Effective seismic properties of fractured rocks: the role played by fracture scaling characteristics

The seismic characterization of fractured geological formations is of importance for a wide range of applications throughout the Earth, environmental and engineering sciences, such as, for example, hydrocarbon exploration and production, CO­­₂ sequestration, monitoring of enhanced geothermal reservoirs, nuclear waste storage, and tunneling operations. Seismic methods are indirect in nature, and, hence, comprehensive modelling techniques are required to translate corresponding observations into rock physical properties. In this regard, numerous works have employed the theoretical framework of poroelasticity in order to explore the seismic response of particularly complex and elusive parameters of fluid-saturated fracture networks, such as their fracture density and interconnectivity. This is motivated by the fact that poroelasticity allows to account for fluid pressure diffusion effects between connected fractures as well as between fractures and their embedding background. Fluid pressure diffusion prevails when zones of contrasting compliance are traversed by a seismic wave, as this results in pressure gradients, which induce oscillatory fluid flow and, consequently, energy dissipation. This form of energy dissipation has a significant impact on seismic velocity dispersion, attenuation, and anisotropic characteristics, which are key seismic observables. While a wide range of approximations are employed to represent fracture properties in order to compute the seismic response of formations, they do tend to inherently ignore the complex interrelationships between the lengths, compliances, apertures, and permeabilities of fractures remains, as of yet, unaccounted for. In this work, we seek to alleviate this in combination with a poroelastic modelling approach to explore how length-dependent fracture scaling characteristics affect the effective seismic properties of fractured rocks. We start by revisiting canonical models with two orthogonally intersecting fractures of different lengths to analyze the interactions occurring when fractures are affected by a seismic wavefield. We then proceed to explore how scaling relations affect these results. Finally, we consider fracture networks with realistic stochastic length distributions, for which we compare the effective seismic response with and without the proposed length-dependent scaling of the fracture characteristics. Our results demonstrate that the scaling of fracture properties does indeed have a significant effect on the seismic response, as it dramatically reduces the contribution of smaller fractures to fluid pressure diffusion between connected fractures, which, in turn, affects the overall seismic characteristics of the formation.