Transcontinental tidal transect: European Atlantic coast-Southern Siberia-Russian Pacific coast

ISSN 1069-3513, Izvestiya, Physics of the Solid Earth, 2008, Vol. 44, No. 5, pp. 388–400. © Pleiades Publishing, Ltd., 2008. Original Russian Text © V.Yu. Timofeev, B. Ducarme, M. van Ruymbeke, P.Yu. Gornov, M. Everaerts, E.I. Gribanova, V.A. Parovyshnii, V.M. Semibalamut, G. Woppelmann, D.G. Ardyukov, 2008, published in Fizika Zemli, 2008, No. 5, pp. 42–54.

Transcontinental Tidal Transect: European Atlantic Coast–Southern Siberia–Russian Pacific Coast V. Yu. Timofeeva, B. Ducarmeb, M. van Ruymbekec, P. Yu. Gornovd, M. Everaertsc, E. I. Gribanovae, V. A. Parovyshniif, V. M. Semibalamute, G. Woppelmanng, and D. G. Ardyukova a

Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch (SB), Russian Academy of Sciences (RAS), Novosibirsk, Russia b Chercheur Qualifie FNRS, Observatoire Royal de Belgique, Av. Circulaire 3, 1180 Brussels, Belgium c Observatoire Royal de Belgique, Av. Circulaire 3, 1180 Brussels, Belgium d Institute of Tectonics and Geophysics, Far East Division, RAS, ul. Kim Yu Chena 65, Khabarovsk, 680063 Russia e Geophysical Service, Siberian Branch, RAS, Novosibirsk, Russia f Institute of Marine Geology and Geophysics, Far East Division, RAS, ul. Nauki 2, Yuzhno-Sakhalinsk, 693002 Russia g Centre Littoral de Géophysique, Université de La Rochelle, Av. Michel Crépeau, 17042 La Rochelle, France Received April 26, 2007

Abstract—The paper presents results of measurements with digital tidal LaCoste–Romberg gravimeters on the European Atlantic coast–Southern Siberia–Russian Pacific coast transect in 1995–2005. The transect includes four West European (Chizé, Ménesplet, Mordelles, and Wikle), two South Siberian (Klyuchi and Talaya), and two Far Eastern (Zabakalskoe and Yuzhno-Sakhalinsk) stations. Gravimetric measurements at the Talaya station (SW Baikal rift zone) are supplemented by long-term laser extensometer observations. The position of the stations within the rectangle (45°–55°N, 0.4°–142°E) allows one to assess existing tidal strain models (WD93 and DDW99) and various ocean tide models (SCW80, CSR3, FES95, ORI96, CSR4, FES02, GOT00, NAO99, and TPX06). Data of intracontinental stations (with a small ocean effect at distances of 2000–3000 km) agree well with the DDW99 tidal strain model (with regard to the mantle viscosity). The uncertainty of digital tidal gravity measurements is 0.25%. Results of laser extensometer measurements are at the same accuracy level. Then, the Love and Shida numbers calculated at midlatitudes of the intracontinental zone of Eurasia from combined data are h = 0.6077 ± 0.0008, k = 0.3014 ± 0.0001, and l = 0.0839 ± 0.0001. The analysis of results of Pacific and Atlantic stations located at distances of 30–300 km from the ocean showed that the FES02, CSR4, GOT00, NAO99, and TPX06 ocean tide models are preferable. PACS numbers: 91.10.Tq DOI: 10.1134/S1069351308050042

INTRODUCTION As is known, the tidal effect on the Earth can be calculated very accurately from astronomic data [Melchior, 1983]. The tidal response of the Earth is determined by current models in various regions at the accuracy level of experimental determinations [Melchior, 1992]. Until recently, measurements made with modern instrumentation were scarce in North Asia [Saritcheva et al., 1998; Molodensky, 1984, 2001; Timofeev et al., 2002; Timofeev, 2004]. However, precise models of the tidal effect are required for fundamental studies of the physics of the Earth and for calculating tidal corrections to measurements of gravity, high-precision geophysical measurements, and satellite altimetry

[Avsyuk, 1996, 1997; Kopaev, 2000; Kalish et al., 2000; Weber et al., 2001]. Tidal gravity studies are the most efficient tool for verifying and improving earth tide deformation models and ocean tide models [Francis and Melchior, 1996]. Profile measurements of earth tides in a unified metrological system have been widely tested in world practice [Crossley et al., 1999]. We selected digital LaCoste–Romberg gravimeters as the most mobile high-precision systems of measurements. More accurate stationary cryogenic gravimeters are most suitable for spectral tidal studies in the resonance range of the liquid and solid core of the Earth [Richter, 1995]. The European Atlantic coast–Southern Siberia–Russian Pacific coast tidal transect crosses the Eurasian conti-

388

TRANSCONTINENTAL TIDAL TRANSECT

389

Talaya, Baikal rift Zabaikalskoe

Klyuchi, Novosibirsk

Yuzhno-Sakhalinsk

Wikle, Belgium Chizé, France

Fig. 1. Position of stations on the transcontinental tidal profile.

nent from 0.4° to 142°E at latitudes of 45°–55°N. The profile includes a few coastal stations at distances of 30−70 km from the Atlantic and Pacific oceans; a reference station for testing instruments in Wikle, Brussels; and stations located in the central part of the continent (3000 km from the ocean) (Fig.1). The studies were conducted from 1995 through 2005. Tidal measurements were first made in eastern Russia. Gravity measurements at the Talaya station located in the southwestern Baikal rift zone were supplemented by laser extensometer measurements in a gallery at a depth of 90 m [Orlov, 2003]. Multidisciplinary studies at intracontinental stations are used for the determination of the tidal Love and Shida numbers. The goal of studies at the profile stations is to gain constraints on contemporary tidal strain models (WD93 and DDW99) and ocean tide models (SCCW80, CSR3, FES95, ORI96, CSR4, FES02, GOT00, NAO99, and TPX06). METHOD OF GRAVITY STUDIES Tidal analysis of diurnal and semidiurnal tidal waves provides determinations of the amplitude A and phase lag α (relative to the astronomic tide Aí), i.e., the vector A(A, α). The amplitude factor δ is the ratio A/Aí [Melchior, 1983]. A model tide is constructed on the basis of the Earth’s tidal response amplitude R (R = Aí · δDDW, 0), for example, from the DDW99 model [Dehant et al., 1999], and the ocean loading vector L(L, λ) calculated with the use of various ocean models. The theoretical vector Am(Am, αm) is given by the expression Am = R + L.

