The effect and correction of non-tectonic crustal deformation for continuous GPS position time series

WANG Min1,2) SHEN Zheng-Kang1,3) DONG Da-Nan4)

1) State Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing

100029, China 2) Institute of Earthquake Science, China Earthquake Administration, Beijing 100036, China 3) Department of Earth and Space Sciences, University of California, Los Angeles, California 90095-1567, USA. 4) Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA.

Chinese Journal of Geophysical Research

vol.48, no.5, 1121-1129, 2005

Abstract GPS observed crustal deformation usually includes both tectonic and non-tectonic deformation signals, and it is vitally important to remove the non-tectonic deformation signals in the data in order to effectively use GPS observations for tectonic deformation studies. Using the Earth satellite data and geophysical models, we calculate non-tectonic crustal deformation caused by the ocean-tide loading, atmospheric mass loading, snow and soil moisture mass loading, and non-tidal ocean mass loading. Based on the quantitative analyses, the effects due to non-tectonic crustal deformation for the position time series of GPS fiducial stations from the Crustal Movement Observation Network of China are studied and corrected. Our study shows that these effects on the vertical components of station positions are remarkable, especially resulted from the atmospheric mass loading and snow and soil moisture mass loading. Using these models to correct for the non-tectonic deformation, we have reduced the RMS of the station vertical position time series by about 1 mm, which is about 11% of the total RMS. The amplitudes of annual vertical position variations are also reduced by about 37%. Moreover, we find that the position time series corrected using geophysical models followed by an empirical fitting of annual and semiannual variations are smoother than that corrected using the empirical fitting of annual and semiannual variations only, indicating that the geophysical model corrections can not be substituted by pure empirical fitting in removing the non-tectonic deformation effects.

Key words Crustal motion Non-tectonic deformation Mass loading GPS

1. Introduction

Along with its rapid development of surveying technology and improvement of positioning accuracy, the global positioning system (GPS) has been playing a increasingly significant role in acquiring crustal deformation information for geodynamic studies[1-5]. However, the deformation signals acquired by GPS usually include effects of non-tectonic deformation. For continuous observation stations, existence of the non-tectonic periodic deformation components may not affect determination of large scale tectonic deformation much, but its effect can result in oscillation of their reference frame. For campaign mode observations, it is rather difficult to isolate the non-tectonic from the tectonic deformation signals through statistical means. To correct quantitatively for the non-tectonic deformation effects, the fundamental solution is to assess their geophysical origins and evaluate their effects. Only by doing so can GPS observations be more effectively used for tectonic deformation studies.

Most of the non-tectonic crustal deformation is due to elastic response of the Earth’s materials to various loadings. The largest periodic non-tectonic deformation is resulted from the solar and lunar gravitational tidal forces. Periodic elastic responses are also caused by the change of eccentric force induced by the wobbling movement of the Earth’s rotation pole (called pole tide), with a periodicity of about 14-month. Another source of the non-tectonic crustal deformation is the fluid mass migration on the surface of the Earth, such as the atmospheric mass and water in various forms. Theoretical models have been developed and are able to describe deformation caused by the Earth tides and pole tide reasonably well, and corrections of these tidal effects can be incorporated in the processing of GPS carrier phase data (the GAMIT, GIPSY, and Bernese softwares have such functions). However, many other geophysical effects are often neglected because of their relatively

smaller amplitudes and/or their association with some less known geophysical processes. In this

paper we use satellite remote sensing data and various geophysical models to quantitatively calculate the non-tectonic crustal deformation resulted from the ocean tides, atmospheric pressure change, snow and soil moisture mass loading, and oceanic non-tidal loading, and to study and correct for the perturbations they cause to the position time series of the continuously observed GPS fiducial stations of the Crustal Motion Observation Network of China (CMONOC).

2．GPS Data Processing

The GPS data from the CMONOC fiducial stations are processed using the GAMIT/GLOBK software. We first use the GAMIT software to obtain loosely constrained regional daily solutions for the 25 fiducial stations and the IGS tracking stations in the region. We then use the GLOBK software to combine the regional daily solutions with the loosely constrained global daily solutions produced by the Scripps Orbital and Permanent Array Center (SOPAC), and tie the final solutions to the ITRF2000 reference frame by performing a 7-parameter transformation via a group of core IGS stations.

