Interval and RMS velocities

The Dix conversion allows to translate RMS velocities (stacking velocities) to interval velocities (borehole velocities). \[V_{int(n)}= \sqrt{ \frac{ V_{rms(n)}^2\tau_{(n)} - V_{rms(n-1)}^2\tau_{(n-1)}} {\tau_{(n)}-\tau_{(n-1)}} }\]

After re-arranging to get RMS velocities from interval velocities: \[V_{rms(n)}= \sqrt{ \frac{ V_{int(n)}^2(\tau_{(n)}-\tau_{(n-1)}) + V_{rms(n-1)}^2\tau_{(n-1)}} {\tau_{(n)}} }\]

See Yilmaz, Vol 2, pp. 1534 for the full demonstration of the result.

Further reading

Oz Yilmaz. Seismic data analysis. Society of Exploration Geophysicists, 2001.