(1)

The amplitude factor δm, defined as the ratio Am/Aí, is used for the calculation of tidal corrections [Zahran IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

et al., 2005] and our major goal is to determine it correctly for Siberian regions (up to the ocean). We can assess the adequacy of the earth and ocean tide models by comparing A and Am, which requires careful calibration and determination of the instrumental lag necessary for estimating the phase lag α. A more effective technique is the calculation of the residual vector X: X = (A – R) – L = B – L, (2) showing actual agreement between models and observations. The vector R depends on the choice of the Earth’s model response to the tidal force. We note here such current models as the model with an elastic Earth [Wahr, 1981] and the DDW99 model, incorporating effects of mantle inelasticity; the MAT01 model [Mathews, 2001] is very close in the amplitude factor value to DDW99. The loading vector L(L, λ) has been studied by many authors (e.g., [Farrell, 1972; Pertsev, 1976]). The SCW80 model [Schwiderski, 1980] was constructed by assimilating data of tide-gauge stations and extrapolating them to the oceanic coasts and islands. For a long time, this model was used as a base model for calculations of corrections in geodesy and geophysics. A series of ocean tide models based on satellite altimetry data have been developed since 1994 [Eanes et al., 1994]. Models of the first generation were CSR3 [Eanes et al., 1995], FES95 [Le Provost et al., 1994], and ORI96 [Matsumoto et al., 1995]. Models that were recently developed are CSR4, NAO99, GOT00, FES02, and TPX06 [Shum et al., 1997; Ray, 1999; Matsumoto et al., 2000; Baker and Bos, 2001, 2003]. Observations at profile stations were made with LCR402, LCR1006, and LCR906 gravimeters, No. 5

2008

390

TIMOFEEV et al. nm/s2

Location:Instrument:Measurement 1 (?)

2000 1500 1000 500 0

March 13, 1997

March 23, 1997

April 2, 1997

April 12, 1997

Fig. 2. Talaya station, 1.5-month curve over the period from March 10, 1997, to April 20, 1997.

equipped with a feedback system [van Ruymbeke et al., 1995, 1998] whose frequency-modulated output signal is recorded. The MICRODAS microprocessor records the frequency with a 1-min sampling interval [van Ruymbeke et al., 1999]. Data are accumulated in a power-autonomous memory of a storage; the atmospheric pressure and the room temperature are also recorded with the help of the EDAS system. Preprocessing and preliminary analysis of data and analysis of instrumental calibration data are performed with the help of the Tsoft program [van Camp and Vauterin, 2005]. Hourly data were processed with the help of the ETERNA 3.4 classical tidal software package [Wenzel, 1996] or the VAV04 code [Venedikov et al., 2003]. Examples of records obtained with the LCR402 Table 1. Calibrations of LCR402 gravimeter at the Zabaikalskoe station (K = 1.06188 nm/s2 per 0.01 scale division)

Epoch

Julian date

April 30, 2001 May 30, 2001 June 29, 2001 October 9, 2001 November 18, 2001 February 13, 2002 June 9, 2002 July 5, 2002 October 10, 2002 November 15, 2002 March 26, 2003 October 2, 2003

52030.00 52060.00 52090.00 52192.00 52232.00 52319.00 52435.00 52461.00 52558.00 52594.00 52665.50 52914.50

Instrument Calibration response d, factor 1 Hz per C = K/d, 0.1 scale nm/(s2 Hz) division 2.711 2.648 2.655 2.707 2.715 2.621 2.718 2.751 2.715 2.630 2.739 2.740

0.3917 0.4009 0.4000 0.3923 0.3911 0.4052 0.3907 0.3860 0.3910 0.4038 0.3876 0.3875

gravimeter in the underground gallery of the Talaya seismic station are given in Figs. 2 and 3. Routine calibration of records of the LCR402 and LCR906 gravimeters was performed by the standard procedure consisting of ten shifts [van Ruymbeke, 1998, 2001]. Apart from usual calibration, the LCR1006 gravimeter was calibrated automatically with the help of a small motor installed on a micrometer and a special calibration program. The calibration sheet is shown in Table 1 for the Zabaikalskoe station. Further, a regression procedure (by the Nakai method) was used for the determination of the sensitivity changes in 48-h intervals. The gravimeters were tested at the reference station of the International Center for Earth Tides (50.7986°N, 4.3581°E; Brussels) with the use of the gravity factor δO1 = 1.1530 [Melchior, 1994]. The results of comparison are as follows. The analysis of a 136-day Brussels record of the O1 wave [van Ruymbeke et al., 2001] yields δ = 1.1560 ± 0.0016 and α = –0.113° ± 0.078° for the LCR1006 gravimeter. The values of δ = 1.154 ± 0.014 and α = –0.19° ± 0.72° are obtained for the LCR402 gravimeter from a 50-day record of 1998, which agrees well with the Brussels system. The results of testing the instrument before its installation at Russian Far East stations (35 days, 2001) yielded δ = 1.1540 ± 0.0040 and α = 0.061° ± 0.195°. The LCR906 gravimeter was compared with the SCINTREX CG3M S265 gravimeter at the Ménesplet station. The analysis of a 72-day record of the M2 wave gave δ = 1.1879 ± 0.0015 and α = 6.10° ± 0.07°, which agrees with the results obtained for the LCR906 gravimeter (δ = 1.1896 ± 0.0004 and α = 6.02° ± 0.02°). METHOD OF EXTENSOMETER DATA ANALYSIS Observations with a two-coordinate laser extensometer have been conducted at the Talaya station since the end of the 1980s [Semibalamut et al., 1995]. Continuous measurements date from 1995. The system

IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

No. 5

2008

TRANSCONTINENTAL TIDAL TRANSECT nm/s2 10000

391

Location:Instrument:Measurement 1 (?)

8000 6000 4000 2000 0 July 1, 1996

January 1, 1997

Fig. 3. Talaya station, record over the period from April 1996 to October 1997 (1.5 years). Seasonal drift is due to the temperature variation in the underground gallery of the station (from +8°C … +12°C in winter to +22°C …+28°C in summer).

includes a laser, system of mirrors, and electronic block. The instrument is installed in the gallery of the Talaya seismic station at a depth of 90 m and measurements are made along two orthogonal 25-m lines oriented at –24°N and 66°N. Data are recorded every second into a computer installed in the building of the seismic station. After decimation, smoothed data were processed according to the ordinary technology of tidal analysis with the use of the Tsoft and ETERNA 3.4 software packages. A difficulty involved in the use of the standard programs of tidal analysis is that they do not provide for the analysis of the strain difference between the two orthogonal arms, enabling the most effective elimination of the atmospheric pressure effect; therefore, we were forced to complement the data processing theory and to use the Gravity subprogram with conversion of the scaling factor. Now we consider theoretical aspects of this problem [Latynina and Karmaleeva, 1978; Melchior, 1983]. In the general form, the strain components along longitude and latitude and direction cosines can be written as e d1 = cos a1 ⋅ e θθ + cos b1 ⋅ e λλ 2

2

∆e = e θθ ( cos α – sin α ) + e λλ ( sin α – cos α ) 2

(3)

e d2 = cos a2 ⋅ e θθ + cos b2 ⋅ e λλ 2

2

(5)

