Wyllie time-average equation

The Wyllie time-average equation is an equation that relates sonic velocities with the porosity of a rock. It was proposed by Wyllie, Gregory and Gardner in 1956. .

The equation is as follows:


 * $$\frac{1}{v}=\frac{\phi}{v_f}+\frac{1-\phi}{v_m}$$

and can be rewritten in terms of interval travel-times as,


 * $$\Delta t=\phi \Delta t_f + (1 - \phi) \Delta t_m$$

where, $$\phi$$ is the total porosity, $$v$$ is the wave's measured phase velocity, $$v_m$$ is the velocity of the rock matrix, and $$v_f$$ is the velocity of the fluid in the pores, $$\Delta t$$ is the measured interval travel-time, $$\Delta t_m$$ is the interval travel-time of the rock matrix, $$\Delta t_f$$ is the interval travel-time of the saturating fluid.