GNGTS 2015 - Atti del 34° Convegno Nazionale

98 GNGTS 2015 S essione 1.2 where A 1 k and v 1 k are, respectively, the intercept and trend (or velocity) of the best fitting straight line, the g 1 kj terms are the N instrumental or seismic steps eventually occurred at the T j epochs, H is the Heaviside step function. These parameters are estimated by a weighted least square method, using as weights the uncertainties associated to the components estimated in the GAMIT processing; 3 spectral analysis: the residual time series obtained modelling the linear motion by means of the parameters 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 Pof the principal signal, in the interval between seven days and 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 with the contribution of the principal periodic signal estimated in the spectral analysis phase. The daily time pattern of each component y 2 k ( t ), k 1, 2 and 3 can be re-written as: (2) where A 2 k and v 2 k are the re-estimated intercept and constant velocity and is the amplitude of the principal periodic signal P. The g 2 kj 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; Santamaria- Gomez et al., 2011; Williams, 2004), the noise ε k (t i ) in time series can be described as a power law process. Different methods have been developed to characterize noise in GPS time series and its impact on velocity uncertainties (Bos et al., 2013; Hackl et al., 2011; Santamaria-Gomez et al., 2011; Williams, 2008). We have used the reformulated computation method of the Maximum Likelihood Estimation introduced to Bos et al. (2013) in order to estimate the characteristics of the noise and the realist uncertainties associated with velocity values. Vertical kinematic pattern. The vertical velocity field shown in Fig. 2 indicates a very heterogeneous kinematic pattern in the Italian area, passing from uplift in most orogenic zones (Alps and Apennines) to subsidence in the Po, Arno and Venetian Plain. In the Alps, the rates are of the order of a few mm/yr, in agreement with previous estimates carried out by repeated levelling in the last century. At present, the uplift of that zone is attributed to the combined effects of tectonic shortening, postglacial isostatic rebound, flexural response to climate-driven denudation and rapid glacier shrinkage. The permanent stations located on the Apennines chain are characterized by a moderate uplift (or stability) with rates lower than 1-2 mm/yr. This evidence is fairly compatible with the velocity pattern recognized by levelling campaigns performed by the Istituto Geografico Militare Italiano (I.G.M.I.) for about 130 years along routes covering the national territory (D’Anastasio et al. , 2006). This last investigation, performed along several lines crossing the chain from the Tyrrhenian to the Adriatic coasts, indicates maximum uplift rates in the range 1-3 mm/yr (under the assumption that most of the Tyrrhenian side of the central-northern Apennines is essentially stable). The uplift of the Apennines is consistent with the effects expected from the longitudinal shortening of the belt suggested to some authors as Mantovani et al. (2009, 2015a, 2015b) and Viti et al. (2015a, 2015b). Some isolated sites located on the Apennines chain are characterized to negative rates often due to anthropogenic local phenomena, as water pumping for civil and agricultural scope. The present kinematic pattern observed in the centralApennines sector is also characterized a negative velocities observed from the sites located on the L’Aquila city and in the surroundings.