Determine the relation between compressional attenuation and wavespeed

Determine whether the residual $P^{1/4}$ pressure dependence of compressional attenuation is connected to compressional wavespeed through a relation analogous to $\hat\beta=\hat c\,\hat\alpha$, and explain why no corresponding relation appears in the shear-attenuation data.

Background

The simulations reveal a residual $P^{1/4}$ dependence in compressional attenuation that resembles the pressure scaling of compressional and shear wavespeed. The authors therefore propose a possible connection between spatial attenuation and wavespeed based on the relation between temporal and spatial attenuation for a propagating mode.

This proposed connection is not established, and its apparent absence from the shear-attenuation results is explicitly identified as an open question.