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.