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Journal of Geodynamics 48 (2009) 253–259

Contents lists available at ScienceDirect

Journal of Geodynamics

journa l homepage: ht tp : / /www.e lsev ier .com/ locate / jog

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

akeo Itoa,c,∗, Makoto Okubob, Takeshi Sagiyaa

Research Center for Seismology, Volcanology and Disaster Mitigation, Graduate School of Environmental Studies, Nagoya University, D2-2(510), Furo-cho,hikusa-ku, Nagoya City, Aichi 464-8602, JapanTono Research Institute of Earthquake Science, 1-63 Akeyo-cho, Yamanouchi, Mizunami City, Gifu 509-6132, JapanSeismological Laboratory, California Institute of Technology, Pasadena, CA 91125, USA

r t i c l e i n f o

eywords:PPP GPSarth tidesEONET

a b s t r a c t

We observe the Earth tidal fields at diurnal and semi-diurnal periods using Kinematic Precise PointPositioning (KPPP) GPS analysis. Our KPPP GPS solutions compare well with super-conducting gravimeter(SG) observations and a theoretical Earth tidal model, that includes both ocean tide loading model and

body tides. We make a high resolution map of the observed Earth tidal response fields using the JapaneseGEONET GPS network which consists of 1200 sites. We find that: (1) the average phase of GPS datalags 0.11 ± 0.04◦ from our theoretical Earth tidal model, (2) the average amplitude ratio between GPSand the theoretical Earth tidal model is 1.007 ± 0.003, (3) the amplitude in the Kyushu district is about1.0–1.5 ± 0.3% larger than in the Hokkaido district, and (4) the amplitude at the Japan Sea side is about0.5 ± 0.2% larger than that at the Pacific Ocean side. These results suggest that we may be able to place

cture

constraints on Earth stru

. Introduction

Historically, great efforts have been made to accurately measurehe Earth tides (e.g., Richter and Warburton, 1998). There have been

any theoretical studies of the Earth’s structure and tidal responsefter Love (1909). Tidal deformations were studied for a sphericallyymmetric, perfectly elastic and isotropic Earth (e.g., Longman,963; Saito, 1967; Farrell, 1972). The response of the Earth to

unisolar attraction is expressed by amplitudes and phases of tidalonstituents, together with the ocean tide loading (OTL) effectse.g., Lambert et al., 1998). The tidal response is mainly related tohe Earth’s elastic properties and local variations in elastic structureMantovani et al., 2005; Fu and Sun, 2007). Thus, the Earth’s tidalesponse can be used to investigate the inner structure. Variousnstruments including super-conducting gravimeters (SG), strain

eters, and tilt observations provide precise point measurementsf tidal responses. However, we have lacked observations with goodpatial coverage. Because of the expense of instruments and the dif-

culties in establishing low-noise sites, it has been difficult to makeonsistent observations to reveal the spatial heterogeneity of theolid Earth tidal field.

∗ Corresponding author at: Research Center for Seismology, Volcanology andisaster Mitigation, Graduate School of Environmental Studies, Nagoya University,2-2(510), Furo-cho, Chikusa-ku, Nagoya City, Aichi 464-8602, Japan.el.: +81 52 789 3038; fax: +81 52 789 3047.

E-mail address: takeo ito@nagoya-u.jp (T. Ito).

264-3707/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.oi:10.1016/j.jog.2009.09.012

using GPS-derived tidal information.© 2009 Elsevier Ltd. All rights reserved.

In previous studies, periodic signals in sub-daily estimates ofpositions were obtained from Global Positioning System (GPS) data.The estimation of sub-daily positions is commonly used for OTL andice movement studies (e.g., King et al., 2003, 2005; Allinson et al.,2004). A widely used procedure to produce the sub-daily solutionsis to segment the continuous GPS data into batches of a few hours(typically 0.5–4 h) and then in order to generate station coordinatesat sub-daily intervals using a differential GPS analysis approach andone can constrain the relative crustal deformation with respect toa GPS station that is several hundred kilometers away. Here in con-trast, we employ a Kinematic Precise Point Positioning (KPPP) GPSapproach, which can estimate the position every 30 s at sub-dailyintervals and without need for a specific reference point. We con-struct a high resolution map of the Earth tidal response field forJapan which is obtained from time series data at 1200 GPS sites inJapan.

