How does seismic attenuation correlate to rheology of crustal rocks? Results from numerical and lab experiments

The crust is characterized by strong thermo-physical heterogeneities, due to lateral and depth variations in the rocks structure and composition. Exploration and exploitation of natural resources require a proper understanding of the mechanical rocks’ properties composing this layer, which is in direct contact with the atmosphere and surface waters and thus control the presence and distribution of available natural resources (e.g., water, oil, gas). The rocks properties are described by their strength variations within a specific geodynamic context (Burov, 2011). The depth of the transition from the brittle to ductile deformation (BDT) commonly refers to a pressure and temperature range, where rocks deform by an interplay of cracking and crystal plasticity, marking the progressive change in crustal rheology with increasing depth. This transition occurs at a variable depth, depending on the rock's structure, composition, hydrous conditions, and amount and type (compression or extension) of tectonic stress (e.g., Burov, 2011). The mechanical behaviour of rocks, and in particular their transition from a brittle to a ductile deformation, has been extensively investigated through a vast amount of rheological experiments (e.g., Burgmann and Dresen, 2008), numerical models (e.g., Burov, 2011), and seismicity studies (e.g., Maggi et al. 2000). In this respect, the analyses of seismic wave propagation in high-enthalpy geothermal regions, in presence of (partial) melting can improve our knowledge on physical rocks behaviour and provide an alternative assessment of the BDT. Indeed, viscous rocks deformation, depending on the rock structure, composition, and fluid content, as well as on the in-situ T-P conditions, can be analysed through the study of seismic attenuation, defined as the dissipation of seismic energy as it propagates through the rock 2 medium. Seismic attenuation is usually described in terms of a “quality factor” Q, given by the inverse of the fractional loss of energy per wave cycle. Therefore, the estimation of the seismic quality factor (Q) can be used to quantify the energy loss of seismic waves, which provides an indirect measure of the anelastic behaviour of the Earth’s materials. The Q-factor can be mathematically described by an Arrehenius-type equation, in a similar fashion to the viscous rocks deformation. Despite previous studies have discussed the existence of a correlation between seismic attenuation and the onset of viscous deformation in rocks, the sensitivity of this quantitative relationship to background tectono-thermal conditions and varying rock‘s physical properties have been not yet properly investigated. Some recent studies (e.g., Farina et al., 2019) computed seismic wave properties relying on the Burgers mechanical model. This model, which is able to capture both transient and steady-state (secondary) creep in a consistent way, is described by a combination in series of a Zener and Maxwell model, being characterized by two (short- and long-term) viscosities (Karato, 2008). In this study, we follow the numerical approach proposed by Farina et al. (2019) to compute the seismic quality factors for shear waves (Qs) for different crustal rocks, under varying temperature and strain rate conditions. We further compare the obtained Qs depth variations with variations in shear viscosities and computed ductile strengths profiles. To this purpose, we chose two sialic rocks (granite and quartzite), under hydrated and anhydrous conditions and three mafic rocks (diabase, OPX and CPX), under anhydrous conditions only. In addition, we compute strength envelopes for all crustal rocks, temperature, and strain rate conditions. The comparison of the obtained results enables us to quantify the sensitivity of the seismic attenuation and strength distribution on the input parameters and therefore to describe in a quantitative manner the correlation between computed Qs 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