GNGTS 2022 - Atti del 40° Convegno Nazionale

154 GNGTS 2022 Sessione 1.3 attenuation and strength distribution on the input parameters and therefore to describe in a quantitative manner the correlation between computed Q s reduction (i.e. seismic attenuation increase) and depth, as induced by the resolved ductile deformation. In addition, we have performed triaxial lab experiments, while monitoring ultrasonic P-waves, on a sample of Carrara marble, at ambient temperature and 180 MPa confining pressure, in order to constrain the energy loss variation at the BDT. Method. As in previous studies (e.g., Farina et al. , 2019), we estimate Q s through the frequency dependent shear modulus of the rock, according to the Burgers mechanical model. The shear viscosity (h s ), needed to calculate the shear modulus, is obtained by modelling viscous flow of the rocks, according to a power-law creep (Goetze and Evans, 1979), computed for seven different rock rheologies. We compute the differential stress using two different geotherms and three fixed values of strain rate (10 -13 s -1 , 10 -15 s -1 , and 10 -17 s -1 , respectively), consistent with global estimates, based on horizontal geodetic velocities (Kreemer et al. , 2014). The η s is then computed as an effective viscosity, considering the relationship between the deviatoric stress and strain rate invariants. The two geotherms (named ‘ warm ’ and ‘ cold ’ geotherm, respectively), used to compute h s , reflect the possible thermal conditions of an old tectonically stable (intracratonic) and young, recently (re)activated area and are obtained with a resolution of 1 km up to a depth of 40 km, following the iterative method of Hasterock and Chapman (2011). We use surface heat flow ( SHF ) values of 50 mWm -2 and 80 mWm -2 , which can be considered as representative of the two end-member tectonic conditions. We assume a linear decrease in the concentration of the radiogenic heat from the surface to the bottom of the crust (e.g., Hasterock and Chapman, 2011), defining two ranges of values (from 2.1 to 0.1 mWm -3 and from 3.0 to 0.2 mWm -3 , respectively). The thermal conductivity is assumed to linearly increase with depth and we define a range between 1.5 and 3.5 Wm -1 K -1 , considering that sialic rocks have on average a thermal conductivity lower than ultramafic rocks (e.g., Goes et al. , 2020). The calculated geotherm presents a decrease in thermal gradients with depth, reflecting the decrease in the concentration of radiogenic heat input. According to Farina et al. (2019), we use the Burgers mechanical model augmented with the Gassmann model to describe the effects of seismic wave’s amplitude loss in wet and dry crustal rock rheologies, respectively. Since the viscoelastic modulus (and the viscoelastic compliance) of the system is a complex number, it can be demonstrated that the attenuation expressed as Q –1 , is equal to the ratio between the imaginary and real component of themodulus, named the “loss modulus” and “storage modulus”, respectively. The ratio between the real and imaginary part of the squared shear complex velocities gives the shear seismic quality factor. Finally, we compute the yield strength envelopes (YSEs) by using the Byerlee’s law (Byerlee, 1978) to approximate brittle conditions, while power-law dislocation creep (Goetze and Evams, 1979), describing ductile deformation, is estimated for all tested rheologies. Results. An example of the yield strength envelopes among the seven selected rheologies, together with computed depth variations of h s , Q s , and Q s reduction is displayed in Figs. 1 and 2 respectively. The Q s reduction has been computed as the percentage of the complementary of the ratio between the Q s value, obtained at each depth, and the maximum value of Q s at the surface. Furthermore, we compute the mean of Q s and h s , between values obtained at the BDT depth for each strength envelope. Among the tested rheologies of the sialic rocks, the dry granite is the stiffest, being characterized by the greatest BDT depth (up to a maximum of 19 km, Fig. 1A) and highest values of yield strength at the BDT (up to a maximum of 1000 MPa, Fig. 1A). The other sialic rheologies show similar strength profiles and BDT depths, due to their similar response,