We processed the data from March 1, 1999 to February 7, 2004, and obtained almost 5 years of

Fig 1. Station position time series: (a) BJFS, (b) LHAS, and (c) URUM. The curves in green, pink, orange, and

light blue denote the position perturbations caused by the ocean-tide, atmospheric, snow and soil moisture, and

non-tidal ocean mass loading respectively. The curves of L1, L2, and L3 in navy blue show station positions

derived from GPS data processing, corrected using geophysical models, and corrected using geophysical models

followed by an empirical fitting of annual and semi-annual variations, respectively. Red curves overlaying on L2

are annual and semi-annual corrections obtained from empirical fitting.

time series for the 25 fiducial stations under the ITRF2000 reference frame. Some of the data are excluded for various reasons, such as antenna malfunction due to water leakage at the station TAIN 1999/7/9-2000/9/3, and monument instability for a pillar used before July 2000 at CHUN. We also modeled and removed position jumps at number of stations due to various causes: coseismic displacement of the November 14, 2001 Ms 8.1 Kunlun Mountain Pass West earthquake at the station DLHA, monument shift on January 26, 2002 at WUHN, and some unknown causes at epochs 2000.1434, 2000.1790, and 2001.2620 for the stations BJSH, XIAA, and XNIN respectively. To better visualize the non-tectonic deformation signals, we have removed the linear trends from the position time series, and show the results (blue curves) in Fig. 1. Due to the page limitation we present only the results from 3 representative stations BJFS, LHAS, and URUM.

3. Quantitative Calculation of the Non-tectonic Deformation

3.1. Ocean tides

Ocean tides are the elastic response of the Earth’s crust to the mass redistribution of sea water caused by the solar and lunar gravitational tidal forces. Corrections of the ocean tide effect is done for each of the tidal harmonics, with their contribution to a station’s east, north, and up components and associated phases with respect to the Greenwich meridian line calculated based on a global ocean tide model, and summed up to become the total correction of the site (IERS Conventions 2000, http://maia.usno.navy.mil/conv2000.html). There are several global ocean tide models available. These models differ mainly by the data sources which they are based upon, some of them may offer biased forecasts in the vicinity of some shallow sea regions where the ocean tidal effects are neglected. Relatively speaking, the GOT00.2 model (with a spatial resolution of 0.5º× 0.5º) developed based on the TOPEX/Poseidon satellite data is more suitable to the Chinese continental region and is used in this study (http://www.oso.chalmers.se/~loading).

Because the 8 major ocean tidal components, M2, S2, N2, K2, O1, K1, P1, and Q1 are diurnal or semi-diurnal tides, under the ideal observational conditions (observations uniformly distributed in space), their influence to daily solutions derived using 24 hours of observations would have been mostly averaged out, with the remaining residuals coming from the difference in frequency between the tides and GPS satellite orbits[7, 12]. Effects of such an influence is pretty complex, and cannot be evaluated quantitatively here. Therefore in this paper we calculate only the correction terms for the monthly, semi-monthly, and semi-annually tides (MR, MM, and SSA) based on the GOT00.2 model.

3.2. Atmospheric mass loading

Atmospheric mass loading varies because of the periodic changes of the solar and lunar gravitational tidal forces. The corresponding station displacements are elastic static deformation, and can be calculated using the loading Green’s functions[13]. The station displacements caused by the snow, soil moisture mass, and non-tidal ocean loadings, to be discussed subsequently, are also obtained using the same method.

The atmospheric pressure data are acquired from the National Center for Environmental Protection NCEP), USA (http://www.cdc.noaa.gov/cdc/data.ncep.reanalysis.html). The temporal resolution of the pressure data is 6 hours, and spatial resolution 2.5º× 2.5º. In the model we use

24-hour averages of the pressure data for the corrections, in alignment with the 24-hour averages of the station position data.

3.3. Snow loading and soil moisture mass loading

We use the data of snow and soil moisture mass distribution obtained from the Atmospheric Model Inter-comparison Project-II Reanalysis, NCEP/DOE/USA (http://wesley.wwb.noaa.gov/reanalysis2). The temporal and spatial resolutions of the data are 1 month and 1.875º(latitude)× 1.904º(average longitude) respectively, and interpolation of the data in time and space is needed in order to be compared with our GPS station position time series. Numerical computations show that the time series of this correction oscillates periodically at all the sites, and trends linearly at some sites. The cause of the linear trends is still not known, we remove them in this study.

