Journal of Geodynamics High Resolution Mapping of Earth Tide

Journal of Geodynamics 48 (2009) 253–259

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High resolution mapping of Earth tide response based on GPS data in Japan

Takeo Ito a,c,∗, Makoto Okubo b, Takeshi Sagiya a a Research Center for Seismology, Volcanology and Disaster Mitigation, Graduate School of Environmental Studies, Nagoya University, D2-2(510), Furo-cho, Chikusa-ku, Nagoya City, Aichi 464-8602, Japan b Tono Research Institute of Earthquake Science, 1-63 Akeyo-cho, Yamanouchi, Mizunami City, Gifu 509-6132, Japan c Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125, USA article info abstract

Keywords: We observe the Earth tidal fields at diurnal and semi-diurnal periods using Kinematic Precise Point KPPP GPS Positioning (KPPP) GPS analysis. Our KPPP GPS solutions compare well with super-conducting gravimeter Earth tides (SG) observations and a theoretical Earth tidal model, that includes both ocean tide loading model and GEONET body tides. We make a high resolution map of the observed Earth tidal response fields using the Japanese GEONET GPS network which consists of 1200 sites. We find that: (1) the average phase of GPS data lags 0.11 ± 0.04◦ from our theoretical Earth tidal model, (2) the average amplitude ratio between GPS and the theoretical Earth tidal model is 1.007 ± 0.003, (3) the amplitude in the Kyushu district is about 1.0–1.5 ± 0.3% larger than in the Hokkaido district, and (4) the amplitude at the Japan Sea side is about 0.5 ± 0.2% larger than that at the Pacific Ocean side. These results suggest that we may be able to place constraints on Earth structure using GPS-derived tidal information. © 2009 Elsevier Ltd. All rights reserved.

1. Introduction In previous studies, periodic signals in sub-daily estimates of positions were obtained from Global Positioning System (GPS) data. Historically, great efforts have been made to accurately measure The estimation of sub-daily positions is commonly used for OTL and the Earth tides (e.g., Richter and Warburton, 1998). There have been ice movement studies (e.g., King et al., 2003, 2005; Allinson et al., many theoretical studies of the Earth’s structure and tidal response 2004). A widely used procedure to produce the sub-daily solutions after Love (1909). Tidal deformations were studied for a spherically is to segment the continuous GPS data into batches of a few hours symmetric, perfectly elastic and isotropic Earth (e.g., Longman, (typically 0.5–4 h) and then in order to generate station coordinates 1963; Saito, 1967; Farrell, 1972). The response of the Earth to at sub-daily intervals using a differential GPS analysis approach and lunisolar attraction is expressed by amplitudes and phases of tidal one can constrain the relative crustal deformation with respect to constituents, together with the ocean tide loading (OTL) effects a GPS station that is several hundred kilometers away. Here in con- (e.g., Lambert et al., 1998). The tidal response is mainly related to trast, we employ a Kinematic Precise Point Positioning (KPPP) GPS the Earth’s elastic properties and local variations in elastic structure approach, which can estimate the position every 30 s at sub-daily (Mantovani et al., 2005; Fu and Sun, 2007). Thus, the Earth’s tidal intervals and without need for a specific reference point. We con- response can be used to investigate the inner structure. Various struct a high resolution map of the Earth tidal response field for instruments including super-conducting gravimeters (SG), strain Japan which is obtained from time series data at 1200 GPS sites in meters, and tilt observations provide precise point measurements Japan. of tidal responses. However, we have lacked observations with good spatial coverage. Because of the expense of instruments and the dif- ficulties in establishing low-noise sites, it has been difficult to make 2. Observation data and analysis method consistent observations to reveal the spatial heterogeneity of the solid Earth tidal field. We use the Japanese continuous GPS network called the GPS Earth Observation Network (GEONET) that has been operating since 1996 and covers all the Japanese islands with more than 1200 sites, enabling quasi-real-time monitoring of the crustal displacement field of Japan. Recently, the accuracy of KPPP GPS analysis has been ∗ Corresponding author at: Research Center for Seismology, Volcanology and remarkably improved by the development of new analytical tech- Disaster Mitigation, Graduate School of Environmental Studies, Nagoya University, niques. KPPP GPS has attracted the attention of the GPS community D2-2(510), Furo-cho, Chikusa-ku, Nagoya City, Aichi 464-8602, Japan. Tel.: +81 52 789 3038; fax: +81 52 789 3047. as it can provide a centimeter level positioning accuracy with a E-mail address: takeo [email protected] (T. Ito). single GPS receiver, which is almost comparable to that obtained

