Rocks’ Rheology and Seismic Attenuation: What do we know?

Rheological properties of the rocks, depending on various parameters (grain size, composition, hydrous conditions), determine their deformation mode in response to the tectonic stress. At shallow depths, the rocks show a pressure-dependent frictional (brittle) behavior, which turns in a viscous (ductile creep) behavior, as temperature increases (e.g., Jacquey and Cacace 2021). The brittle-ductile transition (BDT) occurs at depths where the shear stress, driving the two deformation modes, are equal for some given strain rate, composition, stress regime, and thermal gradient. Such a transition marks the maximum depth of the intraplate earthquakes and of fluids circulation in porous media. Seismological datasets accounts for real media properties, providing wave propagational attributes (e.g., seismic wave velocities and attenuation) that can be exploited to add constraints to the BDT depth. Seismic wave attenuation can be used as a potential attribute for subsurface characterization. Indeed, its inverse, the seismic quality factor (𝑄), depends on the seismic frequency, as well as on temperature, water content, and grain size of the rocks (e.g., Karato & Spetzler, 1990; Jackson & Faul, 2010). 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). In this study, we investigate the quantitative relationships between seismic attenuation and viscous rocks' rheology, especially across the domain where rocks transition from a dominant brittle to a more ductile deformation mode. 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 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 BDT’s depths in tectonically active areas. Ongoing and future works will focus on a further validation of the modelling implications by systematic analyses of observations derived from rocks’ laboratory experiments.