= cos 2α ( e θθ – e λλ ) + sin 2α ⋅ e θλ . For sectorial waves, we have eθθ = [h + 2((1 – 2sin2θ)/sin2θ) · l] · J2/a · g, eλλ = [h – 2((1 + sin2θ)/sin2θ) · l] · J2/a · g,

(6)

e θλ = 4l [ ( cos θ/ sin θ ) ⋅ tan 2H ] ⋅ J 2 /a ⋅ g , 2

where h and l are the Love and Shida numbers, J2 and T2 are components of the tidal potential, a is the Earth’s radius, g is gravity, θ is colatitude, and H is the hour angle. For tesseral waves, we obtain e θθ = ( h – 4l ) ⋅ T 2 /a ⋅ g

e λλ = ( h – 2l ) ⋅ T 2 /a ⋅ g

(7)

We use these expressions for the calculation of the strain difference by the formulas ∆e = cos 2α ⋅ ( e θθ – e λλ ) + sin 2α ⋅ e θλ

where a1 = b1 + 90° and a2 = b2 + 90° are the angles of direction cosines. Hence ∆e = e d1 – e d2 = cos a1 ⋅ e θθ + cos b1 ⋅ e λλ 2

2

= { [ 2l ⋅ cos 2α ⋅ ( 2 – sin θ )/ sin θ ] 2

2

– cos b2 ⋅ e λλ – cos a2 ⋅ cos b2 ⋅ e θλ

+ [ 4l ⋅ sin 2α ⋅ ( cos θ/ sin θ ) ⋅ tan 2H ] } ⋅ J 2 /a ⋅ g 2

(4)

+ sin 2α ⋅ e θλ = { ( – 2l ⋅ cos 2α )

= e θθ ( cos a1 – cos a2 ) + e λλ ( cos b1 – cos b2 ) 2

+ e θλ ( cos a1 ⋅ cos b1 – cos a2 ⋅ cos b2 ) , IZVESTIYA, PHYSICS OF THE SOLID EARTH

(8)

∆e = cos 2α ⋅ ( e θθ – e λλ )

2

2

2

for sectorial waves and

+ cos a1 ⋅ cos b1 ⋅ e θλ – cos a2 ⋅ e θθ 2

2

+ ( e θλ ( sin α ⋅ cos α + sin α ⋅ cos α ) )

+ cos a2 ⋅ cos b2 ⋅ e θλ ,

2

2

e θλ = – 2l ( tan H/ cos θ ) ⋅ T 2 /a.

+ cos a1 ⋅ cos b1 ⋅ e θλ , 2

where a2 = a1 + 90°, b2 = b1 + 90°, and a1 = α; then we obtain a2 = a1 + 90°, b2 = b1 + 90°, a1 = α:

– [ 2l ⋅ sin 2α ⋅ ( tan H / cos θ ) ] } ⋅ T 2 /a ⋅ g for tesseral waves.

Vol. 44

No. 5

2008

(9)

392

TIMOFEEV et al.

Theoretical expressions for sectorial waves are

ANALYSIS OF DATA OF PROFILE STATIONS

Amplitude factor F2 = ( 2l/ sin θ ) ⋅ [ ( 2 cos θ ⋅ sin 2α ) 2

2

2 1/2

+ cos 2α ⋅ ( 2 – sin θ ) ] ; Phase lag 2

2

(10)

∆ϕ2 = arctan ( 2 cos θ ⋅ sin 2α ) / cos 2α ( 2 – sin θ ) or 2

∆ϕ2 = arctan [ cos 2α ⋅ ( 2 – sin θ ) ] / ( 2 cos θ ⋅ sin 2α ). 2

Analogous expressions for tesseral waves are Amplitude factor F1 = 2l ⋅ ( sin 2α + cos 2α ⋅ cos θ ) 2

2

2

1/2

or

F1 = [ 2l/ ( cos θ ) ] ⋅ ( sin 2α ⋅ cos θ + cos 2α ) ; (11) Phase lag ∆ϕ1 = arctan [ sin 2α/ ( cos 2α ⋅ cos θ ) ]. 2

2

2

1/2

Using the azimuth of the first arm as α, the latitude of the observation point, and relation (10), we can determine the Shida number l and the phase lag.

Observations were performed at stations constructed specially for high-precision gravity measurements (Wikle, Klyuchi, and Talaya) or in specially equipped rooms of the surface type (Zabaikalskoe and Yuzhno-Sakhalinsk) and the underground type (Chizé) with passive thermal stabilization. Continuous measurements were usually conducted for one to two years; such time intervals are sufficient for reliable detection of about ten waves of the tidal spectrum. Models were analyzed using the strongest waves of the semidiurnal (M2) and diurnal (O1) ranges. We first consider data of three stations located on the Atlantic coast of France. In the second half of the 1990s, measurements were made at the Chizé Observatory (46.1473°N, 0.42646°E; H = 70 m; LCR1006) at a distance of 70 km from the Atlantic coast of France near La Rochelle [Timofeev et al., 2006]. This is the third station in the network of the Ménesplet station (LCR906) in Aquitaine and the Mordelles station (LCR906) in Brittany, located at a distance of 50 km from the coastline [Ducarme et al., 2001]. It is known that waves of the semidiurnal tide are predominant in the regime of the Atlantic Ocean. Observations at three French stations showed that the effect of the semidiurnal wave M2 on the amplitude factor and phase lag is significant (Tables 2, 3). Table 2 presents results of calculations in terms of the inelastic

Table 2. Results of modeling and tidal analysis with use of various software packages (LCR1006, Chizé station); δ0 is the amplitude factor and α0 is the phase lag Theoretical amplitude, nm/s2 Earlier models SCW80 CSR3 FES95 ORI96 Recent models CSR4 NAO99 GOT00 FES02 Results of analysis ETERNA VAV03 VAV03 7.5%*

O1

M2

310.45

360.60

M2/O1

δ0

α0 , deg

δ0

α0 , deg

1.1463 1.1440 1.1481 1.1458

–0.16 –0.25 –0.10 –0.04

1.1921 1.1944 1.1901 1.1895

5.51 6.14 5.34 5.34

1.040 1.044 1.037 1.038

1.1458 1.1460 1.1466 1.1455

–0.14 –0.05 –0.11 –0.10

1.1952 1.1946 1.1928 1.1956

6.18 5.43 5.37 5.45

1.043 1.042 1.040 1.044

1.1378 ±0.0032 1.1357 ±0.0034 1.1360 ±0.0027

–0.53 ±0.16 –0.50 ±0.18 –0.67 ±0.14

1.1949 ±0.0018 1.1950 ±0.0015 1.1949 ±0.0014

6.22 ±0.09 6.24 ±0.07 6.16 ±0.07

1.050 ±0.004 1.052 ±0.004 1.052 ±0.003

* Percentage of automatically rejected data (this notation is used in some of the next tables as well). IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