Fig. 1. Example of time series of each observation. (a)–(c) Three components of KPPP GPS displacement at Tajimi station (see Fig. 5(a)) obtained by the KPPP analysis method. (d) Time series of SG observation at Inuyama (near the Tajimi GPS station). The observation period is 1 month (May, 2006). Red and green lines are observations and the theoretical Earth tidal model, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) by differential GPS. In this study, we applied KPPP GPS analysis gal of gravity change is equivalent to about 3.2 mm of relative with the GPS Tools ver.0.6.3 software to estimate the position of all height change, which is better than the centimeter accuracy of the GPS sites of GEONET every 30 s (Takasu and Kasai, 2005; Takasu, KPPP GPS data. SG observations are characterized by high sensitiv- 2006). GPS Tools is a Global Navigation Satellite Systems (GNSS) ity, long-term stability, and fidelity over a wide frequency range analysis software package. The strategy of this analysis software is the spans from the seismic normal mode period range to secular based on the extended Kalman filter (EKF, forward/backward) with changes. IGS (International GNSS Service) final ephemerides, Earth rotation Fig. 1 shows the time series for the period of May 1, 2006 to parameters, and two satellite clock coefficients (IGS final and CODE May 30, 2006 of displacements at GPS station 950292 (Tajimi) (Center of Orbit Determination for Europe)). These clock coeffi- and the time series of relative gravity change measured by a SG cients of IGS final and CODE are made by different strategies. The located at the Inuyama observation station (belonging to Nagoya large difference of these strategies is that the sampling rates of University). The distance between the Tajimi GPS station and the SG IGS Final and CODE clock coefficients are 300 and 30 s, respec- station at Inuyama is about 8 km. This SG instrument (CT #036) was tively. In order to estimate precise coefficients at 30 s intervals, IGS installed in a tunnel with a 25 m-long and 40 m-depth in 1999. In final satellite clock coefficients are used as a base and the clock this study we used the TIDE filter output data of the SG. The ampli- coefficients are interpolated every 30 s, using CODE clock informa- tude response of the TIDE filter is flat for periods longer than 1 min. tion. Additionally, the measurement model of this analysis software The scale factor of this SG is −623.5 nm s−2/V, as obtained by Nawa contains precise measurement corrections such as antenna phase et al. (2009). The green curves represent the displacement and center offsets, phase-windup effect, relativistic effects and various gravity time series predicted from a theoretical Earth tide model GPS-specific Solar Radiation Pressure models. Troposphere zenith including OTL obtained by the NAO.99Jb model (Matsumoto et al., total delays and horizontal troposphere gradients at each GPS site 2000). The NAO.99b model is based on assimilating about 5 years are estimated at each epoch assuming a random-walk model. Time of TOPEX/POSEIDON altimeter data into a numerical barotropic series of coordinates are estimated adapting a white-noise stochas- hydrodynamical model. Both TOPEX/POSEIDON data and coastal tic model. The data are not bias-fixed. tidal gauge data are assimilated into the regional high resolution ocean tide model around Japan (NAO.99Jb). The accuracy of recent 2.1. Compare super-conducting gravimeter with Earth tidal global OTL models is believed to be high, except for in regions with model shallow seas and for areas having complex bathymetry and coast- line. For example, according to Matsumoto et al. (2000), the vector We analyzed about 4 months of data, from April 1 to July 31, differences for the M2 constituent between NAO.99b and GOT99.2b 2006, for all of GEONET. We estimated the position of each GPS site (Ray, 1999) are on the order of 1 cm or smaller almost everywhere at 30 s intervals without any Earth tidal corrections. Here we define in the open seas worldwide. The synthetic displacements induced the Earth tide as the sum of body tide and OTL. Before comparing by OTL and body tides were estimated using the NAO.99Jb model, the KPPP GPS solution with the Earth tidal model, we evaluate the which utilizes the mass loading Green’s functions for displacement accuracy of the both the body tide and OTL models by compar- and is based on the 1066A Earth model (see Matsumoto et al., 2001). ing with observations from a SG. The accuracy of SG observations The body tide model is based on the elastic 1066A Earth model, too. is smaller than one microgal (Imanishi et al., 2004). One micro- We use a high resolution grid, with grid interval of 1.5 arcseconds by T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259 255

