Joint project to measure gravity change associated with tidal and earthquake’s effect using absolute and relative gravimeters was started at 2010 year. Well-known coseismic effects in gravity and in displacement field distributed on big territory for the earthquake of Mw ≥ 9. GPS measured displacement jump at 1 cm level was registered at 1500 km from epicenter of Sumatran earthquake 27.12.2004, M > 9 [1,2]. Gravity effect at 15 µGal level was measured by GRACE method at 1000 km distance. The Tohoku-Oki earthquake of 11 March 2011 Mw = 9.0 description is presented in many articles [3-8]. We tried to measure co-seismic gravity effect at south part of Primorye territory (Russia) at 1000 km distance from the epicenter. Some GPS results measured during last years at Far East Russia continental coast are also investigated. List of points for observation is presented at Table 1.

Gravity observation started on 2010. Absolute gravimeter GABL [9] was added to the summer observation with Scintrex gravimeter measurement (Table 2). Observation was developed at Marine Experimental Observatory (MEO) territory “Shults Cape” of V.I. Il’ichev Oceanological Institute Far East Branch Russian Academy of Science. MEO is situated at Gamov peninsula (42.58˚N, 131.15˚E, Russia) on the Coast of Japan Sea (Figure 1). Special underground cellar with passive temperature stabilization was used for gravity measurement. In 2010 and 2011 three months of tidal gravity record have been obtained during summer time with Scintrex gravimeter.

For the main tidal waves we determine the amplitude A and the phase difference α, i.e. the vector A(A, α), with respect to the astronomical tide of amplitude A_th (Figure 2). The amplitude factor δ is defined as the ratio A/A_th [10]. For gravity tides prediction we build the modeled tidal factors based on the body tide amplitude R(R = A_th

Table 1. GPS and gravity points, coordinates and horizontal coseismic jump in mm.

Points marked by^* from work [12].

Table 2. Technical specifications of GABL gravimeter.

δ_DDW, 0) computed from the DDW99 non-hydrostatic inelastic model [11] and the ocean load vector L(L, λ) computed from nine different ocean tides models. The modeled vector A_m(A_m, α_m) is given as

The modeled amplitude factor δ_m is simply given by the ratio A_m/A_th.

The tidal loading vector L, which takes into account the direct attraction of the water masses, the flexion of the ground and the associated change of potential, is generally evaluated by performing a convolution integral between the ocean tide models and the load Green’s function computed by Farrell [12]. We used the program referenced in Melchior et al. [13]. Details and references can be found in [14,15].

The corrected tidal factors are defined as

We built also the residual vector defined as (see Figure 3 for explanation):

The accuracy of the absolute gravity determination depends strongly on the precision of the tidal correction. The Trans-Siberian tidal gravity profile [16] demonstrated that modelled tidal factors, based on the mean of the 6 most recent ocean tides models (CSR4, GOT00, NAO99 with 0.5˚ × 0.5˚ grid; FES02, TPX06 wit 0.25˚ × 0.25˚ grid and FES04 with 0.125˚ × 0.125˚ grid), insure a precision of gravity tides predictions of the order of 5 nm/s² on the Siberian territory.

The situation is more delicate at Shults Cape which is located directly on the coast. The resolution of the grid being at the best of 10 km, the ocean tides models do not follow accurately the coast line and the precision of the numerical evaluation is degraded.

Tidal gravity records remain thus important to try to determine experimentally the tidal parameters, at least in the diurnal (D) and semidiurnal (SD) tides. However long records are required to reach the suitable precision of 0.2% (5 nm/s²) and we have only two summer records of 3month each. Our precision is only of 0.5% in amplitude and 0.25 in phase (Table 3). The analysis results are in agreement with the modelled tidal factors within the RMS errors for O1 (Figure 3(b)), but the difference is a bit larger on the tidal amplitude factor for M2 (Figure 3(c)). The analysis of the 3 summer months 2011 (M2 1.1688 ± 0.0056) confirms this result.

A more detailed comparison is given in Table 4.

For the while our gravity tides predictions remain thus based on the modelled tidal factors. For absolute gravity measurements the modelling of the long period (LP) tides is very important. It is the reason why we used only the three ocean tides models including the LP tides: NAO99 (0.5˚ × 0.5˚), TPX06 (0.25˚ × 0.25˚) and FES04 (0.125˚ × 0.125˚). Figure 4 displays the spectral difference between one month of tidal prediction computed with the three different models. As pointed out in Figure 3(a)-(c), TPX06 and NAO99 are very similar For D and SD tides, but for LP tides TPX06 differs from the two other models. It is thus difficult to make a choice. Differences between models remain below ±5 nm/s². It is the expected precision of the gravity tides prediction at Shults Cape.

