Seismic Wave Travel Time Calculator
Solve the seismic travel-time relation t = D / v for any of its three unknowns, with step-by-step math, a live subsurface ray-path schematic, and companion metrics including two-way travel time, depth conversion for common velocities, and classification of the wave by medium.
Linear in distance
Travel time is directly proportional to the path length D. Doubling the distance doubles the time. This is why seismic reflections from deep horizons arrive later than shallow ones, and why stacking velocities must be applied as a function of offset.
Inversely proportional to velocity
Doubling the velocity halves the travel time. The velocity of the medium is the single most important parameter determining when a seismic arrival appears at the receiver. In heterogeneous subsurface, v changes with depth and t must be computed by integrating 1/v(z) along the ray path.
Two-way travel time (TWT)
In reflection seismology, the source and receiver are at the same location on the surface, so the wave travels down to the reflector and back up: TWT = 2D/v. Reflection sections are almost always plotted in TWT, not depth, because that is what the seismic trace directly records.
Layering complicates things
The simple t = D/v form only holds when the wave travels through a single medium of constant velocity. In a layered Earth, the ray bends at each interface according to Snell's law, and the total travel time is a sum over the segments: t = Σ Dᵢ/vᵢ. Refraction seismology exploits this to map velocity structure with depth.
How to Use This Calculator
The travel-time relation links three quantities: the travel time, the path distance, and the wave velocity. Pick which one you want the tool to solve, then fill in the others.
1. Choose what to solve for
Pick t, D, or v — the tool rearranges the relation automatically for whichever you choose.
2. Use realistic presets
Travel-time presets span 0.01 s (shallow engineering) to 10 s (deep mantle). Distance presets span 100 m to 200 km. Velocity presets include air (340 m/s), water (1,500 m/s), crustal rock (4,000 m/s), deep crust (6,000 m/s), and mantle (8,000 m/s).
3. Read the result and steps
The result card shows the solved quantity with engineering notation. The step-by-step panel walks through the division and reports the result in alternative units (milliseconds, minutes) and as two-way travel time.
4. Check the subsurface ray path
The diagram shows a layered Earth model with four velocity zones, a seismic source on the surface, a receiver, the direct wave along the surface, and the reflected/refracted ray path down to the reflector and back up. The distance, velocity, one-way travel time, and two-way travel time labels all update live.
5. Switch to Advanced for depth
Advanced mode adds a chart of travel time vs. wave velocity, a 1% sensitivity check, and companion metrics including the travel time in milliseconds, the two-way time, the apparent frequency response for a reference wavelength, and a classification of the medium by velocity.
6. Cross-check with the reference table
The reference section lists typical seismic velocities for common geological materials, plus a lookup grid of travel times across the D–v envelope.
What This Tool Offers
Built around the fundamental travel-time relation used throughout reflection and refraction seismology, earthquake location, and subsurface velocity analysis.
Three-way solving
Solve for travel time, path distance, or wave velocity — whichever the problem gives you.
Live subsurface ray path
A layered Earth cross-section with source, receiver, direct wave, and reflected/refracted ray path, plus depth and velocity annotations.
Dual comparison charts
t vs. distance at three velocities, plus t vs. velocity at three distances.
Companion seismology metrics
Advanced mode reports travel time in milliseconds and minutes, two-way travel time, apparent wavelength for a reference frequency, and a medium classification based on velocity.
Built-in sensitivity check
See how much t moves for a 1% change in distance or velocity. The sensitivities have opposite signs and equal magnitude.
Reference tables
Typical seismic velocities for soils, sediments, sedimentary rocks, crystalline rocks, and the mantle, plus a lookup grid of t across the D–v envelope.
Reference Tables
Typical seismic velocities for common geological materials, and a lookup grid across the distance–velocity envelope.
Travel time quick lookup (ms) — D in km, v in m/s
t = D / v, expressed in milliseconds for various combinations of distance and velocity.
| v (m/s) | D = 0.1 km | D = 1 km | D = 5 km | D = 30 km | D = 200 km |
|---|
Typical Seismic Velocities
Representative P-wave velocities at shallow to moderate depth. S-wave velocities are typically 0.5–0.6 times the P-wave values in the same material.