Fig. 2. (a)–(c) Time series of the differences between KPPP GPS observations and the theoretical Earth tidal model. The NS, EW, and vertical components of displacement are displayed. (d) Time series of the differences between SG observations and the theoretical Earth tidal model. Units of the left-hand and right-hand scales are mgal and cm, respectively. (e) Time series of atmospheric response. Units of the left-hand and right-hand scales are mgal and hPa, respectively.

2.25 arcseconds in latitude and longitude directions, respectively (over few days) in the time series of SG data in Fig. 2(d). These fluctu- (i.e., corresponding to about 50 m × 50 m, respectively). ations correlate with atmosphere pressure (compare Fig. 2(d) with We show the time series of the differences between observa- (e)). The coefficient of correlation between atmosphere pressure tions and the theoretical Earth tidal model in Fig. 2(a)–(d). The and SG data, which is low pass filtered (over 1 day), is 0.93. We show standard deviations of the differences are listed in Table 1. The the time series of local atmosphere pressure (see right-hand scale standard deviation of SG data is smaller than that of the other com- in Fig. 2(e)) recorded near the SG site, and represent atmosphere ponents. However, we can also see long-term period fluctuations response (see left-hand scale in Fig. 2(e)) using a response coeffi-

Table 1 Summary of tidal coefﬁcients at Tajimi GPS station and super-conducting gravimetry at Inuyama. Each second row indicates the estimated error.

Comp. Coef. Lag Std. M2 S2 K1 O1

Amp. Phase Amp. Phase Amp. Phase Amp. Phase

N-S 0.61 146 2.13 1.068 1.44 1.534 −2.91 0.928 −27.05 0.939 1.22 0.0006 0.023 0.0033 0.070 0.0014 0.056 0.0002 0.012

E-W 0.76 971 2.09 0.984 0.26 0.737 −32.45 0.996 −28.73 1.151 0.47 0.0006 0.026 0.0003 0.001 0.0010 0.049 0.0023 0.075

Vertical 0.94 −363 4.17 1.010 0.19 1.195 −0.91 1.025 3.86 0.977 0.78 0.0001 0.005 0.0005 0.015 0.0492 0.009 0.0001 0.001

Grav. 0.99 4 1.00 1.009 0.10 1.013 0.31 0.976 −0.196 0.995 0.04 0.0002 0.002 0.0007 0.005 0.0032 0.003 0.0001 0.001

Coef.: correlation coefﬁcients between observations and the theoretical Earth tidal model. Lag: differences between observed time series and the theoretical Earth tidal model. Positive and negative values represent observations that are lagging and leading with respect to the theoretical model. Unit is second of time. Std.: standard deviation of differences between observations and the theoretical Earth tidal model. Unit is centimeter. Amp.: ratio of the amplitudes between observations and the theoretical Earth model. Phase: phase differences between observations and the theoretical model. Positive and negative values represent observations that are lagging and leading with respect to the theoretical Earth tidal model. Unit is degree of angle. Grav.: super-conducting gravimeter at Inuyama station. 256 T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259

