To analyse which parameters (fracture length, thickness or spacing) control the frequency dependence of attenuation and dispersion, we consider two theoretical models. The first model considers fractures as planes of weakness (or highly compliant and very thin layers) of infinite extent. In the second model fractures are modelled as thin penny-shaped voids of finite radius.<br><br>In both models attenuation exhibits a typical relaxation peak around a normalised frequency of about 1. This corresponds to a frequency where the fluid diffusion length is of the order of crack spacing for the first model, and the crack diameter for the second. This is consistent with an intuitive understanding of the nature of attenuation: when fractures are closely space, the waves reflected/scattered by cracks interfere with each other, with the interference pattern controlled by the fracture spacing. Conversely, if fracture length is smaller than spacing, then fractures act as independent scatterers and the attenuation resembles the pattern of scattering by an individual crack.


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