3.4. Non-tidal ocean loading

The non-tidal ocean loading is produced by the sea wind, atmospheric pressure change, and thermo-exchange between the ocean and the atmosphere. The data we use are from the ocean surface model (http://www.csr.utexas.edu/sst), developed by the Center for Space Research, University of Texas at Austin, USA (CSR), from analyzing data from the TOPEX/Poseidon and Josan-1 satellites. The temporal and spatial resolutions of the data are ~10 days and 1.0º× 1.0º respectively. The data are interpolated using the same method mentioned in the previous section.

4. Results and Analysis of Non-tectonic Deformation Corrections

Fig 2 Earth's surface barometric pressure change: July to January of next year (1989-1996average)

Fig. 1 shows the station position changes caused by the ocean tide, atmospheric mass, snow and soil moisture mass, and non-tidal ocean loadings respectively. Examining the figure it is evident that, as the loadings are imposed primarily on the Earth’s radial direction, the 4 loading terms affect mainly the vertical motions of the stations. Among the 4 terms the atmospheric mass loading contributes to the vertical motion the most, ranging 8.5-24.5 mm for the 25 fiducial stations. The largest corrections appear at stations located in the northeast China, followed by the stations in North China. It can be seen from the diagram of global atmospheric pressure change at the surface of the Earth from July to January, next year (Fig. 2), that the Chinese continent is among the regions in the world with the most severe pressure change; its induced non-tectonic deformation, therefore, cannot be neglected. The correction terms contributed by the ocean tidal effect is merely 1-2 mm. They are relatively larger at the coastal stations, with the largest of ~4 mm at the station YONG, followed by the sites QION, GUAN, and SHAO. The amounts of corrections are consistent with their geographic locations. The largest correction for the snow and soil moisture mass loading, about 16 mm, appears at the station KMIN, followed by 15 mm at XIAG and 10 mm at LHAS. These estimates are consistent with the result of continental water induced crustal deformation, obtained from synthesizing global meteorological data of multiple sources by VanDam et al.[14]. The average position change of the 25 fiducial stations induced by the non-tidal ocean loading is 2-3 mm.

We calculated the root mean squares (RMS) of the errors for the station time series before and after applications of the 4 non-tectonic loading corrections, and show the result in Table 1. Our result suggests no significant error reduction for the horizontal components after removal of the model predicted loading effects. However, the RMS for the vertical components of the 25 sites, on average, are reduced for about 1 mm, or 11% in amplitude, from 8.89 mm before to 7.80 mm after the corrections. The raw station position time series demonstrate significant periodic variations, we use the least-squares method to fit the time series before and after the corrections and obtain the amplitudes and phases of the annual and semi-annual variations respectively. Our result shows that

Fig 3 Annual terms of vertical position variations for the fiducial stations

before (green) and after (red) the corrections caused by mass loading (fitting

for a yearly sinusoidal curve, with the reference time as 1999.0). The arrows

denote the amplitudes. The azimuthal angles counted counterclockwise from

the east represent the initial phases of the sinusoidal function. The arrows

pointing to the east, south, west, and north indicate that the maximum occurs

at the 0.25, 0.50, 0.75, and 0.0 years respectively.

the amplitudes after the corrections are reduced by 2-6 mm relative to the ones before, with an average reduction of 37% (Table 2 and Fig. 3). Both statistics attest that the loading corrections of the 4 terms are effective in reducing the errors in vertical direction.

It is worth to note that, significant changes appear not only in the amplitudes, but also in the phases systematically, for the annual variations of the vertical displacements after the corrections (Table 2 and Fig. 3). Before the corrections the annual variations in the Ordos, North China, and Southeast China regions reach the maximum during a time period of June-July, and the Southwest China and South China-South China Sea regions reach the maximum March-May respectively. After the corrections, however, the Ordos and North China stations reach the maximum July-August, lagging 1-2 months behind the phase of maximum before the correction. The Southeast China, Southwest China, and South China Sea regions still peak around March-May, the same time as before the correction. The cause of the regional differences and the systematic biases is yet not known, and awaits for future studies.

Time series analysis of the station positions has been one of the foci in the researches of GPS application to crustal deformation in recent years. Significant periodic oscillations demonstrated in the station position time series have lead researchers to attempt employing a pure emperical approach to analyze and remove such periodic variations. To assess the effectiveness of this approach we do a test as following. For the station position time series before and after the loading corrections, we do a regression analysis to estimate the annual and semi-annual harmonics, and remove their contributions to the time series to obtain the post fit RMS respectively. Statistics of the results is listed in Table 1. It shows that the time series RMS, after fitting the annual and semi-annual harmonics for the station vertical components, can be reduced ~10% further, if it is done after making the non-tectonic loading corrections. It is worth to point out, that if the effects of the 4 non-tectonic loadings were purely annual and semi-annual oscillations and could be eliminated by simple means, the 2 post-harmonic fitting residual time series with and without the non-tectonic loading corrections would be virtually the same. In reality, however, the one with the non-tectonic loading corrections is less scattered than the one without, as the former demonstrates ~1 mm less in RMS than the latter in all the 25 stations. Therefore we conclude that perturbations of station positions due to various geophysical forces cannot be eliminated completely through harmonic analysis, and it is absolutely necessary to investigate each individual geophysical force and its effect in order to make corresponding corrections.

