Time vs depth: the two domains of seismic

Why time, not depth?

A seismic source fires and a receiver records the arrival time of returning echoes. That time is all the instrument knows. To turn time into depth, you need the velocity of the rocks the wave travelled through, and velocity is not constant. Shallow shales are slow (1800 to 2400 m/s), carbonates are fast (4000 to 6500 m/s), and every boundary in between changes the local rate at which time converts to depth. The seismic section plots time because time is what was measured; the velocity model plus integration gives you depth.

Almost every display axis labeled "ms" or "s" in interpretation software means two-way travel time. A reflector at 1200 ms TWT means the acoustic wave travelled from the surface down to the reflector and back in 1.2 seconds. Half that, the one-way time, is what you multiply by the velocity to get depth: $z = V\,t_{\mathrm{TWT}}/2$.

Average, interval, and RMS velocities

• Interval velocity ($V_{\mathrm{int}}$): the velocity inside a single layer. This is what a sonic log gives you at a specific depth, and what the Dix equation extracts from RMS velocities.
• Average velocity ($V_{\mathrm{avg}}$): the single velocity that, if the entire overburden had that velocity, would produce the same total time-to-a-given-depth as the actual layered medium. $V_{\mathrm{avg}} = 2 z_\text{total} / t_\text{total}$.
• RMS velocity ($V_{\mathrm{rms}}$): the root-mean-square of the interval velocities, each weighted by the time spent in its layer, $V_{\mathrm{rms}}^2 = \sum_i V_{\mathrm{int},i}^2\,\Delta t_i / t$. For flat layers and short offsets it is the velocity in the NMO equation, so it is, approximately, what a stacking-velocity analysis picks.

The distinction matters. Stacking velocities approximate RMS velocities, and $V_{\mathrm{rms}}$ is never less than $V_{\mathrm{avg}}$: it weights the fast layers more, and the two are equal only where the velocity does not change. Converting time to depth with the stacking velocity as if it were the average velocity therefore puts every reflector too deep, by a few percent in a simple layer cake like the one below and by more where velocity contrasts are strong: on a deep prospect, a hundred metres or more.

The Dix relation

What you pick in velocity analysis is a stacking velocity, which approximates $V_{\mathrm{rms}}$. If you have RMS velocities at two successive times $t_1$ and $t_2$, the interval velocity of the layer between those two times is given by the Dix equation:

This is the Dix inversion: it turns a set of time-and-RMS-velocity pairs from your stacking analysis into a layer-cake interval-velocity model. The model is noisy, because Dix amplifies a pick error by about $(V_{\mathrm{rms},2}/V_{\mathrm{int}})^2\, t_2/(t_2 - t_1)$, most in intervals that are thin in time, but it is the bridge between what processing gives you and the velocity field you need for depth conversion. In practice, interval-velocity models are smoothed and cross-checked against well sonic data before being trusted for depth work.

Depth uncertainty, rule of thumb

For a layer with interval velocity $V$ and two-way time thickness $\Delta t$, a fractional velocity error $\Delta V / V$ produces a depth error of $(\Delta V / V)(V \Delta t / 2) = (\Delta V / V)\, h$, where $h$ is the layer's thickness. Errors accumulate downward: every shallow-layer velocity error propagates to every deeper target. Fields with good well control can get to 1 to 3% depth accuracy at the target level; fields with poor control may see 5 to 10%, meaning a 3000 m prospect could be anywhere between 2850 and 3150 m at 5% and between 2700 and 3300 m at 10%. This is why interpreters and drill engineers spend so much time on the velocity model.