No. 5

2008

TRANSCONTINENTAL TIDAL TRANSECT

393

Table 3. Comparison of theoretical values estimated with regard for the ocean and experimental results at three stations on the French Atlantic coast Station code, gravimeter Wave

Chizé LCR1006

Ménesplet LCR906

Mordelles LCR906

O1

M2

M2/O1

O1

M2

M2/O1

O1

M2

M2/O1

1.1460

1.1915

1.040

1.1460

1.1859

1.035

1.1425

1.2338

1.080

Models Group a (δ) α, deg

–0.14

Group b (δ) α, deg

5.58

1.1460 –0.10

Observed

–0.18

1.1945

1.042

5.61

1.1458 –0.13

5.97

–0.17

1.1882

1.037

6.01

1.1422 –0.13

7.55 1.2487

1.093

7.43

1.1378

1.1949

1.050

1.1490

1.1896

1. 035

1.1389

1.2459

1.094

δ

±0.0032

±0.0018

±0.004

±0.0018

±0.0004

±0.002

±0.0006

±0.0005

±0.001

Observed

–0.53

6.22

–0.24

6.02

–0.11

7.60

α, deg

±0.16

±0.09

±0.09

±0.02

±0.03

±0.02

Note: δ is the amplitude factor and α is the phase lag. Averages are given for group a consisting of SCW80, CSR3, FES95, and ORI96, and for group b consisting of CSR4, FES02, GOT00, and NAO99.

Table 4. Comparison of inelastic (DDW99) and elastic earth models at the Klyuchi (Novosibirsk) and Talaya stations Station

Klyuchi

Talaya Ratio M2/O1

Wave

δt inelastic

δt elastic

δt inelastic

δt elastic

O1

1.1543

1.1528

1.1543

1.1528

1.0013

K1

1.1343

1.1322

1.1344

1.1324

1.0018

M2

1.1620

1.1605

1.1620

1.1605

1.0013

Mf

1.1562

1.1553

1.1562

1.1553

1.0008

DDW99 model and oceanic models developed before 1996 (SCW80, CSR3, FES95, and ORI96) and after 1996 (CSR4, NAO99, GOT00, and FES02). The standard deviation for all profile stations averages 0.0012 (0.079°) for O1 and 0.0018 (0.099°) for M2. Grids with a higher resolution were used in more recent models, for example, 0.5° × 0.5° in FES95, 0.25° × 0.25° in FES99 and FES02, and 0.125° × 0.125° in FES04. The results of calculations with the use of various tidal software including automatic procedures of data control are also presented in Table 2. Amplitude and phase characteristics and the ratio M2/O1, independent of the instrument calibration, can be used for the comparison of models. Models of the new generation (CSR4, NAO99, GOT00, and FES02) are, on the whole, in good agreement with data of the three stations (Table 3). The Klyuchi station (54.8417°N, 83.2467°E; H = 120; measurement periods of 1995–1996, 2003–2004) and the Talaya station (51.6810°N, 103.6440°E; H = 550; 1996–1997), which are located in the middle of the continent at a distance of 3000 km from oceans, are IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

subject to a very weak effect of the ocean. The tidal effect is mostly determined here by the Earth response and is nearly the same at both stations due to an insignificant distinction in their latitudes (Table 4). Tables 5 and 6 present the tidal effect values calculated in the framework of the DDW99 model and the nine ocean models and the results of the analysis of experimental data. As seen from the tables, all ocean models give similar results. As regards the experimental results, we should note a stronger response in the Baikal rift zone that is apparently associated with the thinner lithosphere and hot mantle [Mordvinova et al., 2000; Baikal Interiors …, 1981]. The modeling results obtained for the Far East stations Zabaikalskoe (47.6296°N, 134.7472°E; H = 65 m; 2001–2003; 300 km from the Tatar Strait) and YuzhnoSakhalinsk (47.0297°N, 142.0717°E; H = 80 m; 2004– 2005; 30 km from Aliva Bay) are also beneficial for the analysis of ocean models. The effects of the Pacific and Atlantic oceans are different. Tables 7 and 8 No. 5

2008

394

TIMOFEEV et al.

Table 5. Results of modeling and tidal analysis (LCR402)of data of the Klyuchi station (Novosibirsk) Models AT , nm/s2 Group 1–4 Group 5–9 Experiment ANALYZE VAV04 VAV04 12.9%*

O1

S1K1

M2

292.7

411.6

249.3

M2/O1

δm

αm , deg

δm

αm , deg

δm

αm , deg

1.1540 1.1544

0.303 0.308

1.1343 1.1335

0.282 0.277

1.1588 1.1606

–0.200 –0.261

δ0

α0 , deg

δ0

α0 , deg

δ0

α0 , deg

1.1577 ±0.0047 1.1546 ±0.0058 1.1580 ±0.0039

0.454 ±0.235 0.647 ±0.286 0.132 ±0.193

1.1402 ±0.0036 1.1366 ±0.0043 1.1363 ±0.0030

0.364 ±0.182 0.140 ±0.222 0.214 ±0.152

1.1555 ±0.0060 1.1566 ±0.0057 1.1599 ±0.0037

–0.368 ±0.150 –0.460 ±0.179 –0.230 ±0.183

1.0041 1.0046 0.9981 ±0.0076 1.0018 ±0.0082 1.0016 ±0.0054

Note: δ0 is the amplitude factor and α0 is the phase lag. Group 1–4 (earlier models) consists of SCW80, CSR3, FES95, and ORI96. Group 5–9 (recent models) consists of CSR4, NAO99, GOT00, FES02, and TPX06.

Table 6. Results of modeling and tidal analysis (LCR402) of data of the Talaya station (Baikal) Models AT , nm/s2 Group 1–4 Group 5–9 Experiment ANALYZE VAV04 VAV04 18.6%*

O1

S1K1

M2

302.4

425.2

289.0

M2/O1

δm

αm , deg

δm

αm , deg

δm

αm , deg

1.1592 1.1597

0.398 0.391

1.1402 1.1393

0.284 0.294

1.1622 1.1629

0.118 0.054

δ0

α0 , deg

δ0

α0 , deg

δ0

α0 , deg

1.1653 ±0.0055 1.1673 ±0.0066 1.1622 ±0.0043

0.313 ±0.270 0.260 ±0.331 –0.098 ±0.213

1.1380 ±0.0037 1.1410 ±0.0045 1.1346 ±0.0030

0.411 ±0.186 0.490 ±0.225 0.127 ±0.151

1.1597 ±0.0032 1.1602 ±0.0034 1.1626 ±0.0024

0.140 ±0.157 0.112 ±0.166 0.000 ±0.118

1.0026 1.0027

0.9952 ±0.0064 0.9939 ±0.0074 1.0004 ±0.0049

Note: δ0 is the amplitude factor and α0 is the phase lag. Group 1–4 (earlier models) consists of SCW80, CSR3, FES95, and ORI96. Group 5–9 (recent models) consists of CSR4, NAO99, GOT00, FES02, and TPX06.

