Can Hudson-Crampin effective model be applied in cracked medium in which the background is weakly anisotropic (VTI)?

Abstract

To understand the effect of aligned cracks in a vertical transversely isotropic (VTI) background medium, we measured P- and S-wave velocities of seventeen synthetic anisotropic samples with crack densities ranging from 0.0092 to 0.12 and the crack aspect ratios ranging from 0.08 to 0.52. Each one of the cracked synthetic samples is composed by a layered elastic porous matrix (constructed with sand and cement), that shows a background VTI (weak) anisotropy, with penny-shaped void spaces. We compared measured velocities to predictions by the Hudson-Crampin's model. We observed a good fitting for VP and VS waves propagating perpendicular to the crack planes. The best fittings were observed in the cases where the crack density was lower than 0.06 and crack aspect ratio was lower than 0.32. We also investigated Thomsen's parameters ε, γ and δ. The best theoretical predictions was observed for ε and γ for samples with crack density lower than 0.06 and crack aspect ratio lower than 0.20.