Fig. 3. Power spectral density of time series of the three components and ZTD at Tajimi. Observation period is April 1 to July 31, 2006. cient of atmosphere pressure value of −3.4 × 10−4 mgal/h Pa (Nawa (GPS N-S), 0.76 (GPS E-W), 0.94 (GPS Vertical), and 0.99 (Grav.) et al., 2009). These long-term period fluctuations of SG data are for the observation period (see Table 1). The best correlation is explained well corresponding to atmosphere response. The short- obtained for the SG data. The time lag between the observed gravity term period fluctuations (at periods less than a few days) of SG data data and the complete theoretical Earth tidal model is only 4 s with are mainly caused by the inaccuracy of the observations, the ocean respect to the Earth tidal model. The best correlation among the tidal model, and Earth structure model. We can see semi-diurnal displacement time series is obtained for the vertical component, and diurnal cyclic fluctuations in Fig. 2(d). As a result, we estimate because the amplitude of vertical components is the largest (over that the total error (including all frequencies) of the theoretical 40 cm) among the three displacement components. As a result, the Earth tidal model is less than 1 cm in this region. The error of each signal-to-noise ratio of the vertical component is better than that tidal constituent is at the millimeter level. of the other displacement components (see Fig. 1). We analyzed four major tidal constituents, M2, S2, K1, and O1. 2.2. Comparison of KPPP GPS with predictions from Earth tidal The theoretical M2 and O1 tidal constituents are well reproduced models by the observation. On the other hand, fitting of the S2 and K1 tidal constituents is rather poor, probably because double the period of In Fig. 1, we can easily see that KPPP GPS resolves the tidal the S2 tide (12.00 h) and a cycle of daily orbit discontinuities of the response of the Earth fairly precisely. However, these KPPP GPS precise ephemeris are at the same period. The period of the K1 tide time series include cyclic outliers (see Fig. 2 (a)–(c)). We believe that (23.93 h) and the orbital repeat period of the GPS satellite is also these outliers are caused by errors in the IGS final orbit ephemeris. the same, making it difficult to separate the K1 constituent from According to Griffiths and Ray (2009), IGS final orbit ephemeris has multipath-bias and orbital errors (Allinson et al., 2004; Choi et al., daily orbit discontinuities causing an apparent satellite positional 2004). The K1 and S2 tidal constituents are very noisy and it is thus discontinuity from the end of the day to the beginning of the next difficult to separate these tides from artificial signals. We observe a day, and these discontinuities reach a few centimeters. To improve phase lag between the theoretical model and the well-resolved M2 ◦ ◦ the positioning performance these effects were reduced by imple- tide from the gravity observation of 0.1 of angle, and 0.19 of angle menting a simple outlier removal filter which removes points that for GPS. Here we define positive value as lagging with respect to the are more than three standard deviations off the residual time series theoretical Earth tidal model. The M2 phase difference between between observation and the Earth tidal model. gravity and the vertical displacement component from GPS is less ◦ We obtain correlation coefficients between the theoretical Earth than 0.1 of angle. The signal-to-noise ratio of the M2 tidal con- tidal model, including OTL and body tide, and observations of 0.61 stituent is better than that of the other tidal constituent. The M2 T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259 257

Fig. 4. Hourly snapshots of displacements on the Japanese islands from 00:00:00–11:00:00 on April 1, 2006. Red and blue colors show uplift and subsidence of GPS stations, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) tidal constituent derived from the vertical component of the dis- 3. High resolution mapping of Earth tide response and placement is the most robust and aculeate observation. We employ discussion the M2 constituent of vertical component for our analysis. We used the KPPP GPS analysis method for all stations of the 2.3. Spectral analysis GEONET, which covers the Japanese islands at an average spacing of about 20 km. Fig. 4 gives hourly snap shots of displacement at all Fig. 3 shows the power spectral density (PSD) of the 4 months stations for April 1, 2006. These displacements include all the Earth of time series of KPPP GPS and troposphere zenith total delays tidal signals. We can clearly see the propagation of the Earth tide (ZTD) at Tajimi station. We find peaks in the PSD at various tidal over the Japanese islands. We can easily detect the wave front of modes for the KPPP GPS time series including diurnal, semi-diurnal, the Earth tide from east to west. We use this estimate of the spatio- ter-diurnal, and quarter-diurnal modes. The ratio of the tidal ampli- temporal change of sub-daily crustal deformation at all GPS sites tudes between the diurnal and quarter-diurnal modes is about to discuss the spatial variation of the Earth tidal response. 1/100, showing that KPPP GPS have amplitudes of less than a centimeter for the quarter-diurnal tide. It is noteworthy that there is no other peak in the PSD plot of KPPP GPS results. In general, the 3.1. The spatial distribution of phase differences peaks of troposphere ZTD are between 2 and 4 days in PSD (see Fig. 3). We do not find any peaks at various tidal periods in the PSD Fig. 5(a) shows the GPS-derived M2 phase of vertical compo- of troposphere ZTD. Hence, we can successfully separate the tidal nent with respect to the theoretical tidal model at 405 sites, where and tropospheric effects. the correlation coefficient is bigger than 0.5. These results show the 258 T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259

