,the post-seismic effects also need to be considered in the more refined results (3)Choose unified geophysical model and processing strategy.

Fig.4. Distribution of GNSS stations of CMONOC.

Fig.5. Statistical histogram of the wrms of CMONOC.

Fig.6. Horizontal velocity field of the Chinese mainland and surrounding areas with respect to Eurasian plate.Deep and light blue arrows indicate GNSS velocities from this study and previous studies,respectively.Error ellipses represent 70% confidence.(quoted from Wang M.and Shen Z.K.,2020).

4.2.Earthquake monitoring

Earthquakes are concrete manifestations of the rapid release of elastic strain energy induced by crustal deformation,tectonic strain,or sudden failure of source-body rock.Elastic crustal deformation is caused by the accumulation of stress and strain.Throughout the whole process from gestation and occurrence to post-seismic adjustment,tectonic earthquakes are accompanied by different degrees of crustal deformation.However,with the assistance of GNSS observations around the epicenters and high-precision GNSS data processing software,such as GAMIT/GLOBK,we are not only able to obtain the permanent,quantitative,coseismic deformation for guiding emergency rescues,but also obtain the motion state of the surface during the earthquake,which is used to study the causal mechanism of the earthquake.

Fig.7. Map of ground motion during earthquake.

Fig.8. Permanent horizontal co-seismic displacement of MW7.8 Nepal earthquake observed by GNSS.

Fig.7 shows the co-seismic displacement of theMW7.8 Nepal earthquake obtained from the GNSS data processed by the TRACK module of GAMIT/GLOBK.Fig.8 indicates that the co-seismic effect of the earthquake displaces the KKN4 and NAST station,located in Nepal,nearly 2 m horizontally and 1 m vertically.All the stations in China with an epicentral distance less than 1200 km have shown vibrations to a certain extent.The vibration magnitudes are essentially dependent on the epicentral distance,the underground geological structure beneath a station,and,in a larger scale,the position of a station relative to the wave propagation direction from the source rupture.For instance,the vibration amplitude of Station XZZF,which is 220 km northeast of the epicenter,is much greater than that of Station XZZB,which is 181 km northwest of the epicenter,although the latter is at a shorter epicentral distance.With increasing epicentral distance,the amplitude of seismic response of each station decreases,and significant differences appear between stations with the same epicentral distance on both sides of the epicenter (e.g.,XZGE,LHAS,XZBG,and XZRK).The maximum deformation in the east-west direction is about 280 mm;by contrast,in the north-south direction,the value is approximately 150 mm (XZZF).The deformation east of the epicenter clearly exceeds that west of the epicenter,which is consistent with the result of the unilateral rupture in the east.The time for the seismic response of each station gives an intuitive feeling for the propagation of seismic waves from the epicenter.In this process,the motion trajectories of each station are different.

Fig.7 shows the high-frequency (5 Hz sampling rate in Nepal and 1 Hz in China)results of GNSS stations located in Nepal and China.In the time-series for each station,thexaxis is time in minutes,the solid curves are for stations east of the epicenter(solid black curves)and west of the epicenter(red solid curves).Numbers in the upper-right corner give the epicentral distance of the given station,the black solid curves give the earthquake occurrence time,and the vertical dashed lines give the Pwave arrival time (blue dashed lines) and S-wave arrival time (green dashed lines) calculated by the TAUP software (Crotwell et al.,1999)using standard models.