present the results of modeling and analysis of experimental data. The complex conditions of observations (high humidity in summer periods) at the Zabaikalskoe station affected results in the diurnal part of the tidal spectrum, which required careful selection of data (Table 7). Far East stations showed good agreement between experiment data and modeling results (the earth model DDW99 and the ocean models CSR4, NAO99, GOT00, FES02, and TPX06). Now, we again address the mid-continent setting and consider the results of the tidal analysis of data obtained with the laser extensometer installed in the gallery of the Talaya station. The results calculated with

the use of the ETERNA 3.4 package are presented in Table 9. The Shida number l and phase lag can be determined using α = –33°N, the observation point latitude 51.68°N, and relations (10) and eliminating the effect of the cavity and the influence of the E–W Main Sayan fault; according to long-term tiltmeter and extensometer observations and theoretical and experimental results (the “cleft” model) [Beaumont and Berger, 1974; Simon et al., 1986]; the effect amounts to –9° [Gridnev et al., 1990, Timofeev et al., 2000]. For the M2 wave, the theoretical value of the phase lead is ∆ϕ2 = 64° (its experimental value is 65.36°, see Table 9). The Shida number lM2 determined from the values pre-

IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

No. 5

2008

TRANSCONTINENTAL TIDAL TRANSECT

395

Table 7. Results of modeling and tidal analysis (LCR402) of data of the Zabaikalskoe station (southern Khabarovsk Territory) Models AT Group 1–4 Group 5–9 Experiment ANALYZE VAV04 VAV04 (winter)

O1

K1

M2

309.4

435.08

341.26

M2/O1

δm

αm , deg

δm

αm , deg

δm

αm , deg

1.1842 1.1841

0.866 0.818

1.1636 1.1624

0.248 0.268

1.1730 1.1718

0.449 0.403

δ0

α0 , deg

δ0

α0 , deg

δ0

α0 , deg

1.1924 ±0.0054 1.1847 ±0.0075 1.1840 ±0.0084

0.719 ±0.262 0.452 ±0.362 0.750 ±0.406

1.1608 ±0.0042 1.1684 ±0.0063

0.191 ±0.208 0.084 ±0.306

1.1745 ±0.0036 1.1754 ±0.0045 1.1734 ±0.0049

0.340 ±0.150 0.238 ±0.217 0.680 ±0.239

0.9905 0.9893 0.9850 ±0.0067 0.9921 ±0.0086 0.9911 ±0.0094

Note: δ0 is the amplitude factor and α0 is the phase lag. Group 1–4 (earlier models) consists of SCW80, CSR3, FES95, and ORI96. Group 5–9 (recent models) consists of CSR4, NAO99, GOT00, FES02, and TPX06.

Table 8. Results of modeling and tidal analysis (LCR402) of data of the Yuzhno-Sakhalinsk station (southern Sakhalin Island) Models AT Group 1–3 Group 5–9 Experiment ANALYZE VAV04 VAV04 23.2%*

O1

K1

M2

309.9

435.8

349.1

M2/O1

δm

αm , deg

δm

αm , deg

δm

αm , deg

1.2198 1.2206

1.360 1.244

1.1910 1.1909

0.128 0.160

1.1813 1.1770

1.625 1.460

δ0

α0 , deg

δ0

α0 , deg

δ0

α0 , deg

1.2188 ±0.0055 1.2175 ±0.0056 1.2235 ±0.0035

0.515 ±0.258 0.500 ±0.264 1.111 ±0.169

1.1896 ±0.0045 1.1942 ±0.0045 1.1935 ±0.0028

1.068 ±0.210 1.029 ±0.210 0.776 ±0.133

1.1718 ±0.0031 1.1708 ±0.0037 1.1750 ±0.0022

1.218 ±0.150 1.174 ±0.179 1.530 ±0.107

0.9684 0.9643

0.9614 ±0.0063 0.9616 ±0.0067 0.9604 ±0.0040

Note: δ0 is the amplitude factor and α0 is the phase lag. Group 1–3 (earlier models) consists of SCW80, CSR3, and ORI96. Group 5–9 (recent models) consists of CSR4, NAO99, GOT00, FES02, and TPX06.

sented in Table 9 with the use of relations (10) is 0.0839 ± 0.0001, which is close to its value inferred for the earth tide model DDW99. The laser measuring system is distinguished by stability of its parameters and, using yearly values of these data, variations in the strain amplitude and phase can be estimated for the deep fault area in relation to the development of the seismic process in the Baikal rift zone. The variations in the strain amplitude and phase with time are shown in Fig. 4 beginning from the single determination in 1990 up to the present. The arrows in the plot show strong earthquakes (M > 5) that occurred in the 500-km zone around the Talaya station. IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

As regards the modeling of the tidal effect for the fortnightly (Mf) and other long-period waves, good agreement has been recently achieved between the effect determined by modern ocean models and the data obtained with superconducting gravimeters in the framework of the global geodynamics project [Ducarme et al., 2004; Boy et al., 2006]. For example, the agreement with the models in Europe at latitudes of the Siberian stations is better than 0.5%, or 2.5 nm/s2, i.e., comparable with the level of uncertainties in the diurnal and semidiurnal ranges at Siberian stations. It was also shown that the loading vector of the Mm wave can be modeled using the Mf wave with the same phase No. 5

2008

396

TIMOFEEV et al.

Table 9. Tidal analysis of difference strain recorded by the 25-m-base laser extensometer in the gallery of the Talaya seismic station from January 1995 through November 2003: standard output of the Gravity version of Wenzel’s tidal analysis code ETERNA 3.4 EARTH TIDE STATION NR. 1301, BAIKAL, RUSSIA LAZER OBSERVATORY&GEOPHYSICAL INSTITUTES, SIBERIAN BRANCH OF RUSSIAN ACADEMI OF SCIENCE. 51.681N 103.644E H550M P3000M LAZER EXTEN. (DIFF.) PROCESSING TIMOFEEV, GRIBANOVA, ZAPREEVA ALL WAVES WITH AMPLITUDE FACTOR 1, PHASE LAG 0.0000 DEG. Summary of observation data : 19950128110000…19950310210000 19950313 40000…19950321 40000 ………………………………………………………………………………. 20030721 10000…20031004 80000 20031004 90000…20031116 40000 Initial epoch for tidal force: 1995. 1.28. 0 Number of recorded days in total: 1966.50 TAMURA 1987 tidal potential used. Rigid Earth model used. Adjusted tidal parameters: from

to

wave

286 429 489 538 593 635 737 840 891 948 988 1122 1205

428 488 537 592 634 736 839 890 947 987 1121 1204 1214

Q1 O1 M1 K1 J1 OO1 2N2 N2 M2 L2 S2 M3 M4

amplitude, signal/noise nm/s2

ampl.fac.

