GNGTS 2013 - Atti del 32° Convegno Nazionale

(2) The linear trend with other parameters of Eq. 1, the amplitude E c ( ) and phase φ ( ) of the principal periodic signal F are estimated by a weight least square approach. As argued in several papers (e.g., Hackl et al. , 2011; Bos et al. , 2008; 2010; King and Williams, 2009; Santamaria-Gomez et al. , 2011; Williams 2004, 2008), the noise ε i ( t ) in the GPS position time series can be described as a power law process. Some different methods have been developed in order to estimate the characteristics of noise in the GPS time series and a more realistic values of the velocity uncertainties. In this note we have estimated the uncertainties associated to the velocities by the Allan Variance of the Rate (AVR) method, introduced by Hackl et al. (2011). This method, derived from the analysis of the frequency stability in atomic clocks or crystal oscillators (Allan, 1966), gives the possibility of dealing the time correlated noise in a time series. The estimate of velocity uncertainties is carried out in two independent steps: first the variance is computed and successively the choice of the error model is performed. Horizontal velocity field. The horizontal velocity pattern obtained by the above analysis (Fig. 1) indicates that the outer part of the Northern Apennine belt moves significantly faster (3-4 mm/yr) and more easterly with respect to the surrounding zones, where velocities are mostly lower than 2 mm/yr. This evidence is fairly significant, being coherently indicated by many velocity vectors. One may note that the faster domain roughly corresponds to the Apennine sector that has been characterized by greater mobility since the middle Pleistocene (e.g., Mantovani et al. , 2011, 2012, 2013; Cenni et al. , 2012, 2013). This correspondence may suggest that the dynamic context that acted in the most recent tectonic evolution, causing the lateral escape of the above mentioned wedges, is still going on. In order to minimize local eventually anomalies in a possible regional kinematic field, an interpolation approach has been applied. To this purpose, we have used a weighted least- square procedure with a dis- tance-decaying parameter D which takes into account the distances between the grid node and GPS stations (Shen et al. , 1996). This computation, starting from the GPS velocity Fig. 2 – Horizontal strain rate field estimated using the weighted least square method described in text and in Cenni et al. (2012). This pattern has been obtained by using a distance decay factor of 50 Km, that is a val- ue about three times larger than the average spacing of the network. Con- verging and diverging black arrows indicate principal axes of shortening and lengthening, respectively. The 2D dilatation-rate field (red extensional and blue compressional) is also shown in the figure. 31 GNGTS 2013 S essione 2.1