Table 1. Station position RMS (mm)

Raw Data After Harmonic

Corrections After Loading

Corrections After Harmonic

+ Loading Corrections Station

E-W N-S UP E-W N-S UP E-W N-S UP E-W N-S UP

BJFS 3.11 3.71 8.34 2.84 3.69 6.62 3.20 3.66 7.06 2.98 3.63 5.75

BJSH 2.67 3.60 7.73 2.61 3.59 6.19 2.75 3.59 6.56 2.70 3.57 5.42

CHUN 2.77 3.58 6.79 2.68 3.53 6.13 2.86 3.62 5.60 2.72 3.49 5.19

DLHA 2.38 3.51 6.54 2.37 3.43 6.17 2.60 3.41 5.87 2.47 3.21 5.43

DXIN 2.60 3.63 7.87 2.53 3.58 6.82 2.73 3.53 6.65 2.63 3.41 5.77

GUAN 3.70 5.18 10.65 3.31 5.15 9.77 3.76 5.18 9.78 3.28 5.15 9.17

HLAR 2.68 3.30 8.70 2.56 3.30 6.58 2.77 3.34 6.79 2.68 3.27 5.20

JIXN 2.77 3.82 8.30 2.75 3.80 6.45 2.88 3.82 6.80 2.86 3.77 5.65

KMIN 2.84 4.99 11.85 2.71 4.93 10.34 2.95 4.96 10.43 2.70 4.83 10.02

LHAS 2.50 4.72 7.80 2.50 4.62 6.01 2.62 4.77 6.07 2.46 4.37 5.39

LUZH 2.94 4.25 8.47 2.85 4.23 7.51 3.04 4.23 7.61 2.81 4.16 7.22

QION 3.90 5.83 12.30 3.48 5.75 10.79 4.04 5.79 11.38 3.45 5.73 10.25

SHAO 3.29 4.36 8.66 3.13 4.35 8.25 3.37 4.39 8.15 3.12 4.34 7.85

SUIY 2.91 3.92 7.67 2.76 3.85 7.26 2.96 4.02 6.92 2.79 3.80 6.44

TAIN 3.28 4.22 10.23 3.14 4.14 8.20 3.38 4.22 8.37 3.10 4.10 7.18

TASH 2.82 4.09 6.16 2.66 3.98 6.16 2.84 4.21 5.85 2.72 3.95 5.78

URUM 3.45 4.10 9.30 3.01 3.91 7.01 3.42 4.18 7.17 3.06 3.80 5.94

WUHN 3.40 4.92 8.20 3.24 4.91 7.87 3.56 4.91 7.46 3.28 4.84 7.30

WUSH 2.65 4.08 6.71 2.40 3.94 6.35 2.72 4.15 5.84 2.50 3.90 5.79

XIAA 3.16 3.95 8.20 2.90 3.87 6.42 3.27 3.92 7.20 3.04 3.84 5.86

XIAG 3.82 7.43 13.67 3.68 7.21 12.13 3.85 7.38 12.20 3.63 7.18 11.39

XIAM 3.48 5.40 10.40 3.29 5.34 9.29 3.60 5.51 9.41 3.25 5.38 8.49

XNIN 2.40 3.56 6.49 2.33 3.45 5.65 2.52 3.53 6.04 2.40 3.28 5.10

YANC 2.63 3.66 8.45 2.45 3.65 7.15 2.70 3.62 7.52 2.57 3.58 6.36

YONG 3.50 4.90 12.76 3.04 4.85 11.64 3.57 4.92 12.15 3.00 4.85 11.04

Average 3.03 4.35 8.89 2.85 4.28 7.71 3.12 4.35 7.80 2.89 4.22 7.00

Table 2 Statistics of annual and semiannual variations of station vertical positions

Station Lat Lon Raw Time Series After Loading Correction Annual Semi-Annual Annual Semi-annual

o N oE a(mm) φ(o) a(mm) φ(o) a(mm) φ(o) a(mm) φ(o)

