Wyllie's model

For many years, traditional seismic processing approximated the propagation of seismic waves by the acoustic wave equation 18. Wyllie 1956 suggested a simple empirical time-average equation to relate the wave's phase velocity v to porosity $\phi$, fluid velocity v_f, and rock matrix velocity v_m:

$$\frac{1}{v} = \frac{\phi}{v_f} + \frac{1-\phi}{v_m}$$ (45)

This relationship was used extensively in the interpretation of sonic well log measurements. Raymer 1980 suggests an improved expression for sandstones.