Frequency-dependent anisotropy in a partially saturated fractured rock

Seismic wave propagation through fractured rocks is greatly influenced by their fracture system and fluid content. In this paper, we derive expressions for the anisotropic frequency-dependent elastic constants. These depend on the relativemobilities of the saturating fluids and the coupled impact of 'squirt' and 'patch' effects, which have typically been considered independently, on anisotropic seismic wave propagation. The effect of relative permeability is pronounced; fluid mobility can be lower in partially saturated rocks compared to the fully saturated case, and this can lead to a stiffening which dominates compressibility effects. This can result in unexpected non-monotonic relationships between moduli and water saturation, complicating attempts to invert saturation from seismic data. We use our model to explain laboratory measurements of seismic anisotropy in partially saturated fractured rocks, concluding that both squirt and patch mechanisms are significant.