Seismic Velocity Converter: Interval, Average, and RMS Velocity Using the Dix Equation

Convert between interval, average, and RMS velocity, build a layered velocity model, or solve the Dix equation for interval velocity from stacking velocities. Everything updates live.

Pick up almost any seismic velocity analysis output and you’ll find three different numbers all called “velocity,” and they are not interchangeable. There’s interval velocity, the actual speed of sound through one specific rock unit. There’s average velocity, the single blended number you’d use to convert a time straight to a depth. And there’s RMS velocity, the specific kind of average that comes directly out of stacking a seismic section during processing. Mixing these up, or assuming any one of them stands in for another, is one of the more common ways a depth conversion or a velocity model quietly goes wrong.

This tool handles the conversions between all three. Build a layered interval velocity model and watch the average and RMS velocity get worked out automatically at the base of every layer, or go the other direction and pull a true interval velocity out of two stacking velocities using the Dix equation. A quick-convert mode is also there for the simplest case, back-calculating an average velocity from a known depth and two-way time. Switch between metric and imperial units at any point, and every mode updates as you type.

Interval Velocity: The True Rock Velocity

Interval velocity is the velocity of a seismic wave traveling through one specific layer, and only that layer. It’s the number that actually corresponds to physical rock and fluid properties, since it reflects the lithology, porosity, and pore fluid of the interval it’s measured across, not some blend of everything above it.

In practice, interval velocity is calculated by taking the two-way time picked at the top and base of a layer, finding the difference, and dividing the layer’s thickness by that time difference (or, run the other way, using a known interval velocity and travel time to solve for thickness). It’s the building block every other velocity number in this tool is constructed from.

Average Velocity: The Vertical Blend

Average velocity is what you get when you divide total depth by total one-way travel time, straight down from the surface. It’s a single number, and it’s exactly what its name says: an average, weighted by how much time the wave actually spends in each layer on its way down.

That makes it convenient (it’s exactly what you multiply by one-way time to get a quick depth estimate) but it also means it hides structure. A section with a slow near-surface layer sitting on much faster rock underneath produces an average velocity that doesn’t match either layer’s true velocity, and using it to convert time to depth at intermediate points introduces error that grows the more the real velocity structure deviates from a straight blend.

RMS Velocity: What Velocity Analysis Actually Gives You

RMS (root-mean-square) velocity is a different kind of average from average velocity, one built by giving more weight to faster layers, using the sum of each interval velocity squared and multiplied by its travel time, divided by the total travel time, then square-rooted. It always comes out slightly higher than average velocity, and the two only converge in the special case where velocity doesn’t change with depth at all.

RMS velocity matters because it’s approximately what standard seismic velocity analysis produces as “stacking velocity,” a number picked by testing which velocity best flattens (removes the moveout from) reflections across a range of source-receiver offsets during processing. Stacking velocity is not exactly RMS velocity, that equivalence relies on flat layering and small offsets relative to depth, but it’s a close enough approximation in typical conditions that the terms get used almost interchangeably in practice.

The Dix Equation: Recovering Interval Velocity from Stacking Data

Since seismic processing naturally produces stacking (effectively RMS) velocities rather than interval velocities, C. Hewitt Dix worked out, in the 1950s, how to invert that relationship and recover the true interval velocity of the layer sitting between two reflectors, given the stacking velocities and two-way times picked at each one.

The Dix equation is:

Vint = √[(V2²T2 − V1²T1) / (T2 − T1)]

where V1 and T1 are the stacking velocity and two-way time to the shallower reflector, and V2 and T2 are the same for the deeper one. The arithmetic is mechanical once you have the four inputs, but the assumptions underneath it matter: it assumes horizontally flat layering and offsets that are modest relative to depth. Where there’s real structural dip, or offsets get large, Dix-derived interval velocities start drifting from the true value, sometimes by a meaningful margin. It’s a workhorse equation, not an unconditionally exact one.

A Worked Example

Take a three-layer model. Layer 1 has an interval velocity of 2,000 m/s and 400 ms of two-way time within it. Layer 2 has an interval velocity of 3,200 m/s and 350 ms of two-way time. Layer 3 has an interval velocity of 3,800 m/s and 300 ms of two-way time.

Layer 1 alone: one-way time is 200 ms, thickness is 2,000 × 0.2 = 400 m. Since it’s the first layer, average velocity and RMS velocity to its base both equal 2,000 m/s, its own interval velocity, because there’s nothing else blended in yet.

At the base of Layer 2: cumulative depth is 400 + (3,200 × 0.175) = 960 m, cumulative two-way time is 750 ms. Average velocity works out to 960 ÷ 0.375 s = 2,560 m/s. RMS velocity, weighting the faster layer more heavily, comes out a bit higher at roughly 2,629 m/s.

At the base of Layer 3: cumulative depth is 960 + (3,800 × 0.15) = 1,530 m, cumulative two-way time is 1,050 ms. Average velocity is 1,530 ÷ 0.525 s = 2,914 m/s, while RMS velocity comes out around 3,010 m/s. Notice the gap between average and RMS velocity widens as the velocity contrast between layers grows, exactly what the weighting difference between the two predicts.

Common Mistakes

Treating RMS (or stacking) velocity as if it were interval velocity directly, without running it through the Dix equation first.

Using a single average velocity to convert time to depth across a section where velocity clearly changes with depth, and being surprised when the result doesn’t match a well tie.

Applying the Dix equation across reflectors with real structural dip or at large offsets, then treating the resulting interval velocity as exact rather than approximate.

Feeding cumulative two-way time into a layered model’s per-layer time field, instead of the time spent within each individual layer, which double-counts time from shallower layers.

Who Uses This

Geophysicists and seismic processors converting stacking velocities from velocity analysis into interval velocities for depth conversion or lithology work.

Students working through the relationships between interval, average, and RMS velocity, and wanting to check Dix equation arithmetic by hand.

Well planning and formation evaluation teams cross-checking a velocity model’s interval velocities against sonic log or checkshot data.

Anyone building a layered earth model who wants to see how much average and RMS velocity diverge as interval velocity contrasts increase with depth.

Try It Above

Use the quick-convert mode for a fast average-velocity check from a known depth and time, build out a full layered model to see average and RMS velocity worked out automatically at every horizon, or switch to the Dix equation mode if you’re starting from stacking velocities instead of already-known interval velocities.

Related Calculators and References

For background on the formulas used above, see SEG Wiki: Dix conversion.