2. Observation data and analysis method

We use the Japanese continuous GPS network called the GPSEarth Observation Network (GEONET) that has been operating since1996 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 beenremarkably improved by the development of new analytical tech-niques. KPPP GPS has attracted the attention of the GPS communityas it can provide a centimeter level positioning accuracy with asingle GPS receiver, which is almost comparable to that obtained

254 T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259

F P GPS( servat olor in

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ig. 1. Example of time series of each observation. (a)–(c) Three components of KPPd) Time series of SG observation at Inuyama (near the Tajimi GPS station). The obheoretical Earth tidal model, respectively. (For interpretation of the references to c

y differential GPS. In this study, we applied KPPP GPS analysisith the GPS Tools ver.0.6.3 software to estimate the position of allPS sites of GEONET every 30 s (Takasu and Kasai, 2005; Takasu,006). GPS Tools is a Global Navigation Satellite Systems (GNSS)nalysis software package. The strategy of this analysis software isased on the extended Kalman filter (EKF, forward/backward) withGS (International GNSS Service) final ephemerides, Earth rotationarameters, and two satellite clock coefficients (IGS final and CODECenter of Orbit Determination for Europe)). These clock coeffi-ients of IGS final and CODE are made by different strategies. Thearge difference of these strategies is that the sampling rates ofGS Final and CODE clock coefficients are 300 and 30 s, respec-ively. In order to estimate precise coefficients at 30 s intervals, IGSnal satellite clock coefficients are used as a base and the clockoefficients are interpolated every 30 s, using CODE clock informa-ion. Additionally, the measurement model of this analysis softwareontains precise measurement corrections such as antenna phaseenter offsets, phase-windup effect, relativistic effects and variousPS-specific Solar Radiation Pressure models. Troposphere zenith

otal delays and horizontal troposphere gradients at each GPS sitere estimated at each epoch assuming a random-walk model. Timeeries of coordinates are estimated adapting a white-noise stochas-ic model. The data are not bias-fixed.

.1. Compare super-conducting gravimeter with Earth tidalodel

We analyzed about 4 months of data, from April 1 to July 31,006, for all of GEONET. We estimated the position of each GPS sitet 30 s intervals without any Earth tidal corrections. Here we define

he Earth tide as the sum of body tide and OTL. Before comparinghe KPPP GPS solution with the Earth tidal model, we evaluate theccuracy of the both the body tide and OTL models by compar-ng with observations from a SG. The accuracy of SG observationss smaller than one microgal (Imanishi et al., 2004). One micro-

displacement at Tajimi station (see Fig. 5(a)) obtained by the KPPP analysis method.tion period is 1 month (May, 2006). Red and green lines are observations and the

this figure legend, the reader is referred to the web version of the article.)

gal of gravity change is equivalent to about 3.2 mm of relativeheight change, which is better than the centimeter accuracy of theKPPP GPS data. SG observations are characterized by high sensitiv-ity, long-term stability, and fidelity over a wide frequency rangethe spans from the seismic normal mode period range to secularchanges.

Fig. 1 shows the time series for the period of May 1, 2006 toMay 30, 2006 of displacements at GPS station 950292 (Tajimi)and the time series of relative gravity change measured by a SGlocated at the Inuyama observation station (belonging to NagoyaUniversity). The distance between the Tajimi GPS station and the SGstation at Inuyama is about 8 km. This SG instrument (CT #036) wasinstalled in a tunnel with a 25 m-long and 40 m-depth in 1999. Inthis study we used the TIDE filter output data of the SG. The ampli-tude response of the TIDE filter is flat for periods longer than 1 min.The scale factor of this SG is −623.5 nm s−2/V, as obtained by Nawaet al. (2009). The green curves represent the displacement andgravity time series predicted from a theoretical Earth tide modelincluding OTL obtained by the NAO.99Jb model (Matsumoto et al.,2000). The NAO.99b model is based on assimilating about 5 yearsof TOPEX/POSEIDON altimeter data into a numerical barotropichydrodynamical model. Both TOPEX/POSEIDON data and coastaltidal gauge data are assimilated into the regional high resolutionocean tide model around Japan (NAO.99Jb). The accuracy of recentglobal OTL models is believed to be high, except for in regions withshallow seas and for areas having complex bathymetry and coast-line. For example, according to Matsumoto et al. (2000), the vectordifferences for the M2 constituent between NAO.99b and GOT99.2b(Ray, 1999) are on the order of 1 cm or smaller almost everywherein the open seas worldwide. The synthetic displacements induced