Finally we used the theoretical model based on TPX06 ocean tides model and DDW99 non hydrostatic body tides model for station Shults Cape and computed tides with Tamura potential for absolute gravity correction.

Absolute gravimeter situated at Shults Cape station is presented at Figure 5. As usually, we used corrections for: solid earth tide, ocean loading, air pressure, polar motion and instrumental ones. Result of measurements and corrections are presented at Table 5 and on Figure 6.

Absolute gravity observations were performed during two periods: 23-30 October 2010 and 15-30 August 2011. Mean square error of measurements series was 1-2 microgal. Gravity value increased by 5.1 microgal during this period including 11 March 2011 earthquake.

Original and published results [6] computed by GPS data

Table 3. Comparison of the results of SCINTREX CG5 40301 with modeled tidal factors at Shults Cape.

Table 4. Results of tidal analysis. Station 1406, appareil 403, oceanic model TPX06, component V, model Wahr-Dehant: non-hydrostatic inelastic case.

are presented in Table 1. Data were obtained at points situated at far epicentral distance (1000 km - 1700 km). Horizontal vector changes from 4.0 cm to 0.7 cm. Mean square error is ranging from 0.5 cm to 3.0 cm.

GPS measured horizontal displacement jump (5 - 8 cm) was registered at 1000 km from epicenter of Sumatran earthquake 27.12.2004, M > 9 [7]. Horizontal jump more then 1 cm was registered at 1500 km distance. GPS measurement at Primorye (1000 km distance from epicenter of Tohoku earthquake 2011) shows 4 cm horizontal jump (Table 1). Vertical jump was observed at ZMEY station. Subduction was 8 mm ± 3 mm. (Figure 7).

You can see on Figure 8(a) our stations (BRIA, DUKI, HURM, UKTR, ZMEY), which are belonging to northern part of GPS-network of Far East of Russia, and Zmey-station (60 km to SE from Khabarovsk). South profile cross the Sikhote-Alin range. Our measurements, are always performed in September to suppress seasonal effects [17,18]. A similar procedure was already used at Gorny Altay for yearly measurements [19]. Observations were performed during 2 - 5 days at network points

Table 5. Results of GABL observation and corrections for the period: 18-27 August 2011 year.

(BRIA, DUKI, HURM, UKTR) and 15 - 20 days at ZMEY base station by two receivers TRIMBLE4700 type with MICROCENTERED antennas. We used hard benchmarks to monument the network (Figure 8(b)). Examples of observation curves are presented on Figures 8-10.

Horizontal velocity relative to YSSK permanent station for the period 2003-2006 is shown on Figure 8(c). Anomalous motion is registered at Japanese islands (red oval). South part of network and Zmey-station are shown inside a orange oval. Small red point is the epicenter of Nevelskoe earthquake 2/08/2007, M = 6.3. Big red point is epicenter of Tohoku earthquake. G-gravity point, Shults Cape (Gamov peninsula, 42.58˚N, 131.15˚E).

Connection gravity variation with height change may be described as:

where: g-vertical gradient of gravity g, normal value −3.08 × 10^{−6 m/s2}; DZ(t)—height change, ξ—error.

Subduction of Primorye region (Shults Cape) was induced by Tohoku-Oki Megathrust. Preliminary result

gravity change 5.1 microgal means 17 mm subsidence of crust surface. A vertical subsidence of 8 mm was Registered at ZMEY point by GPS method. It is not clear if it is regional or local. From other side, if we have deformation of a medium, the associated variation of g is given by:

where: k—gravity constant, ρ—density of a medium, ε_vol. —volumetric strain jump, H—thickness of a layer (earth crust or lithosphere).

Strain measurements in two orthogonal directions on

the flat surface can be used to calculate areal, volumetric, and vertical strain. For an isotropic medium we get:

where, ν is Poisson coefficient.

Level of regional deformation can be estimated by GPS results (Table 1). We have 0.8 × 10⁻⁸ for EW KULD-VANB line. For orthogonal NS DUKI-ARTM line we have +1.7 × 10⁻⁸. We may estimate Volumetric dilatation at +1.7 × 10⁻⁸ level (Poisson coefficient ν = 0.25). Gravity changes for lithosphere thickness (50 km, 100 km and 150 km) will be −0.1 microgal, −0.2 microgal and −0.3 microgal (ρ = 3.5 × 10³ kg/m³). It is negligible with respect to subsidence effect. Observed gravity variation is connected only with height change or with tectonic plate level down.

Now gravity observation is continued at Shults Cape station. Microg LaCoste&Romberg (gPhone, n111) gravimeter is used for the registration of tidal variation (Figure 11). More precise tidal model will be calculated. We hope to prepare better model for local gravity variation. GPS observation started at gravity point at the end of August 2012 year.