Fig. 5. The spatial perturbation of M2 tidal constituent between the observed vertical component of the Earth tidal field and the theoretical Earth tidal model on the Japanese islands. Active volcanoes are denoted by open squares. (a) The spatial distribution of phase differences between the observations and the theoretical Earth tidal model at GPS stations across Japan. Red and blue colors show phase lagging and leading with respect to the theoretical Earth tidal model, respectively. Unit is degree of angle. (b) The spatial distribution of the amplitude ratio between the observations and the theoretical Earth tidal model at GPS stations across Japan. Red and blue colors show observation values larger and smaller than the theoretical Earth tidal model, respectively. NKTZ is shown as open circle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.) spatial variation of the phase of the observed Earth tidal response tions in material properties of the Earth and to any observation with respect to the theoretical model, including the OTL and body error. tide. The average of phase lag of the vertical component over the ◦ Japanese islands is 0.11 ± 0.04 of angle, and most of the GPS sites 3.2. The spatial distribution of amplitude differences show a lag relative to the Earth tidal model. We hypothesize that this phase lag is mainly caused by the OTL model, the inelastic struc- Fig. 5(b) shows the amplitude ratio between the observed (ver- tures of the real Earth, and observation error. Because the phase lag tical component of GPS) and the theoretical M2 tide. The average represents an integrated effect of the underground structure of the amplitude ratio is 1.007 ± 0.003, indicating a slightly more compli- Earth and OTL modeling error, a thorough knowledge of the three- ant Earth compared to the theoretical Earth tidal model. The spatial dimensional structure, which is currently not available, would be distribution of the M2 tide amplitude ratio depends on the spatial needed to completely interpret the results. variations of rigidity and anelastic effects. Wahr (1981) showed On the other hand, according to the comparison between SG that the effects of rotation and ellipticity within the mantle on observations and the theoretical Earth tidal model, the accuracy tidal observation are about 1%. Moreover, Dehant (1987a,b) showed ◦ of the theoretical Earth tidal model is about 0.1 of angle in this an increase of the gravimetric factors by about 0.4% with respect study. This phase lag anomaly is slightly larger than errors of the to Wahr’s value and an increase of the Love numbers be about theoretical Earth tidal model. The phase differences between elas- 1.3% compared to the elastic case. The positive value of the aver- tic and inelastic Earth models are smaller than the observation age amplitude ratio is consistent with prediction by Fu and Sun error (Dehant, 1987a) and therefore we can neglect inelastic effects. (2007). The Pacific Ocean side has continuous subduction zones As a result, we attribute the observed phase lag to lateral varia- where the downgoing slab results in anelastic structure that rela- T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259 259 tively more rigid than in other regions. These features of positive Acknowledgments amplification indentified from the M2 tidal response can also be compared to the three-dimensional velocity structures obtained We thank Mr. T. Takasu for providing us his GPS analysis codes from seismic tomography (Fu and Sun, 2007). According to Fu and called “GPSTools ver. 0.6.3”. The authors highly appreciate Dr. Koji Sun (2007), the theoretical gravimetric factor change in the Kyushu Matsumoto, Dr. Harald Schuh and an anonymous reviewer for their district is predicted to be 0.08% larger than for the Hokkaido region. careful reviews and helpful comments. We gratefully acknowledge Our result shows that the tidal amplitude in the Kyushu region Dr. Mark Simons for valuable comments and improving the English. is about 1.0–1.5 ± 0.3% (which corresponds to a change of about We have used the GOTIC2 program package (Matsumoto et al., 1 mm) larger than that of the Hokkaido region. This pattern agrees 2001) for the Earth tidal computation. This study is partly supported with the prediction from the Earth tidal model which is based on by Grants-in-Aid for Scientific Research of MEXT of Japan: No. seismic tomography, too. 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