The Gassmann equation, first described by Fritz Gassmann, is used in geophysics and its relations are receiving more attention as seismic data are increasingly used for reservoir monitoring. The Gassmann equation is the most common way of performing a fluid substitution model from one known parameter.
These formulations are from Avseth et al. (2006). Template:Avseth, P, T Mukerji & G Mavko (2006), Quantitative seismic interpretation, Cambridge University Press, 2006.
Given an initial set of velocities and densities,Vp ,Vs , and ρ corresponding to a rock with an initial set of fluids, you can compute the velocities and densities of the rock with another set of fluid. Often these velocities are measured from well logs, but might also come from a theoretical model.
Step 1: Extract the dynamic bulk and shear moduli from Vp ,Vs , and ρ.