To evaluate the permanent surface displacement caused by co-seismic events,we usually use GAMIT/GLOBK software to process GNSS data with a sampling rate of 30 s in order to capture the permanent deformation generated by the earthquake.Fig.8 shows the horizontal coseismic displacement caused by theMW7.8 Nepal earthquake obtained from Nepal and China GNSS data.The detailed processing methods are described in Li et al.(2015).The earthquake produced clear horizontal displacement in southern Tibet.The maximum displacement of 30 mm oriented in south and southwest occurs near station XZZF in Tibet.To the north of station XZZF,XZAR also produces a co-seismic horizontal displacement of about 23 mm in the same direction as station XZZF.However,the nearest XZZB station in Tibet (about 182 km) has experienced a co-seismic horizontal displacement of about 17 mm directed to southeast and south,which may be related to the unilateral eastward rupture of the earthquake.Millimeter-scale displacements of 2–6 mm are also detected southwest of Qinghai and west of Yunnan Province.The maximum horizontal displacement of the continuous GNSS stations in Nepal occurred at KKN4,reaching about 1889 mm directed to nearly due south and accompanied by a rise of 1267 mm.North of the epicenter,the CHLM station also displays a horizontal displacement of about 1408 mm directed to southward and a settlement of approximately 587 mm,compared with the InSAR results given by the ARIA research team(http://aria-share.jpl.nasa.gov/events/20150425-Nepal_EQ/Interferog ram/ARIA_Co-seismicCo-seismicCo-seismic_ALOS2_interferogram_Path A157_20150221_0502_1_5m.jpg).

Thus,the ascending and descending areas are basically consistent.The RMTE and DNSG stations to the east and west of the epicenter have respectively moved to the east and west,indicative of extrusion motion.The whole image has the distribution characteristics of a displacement field caused by an elastic-half-space thrust rupture.The co-seismic displacement field caused by the earthquake initiates from the epicenter and is sectioned in the NNE and SEE directions (earthquake rupture directions).The results show that the co-seismic influence of the Nepal earthquake is concentrated within 600 km of the epicenter.The two directions show exponential attenuation,and the influence of the coseismic effect in the SEE direction corresponds well with the earthquake rupture length.The earthquake has resulted in a minor vertical displacement that is below the positioning accuracy of GNSS and thus has not been detected.

This study concludes that GAMIT/GLOBK uses a relative positioning mode when processing high-frequency data (such as 1 Hz data).Users need to determine the reference station based on the co-seismic impact range,and take into account the regional common mode errors.For lowfrequency data(usually 30 s data),it is mainly used to obtain co-seismic and post-seismic permanent deformation information.In this case,users are required to be cautious about the systematic errors.

The red arrow indicates the horizontal displacement of the four stations in Nepal near the epicenter,the blue arrows indicate the horizontal displacement of co-earthquakes at the stations in China and Nepal,and the error ellipse confidence level is 70%.

5.Development and prospects of GAMIT/GLOBK

After decades of development,current GAMIT/GLOBK users are from all over the world and each function module is constantly being updated and refined.The GAMIT/GLOBK software encourages an innovative attitude,which is reflected in the initial support of the GPS observation data to the support of the GPS,GLONASS,Galileo,and BDS observation data,from item-only support of the ionosphere first-order correction to full support of the ionosphere second-order correction,from the initial static post-processing development to the present real-time dynamic processing,and from the initial support of linear estimation to nonlinear estimation.However,with the development of high-precision GNSS,GAMIT/GLOBK also shows some limitations and problems which need to be addressed.For example,it can only deal with the observation data of a single constellation at present normal processing,instead of joint calculation.According to the latest news,the TRACK module has been able to jointly process multi-constellation high-frequency data (such as GPS/BDS,or BDS/GALILEO),resulting in higher data availability and accuracy.

The satellite navigation and positioning technology (e.g.,trifrequency signals) should further be improved in GNSS data processing methods and various geophysical models(e.g.,tides,multipath models),and we believe that GAMIT/GLOBK will play a role in improving GNSS positioning accuracy and extending its applications.

Acknowledgments

I am grateful to all the contributors to GAMIT/GLOBK software.GAMIT/GLOBK provides free download of authorization(http://geoweb.mit.edu/).Thanks a lot for the contributors of the Crustal Movement Observation Network of China I and II (CMONOC).The Figures were drawn by GMT (Wessel et al.,2013).Sincere appreciations to the two reviewers and editor-in-chief for their valuable suggestions.This work is supported by the Beijing Natural Science Foundation,China (8204077)and Grants from the National Natural Science Foundation of China(42004010).