The problem can be solved by poroelastic (drained or undrained) patrophysical models (the work of Biot, Gertsma are reccomended). In the poroelastic model the elastic wave equation is coupled by pore fluid movement equation. The relative movement of fluid to rock matrix causes frequency dependent energy dissipation. To describe the relative fluid movement the Darcy equation is inserted in the wave equation.

Thanks to the first time derivative in the dissipation part, In the solution complex velocity appears, which results frequency dependent amplitude decrement. This can be identified from Q factor.

So the amplitude decrement depends on elascic properties of rock and porosity, permeability and fluid viscosity.

Carl Reine published two papers in Geophysics in 2012 (Jan/Feb issue) comparing several methods for Q determination. As part of this he derives a number of the key equations to relate Q to the subsurface geomechanical properties, so a good place to start. Additionally, later that year there is a similar paper by Eugene Morgan who also derives the equations you will need in his appendix.

Check Biot's papers