Modeling approach to estimate seismic attenuation from dry and wet upper crustal rock’s rheology

The elementary definition of the attenuation is referred to the damped harmonic oscillator as the fractional loss of energy per wave cycle. In some cases, it is used to describe the physical properties of the system that cause a disturbance (Stein and Wysession, 2003). For instance, the energy decay over time of some of the Earth’s normal modes (directly analogous to a damped oscillator), exhibits attenuation due to the material distribution in the earth. The attenuation can be quantified in terms of the seismic quality factor 𝑄. At given absorption bands, 𝑄 can be considered nearly constant and can be related to the superposition of different mechanisms that causes the conversion of seismic energy into internal heat. These mechanisms in turn depend on the material composition and grain size and vary with temperature and pressure, such that higher pressure decreases attenuation, whereas higher temperature promotes the opposite (Stein and Wysession, 2003). On the other hand, the viscous deformation of crustal rocks occurs through different anelastic mechanisms, including diffusion creep, numerous mechanisms of the dislocation creep, pressure solution that exhibits dependency on their structure, composition, and fluid content, as well as on their P-T conditions (e.g., Burov, 2011). Therefore, it is likely that seismic attenuation and the viscous modes of deformations of rocks can be correlated, based on their dependency on the aforementioned conditions, as expressed by an Arrhenius-type equation (Farina et al., 2019). Despite many studies provided indications that rocks’ seismic attenuation and viscous deformation are intrinsically related (considering their common dependency on composition, grain size, fluid content, and T-P conditions), their quantitative relationships have been very poorly investigated. In this study, we explore plausible relationships, implementing a modeling strategy to derive seismic attenuation from diverse rock’s rheologies and to quantitatively estimate the reduction in the 𝑄 factor in correspondence to the depth of the brittle-to-ductile transition (BDT). For that, we rely on a Burgers mechanical model to derive shear wave attenuation (1/𝑄𝑠 ), for several dry and wet crustal rheology, thermal conditions, and different strain rates values. This allows us to establish geothermal and mechanical conditions at which the BDT occurs and to cross-correlate this transition to computed shear seismic wave attenuation values. In particular, we observe a relatively significant 𝑄𝑠 reduction (10-8 ) for strain rates of 10-13 s -1 , despite the assumed rock‘s rheology and thermal conditions. These first results confirm our hypothesis that variations in the 𝑄𝑠 factor can be effectively used to identify the depth to the BDT in tectonically active areas. This effect is particular relevant in the presence of fluid saturated rheology (Figure 1). Ongoing and future works will focus on a further validation of the modelling implications by systematic analyses of observations, derived from rocks’ laboratory experiments, which will be used to add constraints on the relationship between seismic attenuation and rheological flow laws to be used for geodynamic modelling.