by OTL and body tides were estimated using the NAO.99Jb model,which utilizes the mass loading Green’s functions for displacementand is based on the 1066A Earth model (see Matsumoto et al., 2001).The body tide model is based on the elastic 1066A Earth model, too.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

F e theod reticar ht-ha

2(

tssp

TS

Cmomr

ig. 2. (a)–(c) Time series of the differences between KPPP GPS observations and thisplayed. (d) Time series of the differences between SG observations and the theoespectively. (e) Time series of atmospheric response. Units of the left-hand and rig

.25 arcseconds in latitude and longitude directions, respectivelyi.e., corresponding to about 50 m × 50 m, respectively).

We show the time series of the differences between observa-

ions and the theoretical Earth tidal model in Fig. 2(a)–(d). Thetandard deviations of the differences are listed in Table 1. Thetandard deviation of SG data is smaller than that of the other com-onents. However, we can also see long-term period fluctuations

able 1ummary of tidal coefficients at Tajimi GPS station and super-conducting gravimetry at I

Comp. Coef. Lag Std. M2 S

Amp. Phase A

N-S 0.61 146 2.13 1.068 1.44 10.0006 0.023 0

E-W 0.76 971 2.09 0.984 0.26 00.0006 0.026 0

Vertical 0.94 −363 4.17 1.010 0.19 10.0001 0.005 0

Grav. 0.99 4 1.00 1.009 0.10 10.0002 0.002 0

oef.: correlation coefficients between observations and the theoretical Earth tidal mododel. Positive and negative values represent observations that are lagging and leading w

f differences between observations and the theoretical Earth tidal model. Unit is centimodel. Phase: phase differences between observations and the theoretical model. Posit

espect to the theoretical Earth tidal model. Unit is degree of angle. Grav.: super-conduct

retical Earth tidal model. The NS, EW, and vertical components of displacement arel Earth tidal model. Units of the left-hand and right-hand scales are mgal and cm,

nd scales are mgal and hPa, respectively.

(over few days) in the time series of SG data in Fig. 2(d). These fluctu-ations correlate with atmosphere pressure (compare Fig. 2(d) with(e)). The coefficient of correlation between atmosphere pressure

and SG data, which is low pass filtered (over 1 day), is 0.93. We showthe time series of local atmosphere pressure (see right-hand scalein Fig. 2(e)) recorded near the SG site, and represent atmosphereresponse (see left-hand scale in Fig. 2(e)) using a response coeffi-

nuyama. Each second row indicates the estimated error.

2 K1 O1

mp. Phase Amp. Phase Amp. Phase

.534 −2.91 0.928 −27.05 0.939 1.22

.0033 0.070 0.0014 0.056 0.0002 0.012

.737 −32.45 0.996 −28.73 1.151 0.47

.0003 0.001 0.0010 0.049 0.0023 0.075

.195 −0.91 1.025 3.86 0.977 0.78

.0005 0.015 0.0492 0.009 0.0001 0.001

.013 0.31 0.976 −0.196 0.995 0.04

.0007 0.005 0.0032 0.003 0.0001 0.001

el. Lag: differences between observed time series and the theoretical Earth tidalith respect to the theoretical model. Unit is second of time. Std.: standard deviationeter. Amp.: ratio of the amplitudes between observations and the theoretical Earthive and negative values represent observations that are lagging and leading withing gravimeter at Inuyama station.