BJFS 39.609 115.892 7.07 271.95 2.99 123.08 5.26 246.40 2.70 128.71

BJSH 40.251 116.224 6.46 265.18 2.32 109.26 4.86 235.50 1.93 115.18

CHUN 43.790 125.444 3.99 280.19 2.87 126.67 1.69 226.31 2.73 125.91

DLHA 37.380 97.378 3.23 320.77 2.82 69.56 2.29 264.38 2.02 80.98

DXIN 40.984 100.201 5.51 282.79 2.95 63.81 4.11 261.09 2.21 69.40

GUAN 23.185 113.340 5.66 323.68 4.00 84.61 2.46 313.51 3.84 82.53

HLAR 49.270 119.741 8.11 243.75 1.45 92.18 6.17 224.80 1.22 81.06

JIXN 38.576 117.531 7.27 265.17 2.66 100.91 5.32 239.11 2.24 104.14

KMIN 25.029 102.798 9.13 355.70 3.26 111.57 2.65 349.63 3.19 106.14

LHAS 29.657 91.104 7.17 13.00 2.93 136.91 2.88 356.80 2.84 141.90

LUZH 28.872 105.414 5.62 320.48 1.58 85.32 2.90 269.68 1.55 101.21

QION 19.029 109.845 8.36 300.71 3.80 105.89 5.82 292.72 3.60 102.10

SHAO 31.100 121.200 3.06 272.13 2.73 155.72 1.40 153.58 2.52 161.01

SUIY 44.433 130.908 3.22 253.16 2.78 107.70 2.86 188.30 2.14 104.39

TAIN 36.215 117.123 8.72 287.20 2.42 131.61 5.60 275.05 2.23 132.69

TASH 37.775 75.234 0.33 275.56 1.53 62.84 1.17 38.88 0.51 131.03

URUM 43.808 87.601 8.50 263.08 2.45 20.48 5.47 264.07 1.37 358.00

WUHN 30.532 114.357 3.25 314.42 1.84 116.30 1.19 68.52 1.51 123.25

WUSH 41.202 79.210 3.12 277.50 1.31 57.26 1.07 316.50 0.65 149.20

XIAA 34.178 108.986 7.38 284.80 2.05 102.32 5.88 257.15 1.43 128.43

XIAG 25.608 100.255 9.43 328.47 3.87 121.35 5.19 294.77 3.60 117.79

XIAM 24.450 118.083 6.22 296.03 4.05 90.16 3.68 289.29 3.61 86.91

XNIN 36.601 101.774 4.55 309.54 2.16 79.63 4.42 260.35 1.59 105.61

YANC 37.779 107.437 6.33 277.34 3.30 89.80 4.98 247.43 2.69 100.28

YONG 16.834 112.335 7.69 335.33 5.49 70.32 4.82 350.81 6.05 65.39

Average 5.98 2.78 3.77 2.40

α: amplitude of oscillation; φ: initial phase of oscillation.

5. Other Perturbation Forces

Looking at the station position time series after the loading and harmonic fitting corrections (Fig.

1), it is evident that some non-tectonic deformation still remains. One of the reasons for the existence of the remaining non-tectonic deformation is the regional errors existed in the global geophysical models for the Chinese continent area. In the meantime, the 4 non-tectonic loading forces, ocean tides, atmospheric mass circulation, snow and soil moisture mass, and non-tidal oceanic loading, are not all the causes of the observed non-tectonic motions of the GPS stations. We are not able to analyze quantitatively the effects of other geophysical forces and mechanisms here, instead, we discuss briefly some of the aspects in the following.

5.1. Residuals of ocean tidal corrections

During the calculation of the ocean tidal corrections, we neglected the frequency difference between the ocean tides and the GPS satellite orbits. Theoretically this negligence would not affect the inland station positions much. However, because parameters such as the tropospheric delays and atmospheric gradients are also estimated along with the station positions and satellite orbits, such an effect could be amplified several times and be significant[15].

5.2. Periodic change of reference frames.

In the GPS surveying practice the global reference frame is anchored at the core IGS stations. However, positions of the core IGS stations also change periodically, it is inevitable that periodic variations exist in realization of the global reference frame. Although the widely distributed IGS sites around the globe, to certain degree, compensated this effect, for a particular region this effect can still be systematic.