| Material | v_P (m/s) | v_S (m/s) | Notes |
|---|---|---|---|
| Air | 330 – 350 | — | Reference for acoustic/seismic comparison |
| Water | 1,450 – 1,550 | — | No shear support; controls marine seismic |
| Dry sand / soil | 200 – 800 | 100 – 400 | Velocity strongly depends on saturation |
| Water-saturated sand | 1,500 – 2,000 | 150 – 500 | P-wave jumps at water table |
| Clay / silt | 1,000 – 2,500 | 200 – 800 | Low velocity, low Q |
| Sandstone | 2,000 – 4,500 | 1,000 – 2,800 | Depends on porosity and cementation |
| Limestone | 3,000 – 6,000 | 1,500 – 3,300 | Higher if well-cemented or dolomitic |
| Granite / gneiss | 5,000 – 6,500 | 2,800 – 3,800 | Typical crystalline basement |
| Basalt | 5,500 – 7,000 | 3,000 – 4,000 | Common in oceanic crust |
| Mantle peridotite | 7,800 – 8,500 | 4,400 – 4,900 | Below the Mohorovičić discontinuity |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| t | One-way travel time | 0.001 – 60 | s |
| TWT | Two-way travel time = 2t | 0.002 – 120 | s |
| D | Path distance (or depth for vertical rays) | 1 – 10⁶ | m |
| v | Wave velocity (P or S) | 100 – 15,000 | m/s |
| λ | Wavelength = v / f | 1 – 10,000 | m |
What Does the Seismic Travel Time Measure?
Seismic travel time is the time required for an elastic wave to propagate from a source to a receiver through the Earth. It is the fundamental observable of seismology and seismic exploration: we cannot directly see the subsurface, but we can measure when a wave arrives at each receiver, and from those arrival times infer the structure, velocity, and geometry of the rocks it passed through. The simplest form of the relation, t = D/v, is the starting point for all seismic analysis. Every reflection, refraction, and earthquake location method builds on it, adding corrections for layering, ray bending, anisotropy, and heterogeneity along the path.
Seismic Travel Time Formula
The defining relationship for a constant-velocity medium is:
Where D is the path length and v is the seismic wave velocity. For a vertical reflection survey in which the wave travels down to a reflector at depth z and back to the surface, the two-way travel time is:
In a layered medium, the total travel time is the sum over segments:
Rearranged to solve for distance or velocity:
Travel Time Variables
| Symbol | Meaning | Notes |
|---|---|---|
| t | One-way travel time | Time for the wave to travel from source to receiver |
| TWT | Two-way travel time | Standard display unit for reflection seismology |
| D | Path distance | Length of the ray path, or depth for a vertical ray |
| v | Wave velocity | P-wave, S-wave, or surface-wave velocity of the medium |
| f | Frequency | Related to wavelength by λ = v / f |
| λ | Wavelength | Sets the resolution of the seismic method |
How Each Parameter Moves the Travel Time
Travel time is directly proportional to distance and inversely proportional to velocity. A 1% increase in distance raises t by 1%; a 1% increase in velocity lowers t by 1%. The two effects are symmetric, so the equation is one of the simplest in all of geophysics. In practice, velocity is usually known from well logs or laboratory measurements, and travel time is measured from the seismic record; solving for D therefore recovers depth — this is exactly the "depth conversion" step in every seismic interpretation workflow. Because velocity increases with depth in most sedimentary basins (compaction, cementation), the depth-to-time conversion is not simply linear, which is why a velocity model is essential for accurate depth mapping.
Travel Time Calculation Examples
t = D / v = 5,000 / 4,000 = 1.250 s
In milliseconds: 1,250 ms
Two-way travel time: TWT = 2 × 1.250 = 2.500 s
Apparent wavelength at 30 Hz: λ = v / f = 4,000 / 30 = 133.3 m
D = v · t = 2,500 × 0.8 = 2,000 m
Two-way time from surface: TWT = 1.6 s
Half the reflector depth for a wave that reflects at this depth: yes, 2,000 m is the reflector depth.
v = D / t = 24,500 / 3.5 = 7,000 m/s
Consistent with a ray path sampling the lower crust and uppermost mantle.
Frequently Asked Questions
Travel time (t) is the one-way time for the wave to travel from the source to the receiver along its path. Two-way travel time (TWT) is the round-trip time for a wave that goes from the surface down to a reflector and back up to the same location. In reflection seismology, the source and receiver are both on the surface, so the recorded time is TWT = 2t. Reflection sections are displayed in TWT because that is what the seismic trace directly records; converting to depth requires a velocity model. This calculator solves for t, and reports TWT = 2t alongside it.
