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Abstract:
Dissipation of elastic energy by way of the “squirt-flow” mechanism is considered as a predominant cause of the frequency dependence of the quality factor Q observed in vibrated fluid-saturated rock samples. Models of the process (e.g. BISQ) have long been useful to infer key properties of fluid-saturated granular rocks but extension of such modelling to crustal-scale formations has yet to be thoroughly investigated. Central to the modelling is a micro-scale locus of dissipation represented by a dual pore system, with one part more compliant than the other – a system that is required to have characteristic dimensions. Rock formations in the brittle crust are highly fractured, with fracture-wall topography known to be fractal; thus, ab initio, the rough, porous interstitial space within natural fractures appears to have no “characteristic dimensions”. However, as argued here, a closer look at such inter-space does reveal a characteristic dimension, one that is quantifiable by hydraulic properties of rock formations measured at the crustal scale. The structure of the permeable space in between two fractal fracture walls suggests that a locus of dissipation therein can be modelled as a fluid-saturated dual pore system, with a compliant narrow cylindrical gap centre, surrounded by a less compliant permeable ring. The complex stiffness of such a system under oscillatory forcing is solved for, subjected to boundary conditions imposed by the inter-space structure, and subsequently scaled-up to field-scale measurements. Results are presented in term of seismic Q versus frequency of forcing, under realistic thermodynamic conditions of a brittle crust.
