# Dictionary:Time-average equation

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{{#category_index:T|time-average equation}} 1. An empirical equation stating that the transit time ${\textstyle \Delta t={\frac {1}{V}}}$ through a rock with matrix velocity Vm and porosity ${\textstyle \phi }$ that is filled with fluid of velocity Vf is approximately

${\displaystyle \Delta t={\frac {1}{V}}={\frac {(1-\phi )}{V_{ma}}}+{\frac {\phi }{V_{f}}}}$.

This relation works well in clean consolidated formations with uniformly distributed pores. In formations containing vugs, the sonic log may not reflect the secondary porosity, and in unconsolidated formations, this relationship may overestimate porosity. The formula may be empirically modified to give better values. Also called Wyllie relationship[1].

2. A generalization of the foregoing equation for other constituents, weighting the velocity of each according to its volume fraction.

## References

1. Wyllie, M. R. J.; Gregory, A. R.; Gardner, L. W. (1956). "Elastic Wave Velocities in Heterogeneous and Porous Media". GEOPHYSICS 21 (1): 41–70. doi:10.1190/1.1438217.