GNGTS 2013 - Atti del 32° Convegno Nazionale

(1) where A 1k and v 1k are, respectively, the intercept and trend of the best fitting straight line, the g 1kj terms are the N instrumental or seismic steps eventually occurred at the Tj epochs, H is the Heaviside step function. These parameters are estimated with a weighted least square method, using as weight the uncertainties associated to the components estimated in the GAMIT processing. 3. Spectral analysis: the residual time series obtained modeling the linear motion by mean of the parameter estimated in the previous step (Eq. 1), are analyzed with a nonlinear least squares technique to estimate spectra following the Lomb (1976) – Scargle (1982) approach. The spectrum of each component is analyzed in order to estimate the period P of the principal signal, in the interval between the seven days to half of the observation time span. 4. Parameter estimation: the daily position component y 1k (t) (k =1,2,3, for the North, East and Vertical component) has been modelled only with the contribution of the principal periodic signal estimated in the spectral analysis phase. The daily time pattern of each component y 2k (t) can be re-written as: (2) where A 2k and v 2k are the re-estimated intercept and constant velocity, the B k ( ) is the amplitude of the principal periodic signal P . The g 2kj terms are the re-estimated offset magnitudes for the N identified discontinuities due to instrumental changes or seismic events eventually occurred at the T j epochs, H is the Heaviside step function. As argued in several papers (e.g. Hackl et al. 2011, Bos et al. 2008; 2010), the noise ſ k (t i ) in time series can be described as a power law process (Agnew, 1992). Different methods have been developed to characterize noise in GPS time series and its impact on velocity uncertainties (Dixon et al. , 2000; King and Williams 2009; Hackl et al. 2011; Santamaria-Gomez et al. 2011; Williams 2004, 2008). We have used the Allan Variance of the Rate (AVR) method introduced by Hackl et al. (2011), which is based on the Allan variance, an analysis often used as a measurement of frequency stability in clock and oscillators (Allan 1966). The method provides the velocity uncertainties after an analysis in the time domain, without any assumption about the noise characteristics of the series. As the calculation is done in the time domain, the method is not too sensitive to gaps in the series and it is computationally cheap. Vertical kinematic pattern. The present-day vertical kinematic pattern in the Italian peninsula is showed in Fig. 2. This pattern presents some significant features; in particular the sites located in the Alps and Apennine domains are characterized by a slow uplift velocity, while the Po plan and some Central Apennine basins are affected by subsidence phenomena. In the Alps, the rates are of the order of a few mm/yr, in agreement with previous estimates carried out by repeated leveling in the last century. At present, the uplift of that zone is attributed to the combined effects of tectonic shortening (e.g., Schlunegger and Hinderer, 2001; Persaud and Pfiffner, 2004; Lardeaux et al. , 2006), postglacial isostatic rebound (e.g. Gudmundsson, 1994; Stocchi et al. , 2005, 2009; Barletta et al. , 2006), flexural response to climate-driven denudation and rapid glacier shrinkage. (e.g., Champagnac et al. , 2007, 2009; Korup and Schlunegger, 2009). 164 GNGTS 2013 S essione 1.2