After 7.5 years of continuous measurements, we processed and analyzed the baseline between 2 GPS stations located beside the Moyenne-Durance fault (SE France), in order to evaluate the interseismic loading of this slow active fault. This aim is a priori difficult to reach, because of the low strain rates in France and the amount of noise in GPS series. Nevertheless, the precision of relative velocity of continuous GPS should now reach a few tenth of mm/a over several hundred km. A recent debate on the New Madrid active area (Smalley et al., 2005 ; Calais et al., 2005) clearly shows that the success of the estimation of the slip rate of a slow fault is dependent of the calculation strategy and the noise model. The estimation of the noise characteristics is important because it is needed in order to get realistic and reliable uncertainties of the velocities. In addition, the noise characteristics inform about the precision to be expected with observation time. We thus performed several estimations of velocity to attain the most reliable result. We processed the data in a classical way for geodynamic applications, using the GAMIT freeware. The positions were estimated in a free network with the variance-covariance matrix, with simultaneous estimation of tropospheric and orbital corrections, but also taking into account the movements due to solid earth tides, oceanic loading and earth rotation variations. Then, a 7-parameter transformation was performed, in order to give the positions and variance in the reference framework ITRF2000. We used IGS reference stations, which positions are well defined in the ITRF2000.
After this calculation, we obtain the time series of each point, which slope gives the 1st order velocity after removing the outliers, corresponding to the movement of the Eurasian tectonic plate in a global reference frame. The estimated repeatability is 2 mm for the planimetric components and 5-7 mm for the vertical component. The baseline time series show several offsets with 3-4 mm amplitude. The origin of these (geodetic or tectonic) is unknown, but they are not correlated to any instrumental change. In addition, we notice that the RGP solution baseline is completely consistent with our calculation, meaning that they are not associated to software bias. The most important offset (between November 2000 and March 2001) is correlated in time with an increase in the number of earthquakes (M2-3) recorded by the IRSN network in the area (within a radius of 50 km). Beside these few offsets of the baseline, the noise recorded by the Gina-Mich baseline is time-dependent and a simple white noise model cannot be applied to estimate the uncertainties. This seems to be a common feature in continuous baselines (Zhang et al., 1997, Mao et al., 1999, Calais, 1999, Williams, 2003, Williams et al., 2004). Indeed, the power spectra of the time-series clearly underline that colored noise is dominant towards the low frequencies (i. e. several weeks, between 2 and 10). We used the Williams method (Williams, 2003; Williams et al., 2004) based on the
Maximum Likelihood Estimator, which optimizes the covariance model of the time series, the velocity and the annual fluctuations. We thus simultaneously estimated the velocity (with its standard deviation) and the noise characteristics.
This noise analysis shows that the white noise alone cannot fit correctly the temporal distribution of the residuals. A simple linear regression gives the right velocity value, but it largely underestimates the uncertainty (x30). The best noise model is close to the one combining white noise and flicker noise: we find a power spectrum with a spectral index of -1.3 (-1 for flicker noise). This analysis shows that the amplitude of white noise is 1.5 mm and the amplitude of flicker noise is 3 mm/a v\ The noise analysis indicates that a 7.5 years period of measurements provides a precision of 0.6 mm/y (95%). For this precision level, no clear deformation is revealed by our dataset. Nevertheless, it is possible to infer a deformation range from the Gina-Mich baseline, with a 95% confidence level. This is obtained with the mean of the noise model including white and flicker noise, using 2 regional sets of solutions (RENAG and RGP) : North : -0.1 ±0.5 mm/y ; East : -0.1 ±0.6 mm/y ; Vertical : -0.3±0.9 mm/y ; Shortening : -0.1 ±0.6 mm/y.
Beside the time-series approach for noise estimation, we performed a network solution (Nocquet and Calais, 2003) that allows matching the velocity field of the network. Minimal constraints are applied to the daily solution variance. Then, these solutions are combined to provide the velocity field in the ITRF2000 reference frame. We thus can analyse the velocities with respect to the stable Eurasia. Here, the relative velocity between Gina and Mich is -0.07 ± 0.12 mm/a. The velocities are expressed with respect to a rigid Eurasia whose Euler pole is long. -101.8°E, lat. 56.79°N, co 0.26°/Ma. In south-eastern France, our calculation point out that no site has a residual velocity (with respect to the defined rigid Eurasia) larger than 1 mm/a. Whatever we chose the sites in the Provence region, the obtained strain tensor gives a NS shortening. With the 4 sites of Provence (RSTL, CHRN, GINA, MICH), the azimuth of the shortening axis is 6±13°N ; the magnitude is -11.15 ±4.0 10-9 a-1. This is consistent with the P-axis of the focal mechanisms of small magnitude earthquakes recorded by the local IRSN network.