5.3. Thermo-expansion/contraction of station monuments

All the monuments of the 25 fiducial stations are made of concrete re-enforced with steel rods inside. They undergo thermo-expansion/contraction in response to the seasonal temperature change. Such an effect is regarded as an observational error rather than non-tectonic crustal deformation. Nevertheless its signals are modulated in the GPS deformation signals and contribute to the annual changes.

5.4. GPS antenna phase center model error

Phase center locations of the GPS antennae vary along with temperature change. The phase center location functions currently in use are the results from laboratory calibrations. However, field observation environments differ greatly from the laboratory environment, resulting in calibration errors of the antenna phase centers, and possibly introducing annual variations to the processed station position results[16].

6. Final Remarks

The Earth’s surface loading resulted from temporal variations of surfacial mass circulation is one of the major causes of the non-tectonic crustal deformation at the Earth’s surface, particularly in the vertical direction, is the mass loading resulted from circulations of geophysical fluids. Such non-tectonic deformation signals cannot be eliminated by manipulations using pure empirical functions. The effective approach is to isolate and correct for that quantitatively using geophysical models. Besides the forces of the ocean tides, atmospheric mass circulation, snow and soil moisture

loading, and non-tidal oceanic loading, other geophysical forces, mechanisms, and error sources need to be investigated, in order to make better corrections of the non-tectonic displacements and improve the GPS monitoring capability of tectonic deformation.

Acknowledgments. The GPS daily solutions used in this study are from the GPS Data Center, CMONOC. The authors thank all the colleagues working in the GPS Data Center for their tremendous support in many aspects to this study.

References

[1] Shen Z-K, Wang M, Li Y X, et al. Crustal deformation associated with the Altyn Tagh fault system, western

China, from GPS. J. Geophys. Res., 2001, 106(12):30607~30621

[2] Wang Q, Zhang P-Z, Freymueller T J, et al. Present-day crustal deformation in China constrained by Global

Positioning System measurements. Science, 2001, 294:574~577

[3] Wang X Z, Zhu W Y, Fu Y et al. Present-time crustal deformation in China and its surrounding. Chinese J.

Geophys. (in Chinese), 2002, 45(2):187~209

[4] Wang M, Shen Z-K, Niu Z J, et al. Contemporary crustal deformation of the Chinese continent and tectonic block

model. Science in China (series D), 2003, 46(supp.):25~40

[5] Zhang P-Z, Shen Z-K, Wang M, et al. Continuous deformation of the Tibetan Plateau from Global Positioning

System data. Geology, 2004, 32(9):809~812

[6] Mao A, Harrision C G A, Dixon T H. Noise in GPS coordinate time series. J. Geophys. Res., 1999,

104(B2):2797-2816

[7] Dong D N, Fang P, Bock Y, et al. Anatomy of apparent seasonal variations from GPS derived site position time

series, J.Geophys. Res., 2002, 107(B4): ETG9-1~ETG9-16

[8] Zhang F P, Dong D N, Cheng Z Y, et al. Crustal vertical seasonal variations in China observed by GPS. Chinese

Science Bulletin(in Chinese), 2002, 47(18):1370~1377

[9] Zhu W Y, Fu Y, Li Y. Global elevation vibration and seasonal changes derived by the analysis of GPS height.

Science in China(series D), 2003, 46(8):765~778

[10] King R W, Bock Y. Documentation for the GAMIT GPS analysis software, version 10.03. Cambridge:

Massachusetts Institute of Technology, 2000

[11] Herring T A. GLOBK: Global Kalman filter VLBI and GPS analysis program, version 4.10. Cambridge:

Massachusetts Institute of Technology, 2000

[12] Dragert H, James T S, Lambert A. Ocean loading corrections for continuous GPS: A case study at the Canadian

coastal site Hollberg. Geophys. Res. Lett., 2000, 27(14): 2045~2048

[13] Farrell W E. Deformation of the Earth by surface loads. Reviews of Geophysics and Space Physics, 1992,

10(3):761~797

[14] VanDam T, Wahr J, Milly P, et al. Crustal displacement due to continental water loading. Geophys. Res. Lett.,

2001, 28(4), 651~654

[15] Penna N T, Stewart M P. Aliased tidal signatures in continuous GPS height time series. Geophys. Res. Lett., 2003,

30(23), SDE1-1~SDE1-4

[16] Hatanaka Y, Sawada M, Horita A, et al. Rocken calibration of antenna-radome and monument-multipath effect

of GEONET, part2: Evaluation of the phase map by GEONET data. Earth Plants Space, 2001, 53: 23~30