11.615 30.8 0.20063 59.021 157.3 0.19520 2.306 7.1 0.09699 75.565 214.5 0.17770 4.520 12.3 0.19008 4.051 10.9 0.31132 6.119 22.3 0.69261 36.057 106.4 0.65175 199.400 595.2 0.69008 4.047 14.2 0.49551 100.170 310.4 0.74511 0.649 2.1 0.18405 0.406 1.3 10.18299 Standard deviation of weight unit: 49.373

(namely, their amplitude ratio). A strong gradient in modeling factors is observed in Siberia due to the southward decrease in the astronomic amplitude and the eastward increase in the tidal load of the ocean (Table 10). The oceanic tide load is less significant for the annual (Sa) and semiannual (Ssa) waves. In this case, the contribution of meteorological and hydrological components is more important. The analysis of data obtained by the global network of superconducting gravimeters showed that the Sa tidal factor exceeds 2 [Ducarme et al., 2006]; i.e., a global model should take into account the effect of the atmospheric pressure [Neumeyer et al., 2004] and the seasonal variation in the surface runoff on continents [Neumeyer et al., 2006]. DISCUSSION AND CONCLUSIONS Experimental estimates of tidal parameters in eastern Russia are obtained for the first time. Measure-

stdv.

phase lead, deg

stdv., deg

0.00650 0.00124 0.01360 0.00083 0.01550 0.02863 0.03107 0.00612 0.00116 0.03500 0.00240 0.08863 7.65845

–62.3571 –60.5701 –91.0758 –72.3005 –62.0005 –71.2068 69.8044 66.4791 65.3621 72.5945 68.0752 47.3980 106.9793

0.3729 0.0711 0.7792 0.0475 0.8879 1.6415 1.7799 0.3509 0.0664 2.0042 0.1376 5.0783 438.8836

ments at stations with absent active thermal stabilization failed to separate the waves K1 and S1 at some stations (e.g., at the Yuzhno-Sakhalinsk station). Models of the tidal response of the earth and oceans to diurnal and semidiurnal waves are compared with the use of the residual vector X(X, χ), which must vanish in an ideal case. The values of the vector are found to be less than 1.5 nm/s2 for the O1 and M2 waves, which corresponds to 0.5% of the wave amplitudes. Parameters of the residual vector X (nm/s2) and its phase χ (deg) are given in Table 11 for the stations Klyuchi (Novosibirsk), Talaya (SE Baikal rift zone), Zabaikalskoe (southern part of Khabarovsk Territory), and Yuzhno-Sakhalinsk (southern Sakhalin Island). Minimum values of the residual vector are obtained for the DDW99 tidal strain model, taking into account the mantle viscosity, and for ocean tide models of the last generation (CSR4, NAO99, GOT00, FES02, and TPX06). This conclusion

IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

No. 5

2008

TRANSCONTINENTAL TIDAL TRANSECT

397

(a) 0.72

Variations in the phase lag of wave M2

0.70 0.68 0.66 0.65 0.62 0.60 (b) 72

Amplitude factor of wave M2

68 64 60

*1

99 0* 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 *2 * 00 3 *2 * 00 4 *2 * 00 5* *2 00 6*

56 Time, years Fig. 4. (a) The amplitude factor for the difference strain and its variation with time. The following earthquakes of the region are shown: December 27, 1991, M = 6.5–7.0 (51.0°N, 98.0°E), 400 km west of the station; June 29, 1995, M = 5.5–5.7 (51.71°N, 102.85°E), 67 km west of the station; series of Baikal earthquakes that occurred in from February 25 to May 31, 2000, M = 5.1–5.8, (51.52°–51.71°N, 104.84°–104.89°E) 85 km east of the station. (b) Temporal variation in the phase lag. The theoretical phase shift for the difference strain is not removed from the results of the analysis (63.5 deg).

is supported by measurements on the European Atlantic coast in the same latitude band. Measurements with a digital relative gravimeter and laser extensometer in intracontinental regions provided high-precision values of the Love and Shida numbers: h = 0.6077 ± 0.0008, k = 0.3014 ± 0.0004, and l = 0.0839 ± 0.0001.

in the phase lag, which can be due to changes in the hydrogeological conditions in the Main Sayan fault zone and variations in the seismic regime of the region. In this case, theoretical estimates obtained from gravity data show that temporal variations in tidal parameters are a few orders smaller, i.e., lie within measurement uncertainties.

According to long-term observations in the Baikal rift zone, the variation in the amplitude and phase of tidal strain can reach 3–4% in the amplitude and 1°–3°

The results of the profile studies can be used for the calculation of tidal corrections. The tidal parameters estimated for the Yuzhno-Sakhalinsk station are pre-

Table 10. Tidal factor models for the long-period wave Mf AT , nm/s2

Klyuchi

Talaya

Zabikalskoe

Yuzhno-Sakhalinsk

64.47

54.26

40.76

38.75

Models

δm

αm , deg

δm

αm , deg

δm

αm , deg

δm

αm , deg

NAO99 TPX06 FES04 MEAN STD

1.1511 1.1516 1.1510 1.1513 0.0004

0.219 0.192 0.197 0.203 0.015

1.1503 1.1509 1.1500 1.1504 0.0004

0.154 0.109 0.136 0.133 0.023

1.1301 1.1308 1.1303 1.1304 0.0004

–0.021 –0.215 –0.074 –0.104 0.100

1.1014 1.1024 1.1026 1.1022 0.0006

–0.170 –0.440 –0.266 –0.292 0.137

IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

No. 5

2008

398

TIMOFEEV et al.

Table 11. Values of residual vector X (nm/s2) and its phase χ (deg) for the waves O1, K1, and M2 at Russian stations of the profile O1

K1

M2

292.7

411.6

249.3

Klyuchi AT , nm/s2 Models

X

χ

X

χ

X

χ

earlier 1–4

1.54

–40.79

0.99

–33.92

0.31

–29.31

recent 5–9

1.48

–44.44

1.28

–23.48

0.16

–113.40

Talaya AT , nm/s2

302.4

425.2

289.0

earlier 1–4

1.90

–15.60

1.31

133.78

0.75

170.22

recent 5–9

1.76

–15.43

1.12

118.22

1.07

149.91

Zabikalskoe AT , nm/s2

309.4

435.0

341.2

earlier 1–4

0.75

–95.35

1.31

–157.36

0.91

–56.38

recent 5–9

0.46

–108.32

0.97

–135.48

1.04

–24.57

Yuzhno-Sakhalinsk AT , nm/s2

309.9

435.8

349.1

earlier 1–3

1.99

–54.66

5.97

80.08

2.32

–161.35

recent 5–9

1.26

–42.96

5.01

88.89

0.87

146.19

Table 12. Tidal parameters at the Southern Sakhalinsk station estimated as averages over 5 maps (CSR4, NAO99, GOT00, FES02, and TPX06) for the semidiurnal and diurnal waves and over three maps (NAO99, TPX06, and FES04) for the wave Mf (N is number of waves in the expansion given in [Tamura,1987]) Tidal group M0S0