256 T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259

ents a

ceetatatEt

2m

rttAdddtmab

t

Fig. 3. Power spectral density of time series of the three compon

ient of atmosphere pressure value of −3.4 × 10−4 mgal/h Pa (Nawat al., 2009). These long-term period fluctuations of SG data arexplained well corresponding to atmosphere response. The short-erm period fluctuations (at periods less than a few days) of SG datare mainly caused by the inaccuracy of the observations, the oceanidal model, and Earth structure model. We can see semi-diurnalnd diurnal cyclic fluctuations in Fig. 2(d). As a result, we estimatehat the total error (including all frequencies) of the theoreticalarth tidal model is less than 1 cm in this region. The error of eachidal constituent is at the millimeter level.

.2. Comparison of KPPP GPS with predictions from Earth tidalodels

In Fig. 1, we can easily see that KPPP GPS resolves the tidalesponse of the Earth fairly precisely. However, these KPPP GPSime series include cyclic outliers (see Fig. 2 (a)–(c)). We believe thathese outliers are caused by errors in the IGS final orbit ephemeris.ccording to Griffiths and Ray (2009), IGS final orbit ephemeris hasaily orbit discontinuities causing an apparent satellite positionaliscontinuity from the end of the day to the beginning of the nextay, and these discontinuities reach a few centimeters. To improvehe positioning performance these effects were reduced by imple-

enting a simple outlier removal filter which removes points thatre more than three standard deviations off the residual time seriesetween observation and the Earth tidal model.

We obtain correlation coefficients between the theoretical Earthidal model, including OTL and body tide, and observations of 0.61

nd ZTD at Tajimi. Observation period is April 1 to July 31, 2006.

(GPS N-S), 0.76 (GPS E-W), 0.94 (GPS Vertical), and 0.99 (Grav.)for the observation period (see Table 1). The best correlation isobtained for the SG data. The time lag between the observed gravitydata and the complete theoretical Earth tidal model is only 4 s withrespect to the Earth tidal model. The best correlation among thedisplacement time series is obtained for the vertical component,because the amplitude of vertical components is the largest (over40 cm) among the three displacement components. As a result, thesignal-to-noise ratio of the vertical component is better than thatof the other displacement components (see Fig. 1).

We analyzed four major tidal constituents, M2, S2, K1, and O1.The theoretical M2 and O1 tidal constituents are well reproducedby the observation. On the other hand, fitting of the S2 and K1 tidalconstituents is rather poor, probably because double the period ofthe S2 tide (12.00 h) and a cycle of daily orbit discontinuities of theprecise ephemeris are at the same period. The period of the K1 tide(23.93 h) and the orbital repeat period of the GPS satellite is alsothe same, making it difficult to separate the K1 constituent frommultipath-bias and orbital errors (Allinson et al., 2004; Choi et al.,2004). The K1 and S2 tidal constituents are very noisy and it is thusdifficult to separate these tides from artificial signals. We observe aphase lag between the theoretical model and the well-resolved M2tide from the gravity observation of 0.1◦ of angle, and 0.19◦ of angle

for GPS. Here we define positive value as lagging with respect to thetheoretical Earth tidal model. The M2 phase difference betweengravity and the vertical displacement component from GPS is lessthan 0.1◦ of angle. The signal-to-noise ratio of the M2 tidal con-stituent is better than that of the other tidal constituent. The M2

T. Ito et al. / Journal of Geodynamics 48 (2009) 253–259 257

F 1:00:0r reader

tpt

2

o(mtt1tnpFoa

ig. 4. Hourly snapshots of displacements on the Japanese islands from 00:00:00–1espectively. (For interpretation of the references to color in this figure legend, the

idal constituent derived from the vertical component of the dis-lacement is the most robust and aculeate observation. We employhe M2 constituent of vertical component for our analysis.

