# Difference between revisions of "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.[1].

The equation is as follows:

${\displaystyle {\frac {1}{v}}={\frac {\phi }{v_{f}}}+{\frac {1-\phi }{v_{m}}}}$

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

${\displaystyle \Delta t=\phi \Delta t_{f}+(1-\phi )\Delta t_{m}}$

where, ${\displaystyle \phi }$ is the total porosity, ${\displaystyle v}$ is the wave's measured phase velocity, ${\displaystyle v_{m}}$ is the velocity of the rock matrix, and ${\displaystyle v_{f}}$ is the velocity of the fluid in the pores, ${\displaystyle \Delta t}$ is the measured interval travel-time, ${\displaystyle \Delta t_{m}}$ is the interval travel-time of the rock matrix, ${\displaystyle \Delta t_{f}}$ is the interval travel-time of the saturating fluid.

## References

1. Wyllie, M. R. J., Gregory, A. R., and Gardner, L. W., 1956, Elastic wave velocities in heterogeneous and porous media: Geophysics, 21, no. 1, 41-70