N

Frequency range (cycles per day)

δm

αm , deg

2

0.000000

0.000001

1.0000

0.000

Ssa

32

0.000002

0.020884

1.1560

0.000

Mf

247

0.020884

0.501369

1.1022

–0.292

Q1

143

0.501370

0.911390

1.2197

1.951

O1

106

0.911391

0.981854

1.2206

1.244

P1

17

0.981855

0.998631

1.2057

0.197

K1

40

0.998632

1.023622

1.1909

0.160

J1

145

1.023623

1.470243

1.1560

0.000

N2

149

1.470244

1.914128

1.1622

0.630

M2

95

1.914129

1.984282

1.1770

1.460

S2

17

1.984283

2.002736

1.2033

0.684

K2

116

2.002737

2.451943

1.2066

0.667

M3

81

2.451944

3.381378

1.0700

0.000

IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

No. 5

2008

TRANSCONTINENTAL TIDAL TRANSECT

sented in Table 12. The error in the tidal correction estimated for the Siberian territory and including uncertainties of the Earth and ocean models amounts to 0.15%, or 4 nm/s2. ACKNOWLEDGMENTS This work was performed in the framework of the Russian–Belgian treaty on cooperation in science and technology, project no. BL/33/R09, and was supported by the RAS Presidium, project no. 16.3; the RAS SB Presidium, project no. 87; and the Russian Foundation for Basic Research, project no. 07-05-00077. REFERENCES 1. Yu. N. Avsyuk, Tidal Forces and Natural Processes (OIFZ RAN, Moscow, 1996) [in Russian]. 2. Yu. N. Avsyuk, G. P. Arnautov, E. N. Kalish, and Yu. F. Stus’, “Tidal Variation in Gravity Studied with the GABL-M Absolute Gravimeter,” Fiz. Zemli, No. 9, 57– 59 (1997) [Izvestiya, Phys. Solid Earth 33, 745–747 (1997)]. 3. Baikal Interiors from Seismic Data, Ed. by N. N. Puzyrev (Nauka, Novosibirsk, 1981) [in Russian]. 4. T. F. Baker and M. F. Bos, “Tidal Gravity Observations and Ocean Tides Models,” J. Geodetic Soc. Japan, 76–81 (2001). 5. T. F. Baker and M. S. Bos, “Validating Earth and Ocean Models Using Tidal Gravity Measurements,” Geophys. J. Int. 152, 468–485 (2003). 6. C. Beaumont and J. Berger, “Earthquake Prediction: Modification of the Earth Tide Tilts and Strains by Dilatancy,” Geophys. J. R. Astron. Soc. 39, 111–121 (1974). 7. J. P. Boy, M. Lubes, R. Ray, et al., “Validation of LongPeriod Oceanic Tidal Models with Superconducting Gravimeters,” J. Geodyn. 41, 112–118 (2006). 8. D. Crossley, J. Hinderer, G. Casula, et al., “Network of Superconducting Gravimeters Benefits a Number of Disciplines,” EOS Trans AGU 80 (11), 121/125–126 (1999). 9. V. Dehant, P. Defraigne, and J. Wahr, “Tides for a Convective Earth,” J. Geophys. Res. 104 (B1), 1035–1058 (1999). 10. B. Ducarme, M. van Ruymbeke, and A. El Wahabi, “Tidal Gravity Observations along the Atlantic Coast of France with LCR G906,” J. Geodetic Soc. Japan, 114– 120 (2001). 11. B. Ducarme, A. P. Venedikov, J. Arnoso, and R. Vieira, “Determination of the Long Period Tidal Waves in the GGP Superconducting Gravity Data,” J. Geodyn. 38, 307–324 (2004). 12. B. Ducarme, L. Vandercoilden, and A. P. Venedikov, “The Analysis of LP Waves and Polar Motion Effects by ETERNA and VAV Methods,” Bull. Inform. Marées Terrestres 141, 11 201–11 210 (2006). 13. R. J. Eanes and S. V. Bettadpur, “The CSR 3.0 Global Ocean Tide Model: Diurnal and Semi-Diurnal Ocean Tides from TOPEX/POSEIDON Altimetry,” in CSR Technical Memorandum, Center for Space Research (Univ. Texas at Austin, Austin, 1995). IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

399

14. G. Egbert, A. Bennett, and M. Foreman, “TOPEX/Poseidon Tides Estimated Using a Global Inverse Model,” J. Geophys. Res. 99 (C12), 24 821–24 852 (1994). 15. W. E. Farrell, “Deformation of the Earth by Surface Load,” Rev. Geophys. 10, 761–779 (1972). 16. O. Francis and P. Melchior, “Tidal Loading in South Western Europe: A Test Area,” Geophys. Rev. Lett. 23, 2251–2254 (1996). 17. D. G. Gridnev, V. Yu. Timofeev, Yu. K. Saricheva, et al., “Earth’s Surface Tilts in the Southern Baikal Area,” Geol. Geofiz. 5, 95–104 (1990). 18. E. Kalish, G. Arnautov, B. Ducarme, et al., “Gravity Variations at Novosibirsk Region and Irkutsk Region by Gabl-M Measurements,” Cahiers du Centre Europeen de Geodyn. Seismol. 17, 187–192 (2000). 19. A. V. Kopaev, “Anomalies of Gravity Tides,” Dokl. Akad. Nauk 372 (1), 104–107 (2000). 20. L. A. Latynina and R. M. Karmaleeva, Strain Measurements (Nauka, Moscow, 1978) [in Russian]. 21. C. Le Provost, M. L. Genco, and F. Lyard, “Spectroscopy of the Ocean Tides from a Finite Element Hydrodynamic Model,” J. Geophys. Res. 99 (C12), 24 777–24 797 (1994). 22. P. M. Mathews, “Love Numbers and Gravimetric Factor for Diurnal Tides,” J. Geodetic Soc. Japan 47 (1), 231– 236 (2001). 23. K. Matsumoto, M. Ooe, T. Sato, et al., “Ocean Tides Model Obtained from TOPEX/POSEIDON Altimeter Data,” J. Geophys. Res. 100, 25 319–25330 (1995). 24. K. Matsumoto, T. Takanezawa, and M. Ooe, “Ocean Tide Models Developed by Assimilating TOPEX/POSEIDON Altimeter Data into Hydrodynamical Model: A Global Model and a Regional Model around Japan,” J. Oceanography 56, 567–581 (2000). 25. P. Melchior, The Tides of the Planet Earth, 2nd ed. (Pergamon, Oxford (1983). 26. P. Melchior, “Tidal Interactions in the Earth Moon System,” Chronique U.G.G.I, No. 210, 76–114 (1992). 27. P. Melchior, “A New Data Bank for Tidal Gravity Measurements (DB92),” Phys. Earth Planet. Inter. 82, 125– 155 (1994). 28. M. S. Molodensky, Selected Works. Gravitational Field, Figure, and Internal Structure of the Earth (Nauka, Moscow, 2001) [in Russian]. 29. S. M. Molodensky, Tides, Nutation, and Internal Structure of the Earth (IFZ AN SSSR, Moscow, 1984) [in Russian]. 30. V. V. Mordvinova, L. P. Vinnik, and G. L. Kosarev, “Teleseismic Tomography of the Baikal Rift Lithosphere,” Dokl. Akad. Nauk 372 (2), 248–252 (2000). 31. J. Neumeyer, J. Hagedorn, J. Leitloff, and T. Schmidt, “Gravity Reduction with Three-Dimensional Atmospheric Pressure Data for Precise Ground Gravity Measurements,” J. Geodyn. 38, 437–450 (2004). 32. J. Neumeyer, F. Barthelmes, O. Dierks, et al., “Combination of Temporal Gravity Variations Resulting from Superconducting Gravimeter Recordings, GRACE Satellite Observations and Global Hydrology Models,” J. Geodesy (2006). 33. V. A. Orlov, High Sensitivity Laser Measurements of Small Displacements and Movements in the Presence of No. 5