.3. Spectral analysis

Fig. 3 shows the power spectral density (PSD) of the 4 monthsf time series of KPPP GPS and troposphere zenith total delaysZTD) at Tajimi station. We find peaks in the PSD at various tidal

odes for the KPPP GPS time series including diurnal, semi-diurnal,er-diurnal, and quarter-diurnal modes. The ratio of the tidal ampli-udes between the diurnal and quarter-diurnal modes is about/100, showing that KPPP GPS have amplitudes of less than a cen-imeter for the quarter-diurnal tide. It is noteworthy that there is

o other peak in the PSD plot of KPPP GPS results. In general, theeaks of troposphere ZTD are between 2 and 4 days in PSD (seeig. 3). We do not find any peaks at various tidal periods in the PSDf troposphere ZTD. Hence, we can successfully separate the tidalnd tropospheric effects.

0 on April 1, 2006. Red and blue colors show uplift and subsidence of GPS stations,is referred to the web version of the article.)

3. High resolution mapping of Earth tide response anddiscussion

We used the KPPP GPS analysis method for all stations of theGEONET, which covers the Japanese islands at an average spacingof about 20 km. Fig. 4 gives hourly snap shots of displacement at allstations for April 1, 2006. These displacements include all the Earthtidal signals. We can clearly see the propagation of the Earth tideover the Japanese islands. We can easily detect the wave front ofthe Earth tide from east to west. We use this estimate of the spatio-temporal change of sub-daily crustal deformation at all GPS sitesto discuss the spatial variation of the Earth tidal response.

3.1. The spatial distribution of phase differences

Fig. 5(a) shows the GPS-derived M2 phase of vertical compo-nent with respect to the theoretical tidal model at 405 sites, wherethe 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 Japaneseislands. Active volcanoes are denoted by open squares. (a) The spatial distribution of phase differences between the observations and the theoretical Earth tidal model atG respes tical Ev is shot

swtJsttrEdn

oostteA

PS stations across Japan. Red and blue colors show phase lagging and leading withpatial distribution of the amplitude ratio between the observations and the theorealues larger and smaller than the theoretical Earth tidal model, respectively. NKTZhe reader is referred to the web version of the article.)

patial variation of the phase of the observed Earth tidal responseith respect to the theoretical model, including the OTL and body

ide. The average of phase lag of the vertical component over theapanese islands is 0.11 ± 0.04◦ of angle, and most of the GPS siteshow a lag relative to the Earth tidal model. We hypothesize thathis phase lag is mainly caused by the OTL model, the inelastic struc-ures of the real Earth, and observation error. Because the phase lagepresents an integrated effect of the underground structure of thearth and OTL modeling error, a thorough knowledge of the three-imensional structure, which is currently not available, would beeeded to completely interpret the results.

On the other hand, according to the comparison between SGbservations and the theoretical Earth tidal model, the accuracyf the theoretical Earth tidal model is about 0.1◦ of angle in this

tudy. This phase lag anomaly is slightly larger than errors of theheoretical Earth tidal model. The phase differences between elas-ic and inelastic Earth models are smaller than the observationrror (Dehant, 1987a) and therefore we can neglect inelastic effects.s a result, we attribute the observed phase lag to lateral varia-

ct to the theoretical Earth tidal model, respectively. Unit is degree of angle. (b) Thearth tidal model at GPS stations across Japan. Red and blue colors show observationwn as open circle. (For interpretation of the references to color in this figure legend,

tions in material properties of the Earth and to any observationerror.

3.2. The spatial distribution of amplitude differences

Fig. 5(b) shows the amplitude ratio between the observed (ver-tical component of GPS) and the theoretical M2 tide. The averageamplitude ratio is 1.007 ± 0.003, indicating a slightly more compli-ant Earth compared to the theoretical Earth tidal model. The spatialdistribution of the M2 tide amplitude ratio depends on the spatialvariations of rigidity and anelastic effects. Wahr (1981) showedthat the effects of rotation and ellipticity within the mantle ontidal observation are about 1%. Moreover, Dehant (1987a,b) showedan increase of the gravimetric factors by about 0.4% with respect

to Wahr’s value and an increase of the Love numbers be about1.3% compared to the elastic case. The positive value of the aver-age amplitude ratio is consistent with prediction by Fu and Sun(2007). The Pacific Ocean side has continuous subduction zoneswhere the downgoing slab results in anelastic structure that rela-

