Time vs depth: the two domains of seismic

Part 1 — Foundations of Seismic

Learning objectives

Distinguish two-way travel time (TWT) from real depth and state when each is used
Compute depth from time for a single layer and for a stack of layers
Differentiate average, interval, and RMS velocities and state the Dix relation
Estimate depth uncertainty from velocity uncertainty at a target horizon

Seismic data is almost always displayed with two-way travel time (TWT) on the vertical axis, not depth. This is not a convention invented for display — it is a consequence of what the instrument actually measures. The earth, on the other hand, lives in depth. Every number that matters to drilling — how far down to set casing, how much overburden the well pays for, where a reservoir starts and ends — is a depth number. The process of converting seismic times to real depths is called time-to-depth conversion, and understanding it well is the difference between an interpreter whose maps match reality and an interpreter whose prospects get drilled in the wrong place.

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 (1800–2400 m/s), deep carbonates are fast (5000 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 — one-way time — is what you divide by to get depth when you know velocity: $z = V \cdot (t_\text{TWT} / 2)$ .

Three velocities appear repeatedly in seismic work. It is worth being precise about which is which.

Average, interval, and RMS velocities

Interval velocity ( $V_\text{int}$ ): 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 ( $V_\text{avg}$ ): 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. $V_\text{avg} = 2 z_\text{total} / t_\text{total}$ .
RMS velocity ( $V_\text{RMS}$ ): a weighted-root-mean-square of interval velocities, time-weighted. This is the velocity that appears in the NMO equation. It is also what velocity analysis directly produces from stacking semblance.

The distinction matters. Stacking velocities are RMS velocities; pretending they are interval velocities will give you depth errors of 5–15% — large enough to miss a target by hundreds of metres on a deep prospect.

The Dix relation

RMS velocity $V_\text{RMS}$ is what you pick during velocity analysis. 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:

V_\text{int}^2 = \dfrac{V_{\text{RMS},2}^2 \cdot t_2 - V_{\text{RMS},1}^2 \cdot t_1}{t_2 - t_1}

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 — small errors in RMS velocity blow up quadratically — 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.

The widget above lets you build a simple four-layer model and see how time and depth relate to each other. Try this: set all four interval velocities to the same value (say 2500 m/s) and note that the two axes scale linearly together. Now increase the velocity of the third layer. Watch the third layer stretch on the depth axis while the time axis does not change at all. That is the essence of time-to-depth conversion — time is fixed by what the wave measured, depth is fixed by what you believe the velocities to be.

Drag the "pick a reflector time" slider to 1500 ms (near the base) and note the computed depth. Now bump up the third layer's velocity by 500 m/s (from about 3400 to 3900) and watch the depth jump by roughly 100 metres. A 15% velocity error in one layer produced a 100 m depth error at the target. This is not an edge case; it is the normal situation. Depth uncertainty is always dominated by velocity uncertainty multiplied by the time spent in that layer.

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 roughly $\Delta V / V \cdot (V \cdot \Delta t / 2)$ within that layer. Errors accumulate downward — all shallow-layer velocity errors propagate to every deeper target. Fields with good well control can get to 1–3% depth accuracy at the target level; fields with poor control may see 5–10% error, meaning a 3000 m prospect could be anywhere between 2850 and 3150 m. This is why interpreters and drill engineers spend so much time on the velocity model.

One practical detail. Depth conversion can be done two ways: linear interpolation through a velocity model (what the widget does, and what happens behind the scenes in most interpretation software) or ray-tracing (which also accounts for bent ray paths at dipping layers and is more accurate in structurally complex areas). Time migration gives you a section correctly positioned in time; depth migration goes further and outputs the section directly in depth using a 3D velocity volume. The cleanest workflow in a structurally complex field is: pre-stack depth migration → depth-domain interpretation → no post-hoc time-to-depth conversion needed at all.

References

Bacon, M., Simm, R., & Redshaw, T. (2003). 3-D Seismic Interpretation. Cambridge University Press.
Brown, A. R. (2011). Interpretation of Three-Dimensional Seismic Data (7th ed.). AAPG Memoir 42 / SEG IG13.
Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). Society of Exploration Geophysicists.
Sheriff, R. E. (2002). Encyclopedic Dictionary of Applied Geophysics. Society of Exploration Geophysicists.