2008

400

34. 35.

36.

37.

38. 39.

40.

41.

42. 43.

44.

TIMOFEEV et al. Strong Natural Noise, Extended Abstract of Doctoral (Phys.–Math.) Dissertation, Inst. Laser Physics, Novosibirsk, 2003. B. P. Pertsev, “Effect of Near-Field Zone Ocean Tides on Earth Tide Measurements,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 1, 30–38 (1976). R. D. Ray, “A Global Ocean Tide Model from TOPEX/POSEIDON Altimetry: GOT99 (NASA Tech. Mem. 209478 (Goddard Space Flight Center, Greenbelt, MD, USA, 1999). B. Richter, “Cryogenic Gravimeters: Status Report on Calibration, Data Acquisition and Environmental Effects,” Cahiers du Centre Europeen Geodyn. Seismol. 11, 125–146 (1995). J. K. Saritcheva, V. Y. Timofeev, and S. J. Khomoutov, “The Results of Tidal Observations in Novosibirsk (1991–1996),” in Proc. 13th Int. Symposium on Earth Tides. Brussels, July 22–25, 1997, Ed. by P. Páquet and B. Ducarme (Observatoire Royal de Belgique, Bruxelles, 1998). E. W. Schwiderski, “On Charting Global Ocean Tides,” Rev. Geophys. Space Phys. 18, 243–268 (1980). V. M. Semibalamut, Yu. N. Fomin, V. Yu. Timofeev, et al., “Tidal Parameters from the Results of Laser Deformographic Measurements in the South-West Part of the Baikal Rift, Talaya Station,” Bull. Inform. Marées Terrestres, No. 123, 9355–9364 (1995). C. K. Shum, O. B. Andersen, and G. Egbert, “Comparison of Newly Available Deep Ocean Tide Models by the TOPEX/POSEIDON Science Working Team,” J. Geophys. Res. 102 (C11), 25 173–25 194 (1997). D. Simon, L. Skalsky, and J. Jerabek, “Application of Man-Made Clefts for Systematic Changes of Strain Induced Tilts,” in Proc. Tenth Int. Symp. on Earth Tide (Madrid, 1986), pp. 835–841. Y. Tamura, “A Harmonic Development of the Tide-Generating Potential,” Bull. Inform. Marées Terrestres 99, 6813–6855 (1987). V. Yu. Timofeev, Tidal and Slow Deformations of the Crust in Southern Siberia from Experimental Data, Doctoral (Phys.–Math.) Dissertation, Novosibirsk: Inst. Geophysics, 2004. V. Y. Timofeev, B. Ducarme, Y. K. Saricheva, and L. Vandercoilden, “Tidal Analysis of Quartz-Tiltmeter Observations 1988–1998 at the Talaya Observatory (Baikal Rift),” Bull. Inform. Marées Terrestres 133, 10 447–10 458 (2000).

45. V. Yu. Timofeev, B. Ducarme, M. van Ruymbeke, et al., “Experimental Tidal Models,” Dokl. Ross. Akad. Nauk 382 (2), 250–255 (2002). 46. V. Y. Timofeev, M. van Ruymbeke, G. Woppelmann, et al., “Tidal Gravity Observations in Eastern Siberia and along the Atlantic Coast of France,” J. Geodyn. 41, 30– 38 (2006). 47. M. van Camp and P. Vauterin, “Tsoft: Graphical and Interactive Software for the Analysis of Time Series and Earth Tides,” Comput. Geosci. 31, 631–640 (2005). 48. M. van Ruymbeke, “Internal Precision of Calibration for LaCoste & Romberg Gravimeters Equipped with a Feedback System,” in Proc. 13th Int. Symposium on Earth Tides. Brussels, July 22–25, 1997 (Observatoire Royale de Belgique, Bruxells, 1998), pp. 59–68. 49. M. van Ruymbeke, A. Somerhausen, G. Blanchot, et al., “New Developments with Gravimeters,” in Proc. 12th Int. Symposium on Earth Tides. Beijing, August 4–7, 1993) (Science Press, Beijing, 1995), pp. 89–102. 50. M. van Ruymbeke, F. Beauducel, and A. Somerhausen, “The Environmental Data Acquisition System (EDAS) Developed at the Royal Observatory of Belgium,” in Proc. Seminar 192 der WE-Heraeus-Stiftung “Microtemperature Signals of the Earth’s Crust,” Bas Honef, Germany, 25–27 March, 1998 (1999), pp. 23–35. 51. M. van Ruymbeke, B. Ducarme, and A. Somerhausen, “Determination of the Scale Factor of LCR-PET1006 Gravimeter and Comparison with Brussels T003 Cryogenic Gravimeter,” J. Geodetic Soc. Japan 47 (1), 64-69 (2001). 52. A. P. Venedikov, J. Arnoso, and R. Vieira, “VAV: A Program for Tidal Data Processing,” Comput. Geosci. 29, 487–502 (2003). 53. J. M. Wahr, “Effect of the Fluid Core,” “A Normal Mode Expansion for the Forced Response of Rotating Earth,” “Body Tides,” Geophys. J. R. Astron. Soc. 64 (3), 635– 728, 747–765 (1981). 54. R. Weber, C. Bruyninx, H.G. Scherneck, et al., “GPS/GLONASS and Tidal Effects,” Bull. Inform. Marées Terrestres 134, 10 559–10 565 (2001). 55. H. G. Wenzel, “The Nanogal Software: Earth Tide Data Processing Package ETERNA 3.30,” Bull. Inform. Marées Terrestres 124, 9425–9439 (1996). 56. K. H. Zahran, G. Jenetzsch, and G. Seeber, “World-Wide Synthetic Tide Parameters for Gravity and Vertical and Horizontal Displacements,” J. Geodesy 79, 293–299 (2005).

IZVESTIYA, PHYSICS OF THE SOLID EARTH

Vol. 44

No. 5

2008