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T. Ito et al. / Journal of Ge

ively more rigid than in other regions. These features of positivemplification indentified from the M2 tidal response can also beompared to the three-dimensional velocity structures obtainedrom seismic tomography (Fu and Sun, 2007). According to Fu andun (2007), the theoretical gravimetric factor change in the Kyushuistrict is predicted to be 0.08% larger than for the Hokkaido region.ur result shows that the tidal amplitude in the Kyushu region

s about 1.0–1.5 ± 0.3% (which corresponds to a change of aboutmm) larger than that of the Hokkaido region. This pattern agreesith the prediction from the Earth tidal model which is based on

eismic tomography, too. In addition, the amplitude ratio on theapan Sea side is about 0.5 ± 0.2% larger than that of the Pacificcean side. Almost all areas of larger amplitude ratio are locatedt the backside of a volcanic front. In particular, a zone of high-train-rate, called the Niigata-Kobe Tectonic Zone (NKTZ), shows aarger amplitude ratio than other regions (see Fig. 5(b)). The high-train-rate zone, which is approximately 500 km long in the NE–SEirection and approximately 100 km wide, undergoes contraction

n the WNW–ESE direction (about 10−7/year) (Sagiya et al., 2000).ccording to Nakajima and Hasegawa (2007), the low-velocity zonextends from the upper mantle to the upper crust beneath the mid-le part of NKTZ where volcanoes are concentrated. These resultsuggest that we may be able to place constraints on Earth structuresing GPS-derived tidal information. Latychev et al. (2009) showedhe possibility of performing tidal tomographic inversion usingpace geodetic methods. Their suggestion was limited to longerave lengths of a few thousand kilometers, but this independent

nformation can be potentially fundamental constraints on mantleechanical structure.

. Conclusion

We generated a high resolution map of the regional Earth tidesesponse using KPPP GPS observations of the Japanese islands. Com-arisons of the KPPP GPS results with SG observations confirmedhe validity of the KPPP GPS analyses. We checked that the accu-acy of three components (NS, EW, Vertical) and four major tidalonstituents, M2, S2, K1, and O1 from KPPP GPS observation. Asresult, we conclude that the M2 tidal constituent derived from

he vertical component of the displacement is the most robust andculeate observation. Our KPPP GPS-based of Earth tides analysisor all stations of GEONET finds following features:

1) The average phase of GPS data is delayed from the syntheticEarth tidal model by 0.11 ± 0.04◦ of angle across the Japaneseislands. Most of the GPS sites show a lag relative to the Earthtidal model.

2) The average amplitude ratio between GPS and the syntheticEarth tidal model is 1.007 ± 0.003, indicating a slightly morecompliant Earth compared to the synthetic Earth tidal model.This positive trend of amplitude agrees with predictions frominelastic Earth tidal models.

3) The amplitude in the Kyushu district is about 1.0–1.5 ± 0.3%(which corresponds to a change of to about 1 mm) larger thanin the Hokkaido district.

4) The amplitude on the Japan Sea side is about 0.5 ± 0.2% largerthan that on the Pacific Ocean side.

These observations may provide new constraints on theechanical structure under Japan. For instance, this informationight be used to invert for three-dimensional elastic structure

nside the Earth. Furthermore, temporal changes of the tidalesponse may be monitored to provide information about thehanging inelastic conditions near active faults.

mics 48 (2009) 253–259 259

Acknowledgments

We thank Mr. T. Takasu for providing us his GPS analysis codescalled “GPSTools ver. 0.6.3”. The authors highly appreciate Dr. KojiMatsumoto, Dr. Harald Schuh and an anonymous reviewer for theircareful reviews and helpful comments. We gratefully acknowledgeDr. Mark Simons for valuable comments and improving the English.We have used the GOTIC2 program package (Matsumoto et al.,2001) for the Earth tidal computation. This study is partly supportedby Grants-in-Aid for Scientific Research of MEXT of Japan: No.20740254 and JSPS Postdoctoral Fellowships for Research Abroad.

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