Seismic attenuation across the brittle-ductile transition

Rocks mechanical behaviour, and in particular, their transition from a brittle to a ductile deformation has been prevalently investigated through rheological experiments and numerical models. In conjunction with rocks mechanical studies, the analyses of seismic wave propagation can improve our knowledge of physical rocks behaviour and provide an alternative assessment of the brittle ductile transition (BDT).

In this study, we investigate the quantitative relationships between seismic attenuation and viscous rocks' rheology, especially across the BDT domain. For this purpose, we rely on the Burgers and Gassmann mechanical model to derive shear wave attenuation (1/Q_s ), 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. We observe that the variation with depth is related much more to the input strain rate than to the rock‘s rheology and thermal conditions, so that a fixed amount of Q_s reduction can identify the average BDT depths for each strain rate used. Below the BDT depth, we observe a significant increase of the Q_s reduction (up to 10^-4 % of the surface value), depending also on rocks temperature and rheology. Since the greatest Q_s reduction is estimated for the greatest input strain rate (10^-13 s^-1) and hot thermal conditions, the proposed method can find more applicability in tectonically active/geothermal areas.

We tested the obtained results by performing triaxial lab experiments, while monitoring ultrasonic P-waves, on a sample of Carrara marble, at ambient temperature and 180 MPa confining pressure. The transition from brittle to semi-brittle conditions is characterized by the increase of crack-density with a progressive rate reduction. At the same time, both the seismic velocity and energy significantly decrease during the first phase of deformation (brittle regime) and tend towards an asymptotic value, when the sample approaches the ductile deformation. We interpret the absence of an increase of energy loss at the BDT, as due to the persistent effect of the microfracturation. The last one usually accompanies the deformation mechanisms that occur at the BDT (e.g., pressure solution, twinning), masking the expected increase of attenuation at the beginning of the ductile conditions. This is a matter that still needs to be investigated.