Two main reasons: compaction and cementation. As sediments are buried, the increasing overburden pressure squeezes the grains closer together, reducing porosity and increasing the elastic moduli — both effects raise the velocity. Chemical diagenesis — precipitation of quartz, calcite, or clay cement at grain contacts — further stiffens the rock. In the deep crust and mantle, pressure and phase changes dominate: the transition from granite to granulite to eclogite to peridotite produces a step-wise increase in velocity. This monotonic increase with depth is why depth conversion from TWT requires a velocity model, not just a single average velocity.
The water table marks a sharp increase in P-wave velocity: dry sand may have v_P = 300–800 m/s, while the same sand saturated with water has v_P = 1,500–2,000 m/s. The change is caused by the incompressibility of water filling the pore space, which dramatically increases the bulk modulus of the saturated rock while density changes only slightly. This is why the water table is often one of the strongest reflectors on a shallow seismic section, and why the water table depth can be mapped with a seismic survey — a technique widely used in hydrogeology and in groundwater exploration.
Because P-waves (compressional) are supported by both the bulk modulus and the shear modulus of the rock, whereas S-waves (shear) are supported only by the shear modulus. The velocity ratio is v_P / v_S = √[(2 − 2ν)/(1 − 2ν)] where ν is Poisson's ratio. For typical rocks with ν ≈ 0.25, this gives v_P / v_S ≈ 1.73 (the square root of 3). In very porous, gas-filled rocks, ν drops toward zero and v_P / v_S falls toward √2. This ratio is used in exploration seismology to identify lithology and fluid content — a key application of amplitude-versus-offset (AVO) analysis.
Because real rock is not a single homogeneous medium. Three effects violate the assumptions of the simple equation: (1) Velocity varies with depth, so the wave follows a curved ray path according to Snell's law, and the total travel time is an integral over the path. (2) The Earth is anisotropic in many rocks (especially shales), so velocity depends on the direction of propagation. (3) Velocity can vary laterally, so a simple vertical average does not capture the effect of a dipping or faulted structure. Full seismic imaging uses ray tracing or wave-equation migration to handle these effects — but they all reduce to the same fundamental relation, t = D/v, applied locally along the ray path.
An earthquake is located by combining travel-time measurements from many stations with a velocity model. Each station records the arrival time of the P and S waves, and the difference (S − P time) gives the distance to the hypocentre: distance = (S − P) · v_P · v_S / (v_P − v_S). With distance from three or more stations, the epicentre is found by trilateration. The depth requires additional constraints from arrival times at multiple distances, since the distance relationship is not unique without depth information. Modern location codes iterate on hypocentre position and origin time to find the solution that minimises the misfit between predicted and observed arrival times.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| t | Travel time | s |
| D | Distance traveled | km |
| v | Wave velocity | km/s |
What it means
Seismic wave travel time is the time it takes for a seismic wave to travel from an earthquake source to a receiver. It is calculated as distance divided by velocity. This simple relation is the basis for seismic tomography and earthquake location. Variations in travel times reveal differences in subsurface velocity, which are interpreted as changes in rock type, temperature, or fluid content. Travel times are measured from seismograms and are used to construct 3D models of Earth’s interior. Understanding this concept is fundamental for geophysicists to study Earth’s structure and to locate seismic events accurately.
Worked example
Seismic Wave Travel Time – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| D (km) | 100 |
| v (km/s) | 6 |
| Parameter | Value |
|---|---|
| D | 500 |
| v | 8 |
Common mistakes
- Travel time: t = D/v – where D is distance, v is wave velocity.
- Units: D in km, v in km/s → t in seconds.
- Direct vs. reflected waves: Use the appropriate velocity for the wave type (P or S).
- Layered media: For heterogeneous paths, travel time is a sum of segments – this formula is for a single layer.
- Earth curvature: For large distances (>1000 km), use spherical ray tracing – not this simple formula.
Applications
Seismic wave travel time, t = D/v, relates the travel time to the distance from the source and the wave velocity. This is used to compute arrival times in seismic networks and to locate earthquakes. Geophysicists also use travel‑time analysis to determine the velocity structure of Earth's interior, through seismic tomography. By measuring travel times from known sources (e.g., earthquakes or explosions), we can infer the properties of rocks at depth. This formula is essential for both global and exploration seismology, enabling the construction of crustal and mantle models. Understanding travel times is crucial for interpreting seismic data and for imaging the subsurface.
- Earthquake location and travel‑time correction
- Seismic tomography and velocity modelling
- Interpretation of seismic refraction and reflection surveys
- Calculation of arrival times in early warning systems
- Education on wave propagation and travel‑time curves
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