Seismic Refraction Depth Calculator

Find the depth to a subsurface refractor from a two-layer seismic refraction survey's layer velocities and intercept time.

🌍 Seismic Refraction Depth Calculator
Upper layer velocity (V1)
m/s
1003000
Lower layer (refractor) velocity (V2)
m/s
5006000
Intercept time (ti)
ms
1200
Depth to refractor
—
Crossover distance
—
Critical angle
—

🌍 What is Seismic Refraction Depth?

Seismic refraction depth is the depth to a subsurface layer boundary (refractor) determined from a refraction survey's recorded travel times, using the intercept-time method to convert layer velocities and a refracted wave's zero-offset intercept time into a depth estimate.

Geophysicists and geotechnical engineers use this constantly, to map bedrock depth before building foundations, to locate the water table or subsurface soil layers for site investigations, to plan excavation and blasting by knowing where hard rock begins, and to interpret raw refraction survey field data into a usable subsurface depth model.

A common misconception is that the first geophone to record an arrival always reflects the shortest travel path. It doesn't, beyond the crossover distance, the refracted wave becomes the first arrival even though its path is longer, because most of that path travels through the faster lower layer, this crossover behavior is exactly what makes refraction depth estimation possible.

This calculator computes depth to the refractor, crossover distance, and critical angle from your layer velocities and intercept time, and plots the direct and refracted wave travel-time lines so you can see exactly where they cross.

📐 Formula

z = tiV1V2 / (2√(V2² − V1²))
ti = refracted wave intercept time (s)
V1, V2 = upper and lower (refractor) layer velocities (m/s), V2 > V1
xcross = tiV1V2 / (V2−V1), θc = arcsin(V1/V2)
Example: V1=500 m/s, V2=2000 m/s, ti=50 ms → z=12.91 m.

📖 How to Use This Calculator

Steps

1
Enter layer velocities. Type the upper layer velocity V1 and the faster lower layer (refractor) velocity V2.
2
Enter the intercept time. Type the refracted wave's travel-time intercept at zero offset, read from your travel-time curve.
3
Read the depth and travel-time curve. The calculator reports depth to the refractor, crossover distance, and critical angle, and plots the direct and refracted travel-time lines.

💡 Example Calculations

Example 1 — Shallow Soil Over Weathered Rock

V1=500 m/s, V2=2000 m/s, ti=50 ms

1
z = 0.05×500×2000 / (2×√(2000²−500²)) = 12.91 m
2
xcross = 0.05×500×2000 / (2000−500) = 33.33 m
Critical angle θc = arcsin(500/2000) = 14.48°
Try this example →

Example 2 — Sediment Over Deeper Bedrock

V1=1500 m/s, V2=4000 m/s, ti=80 ms

1
z = 0.08×1500×4000 / (2×√(4000²−1500²)) = 64.72 m
2
xcross = 0.08×1500×4000 / (4000−1500) = 192.00 m
Critical angle θc = arcsin(1500/4000) = 22.02°
Try this example →

Example 3 — Thin Overburden Over Hard Rock

V1=800 m/s, V2=3500 m/s, ti=30 ms

1
z = 0.03×800×3500 / (2×√(3500²−800²)) = 12.33 m
2
xcross = 0.03×800×3500 / (3500−800) = 31.11 m
Critical angle θc = arcsin(800/3500) = 13.21°
Try this example →

❓ Frequently Asked Questions

What is seismic refraction surveying?+
Seismic refraction is a geophysical technique that generates seismic waves at the surface and records their arrival times at a line of receivers (geophones) at varying offsets, using the differing travel times of direct and refracted (head) waves to determine subsurface layer velocities and depths.
How do you calculate depth to a refractor from a seismic refraction survey?+
Using the intercept-time method, depth z = ti*V1*V2 / (2*sqrt(V2^2-V1^2)), where ti is the refracted wave's travel-time intercept at zero offset (read from a straight-line fit to refracted arrival times), and V1 and V2 are the upper and lower layer velocities.
What is crossover distance in seismic refraction?+
Crossover distance is the offset at which the refracted wave's travel time becomes shorter than the direct wave's travel time, beyond this distance the refracted arrival is the first arrival recorded. It is calculated as xcross = ti*V1*V2 / (V2-V1).
What is the critical angle in seismic refraction?+
The critical angle is the angle of incidence at which a seismic wave refracts along the boundary between two layers rather than continuing into the lower layer, given by thetac = arcsin(V1/V2). Waves hitting the boundary at exactly this angle generate the head wave that produces refracted arrivals at the surface.
Why must V2 be greater than V1 for this method to work?+
Refraction seismology depends on a head wave forming, which requires the lower layer to have a faster velocity than the upper layer (V2 greater than V1). If the lower layer were slower, no critical refraction (and therefore no head wave or refracted first arrival) would occur, and this method cannot determine that layer's depth.
How is intercept time (ti) obtained from real field data?+
Intercept time comes from fitting a straight line to the refracted wave's arrival times at multiple offsets (the far-offset portion of the travel-time curve) and extrapolating that line back to zero offset. The travel time where that fitted line crosses the time axis is the intercept time ti.
What causes errors in seismic refraction depth estimates?+
Common error sources include a refractor that dips rather than lying flat, near-surface velocity variations, incorrectly picking the first-break arrival times, and hidden intermediate layers (the blind zone problem), all of which this simplified flat two-layer model does not account for.
What units does this calculator use?+
Layer velocities V1 and V2 are entered in meters per second (m/s), and intercept time is entered in milliseconds (ms). Output depth and crossover distance are in meters, and the critical angle is in degrees.
How is seismic refraction used in practice?+
Seismic refraction surveys are widely used for near-surface site investigation, including mapping bedrock depth for construction and foundation engineering, locating the water table, groundwater and mineral exploration, and characterizing soil and rock layers before excavation projects.
How does this differ from seismic reflection surveying?+
Seismic refraction relies on head waves that travel along a layer boundary and re-radiate upward, best suited to shallow, near-surface layer depths. Seismic reflection instead records waves that bounce directly off boundaries and is used to image much deeper subsurface structure, including the reflection coefficient calculations covered by a separate calculator.
Tags: Seismic Refraction Calculator Seismic Refraction Depth Calculator Refractor Depth Calculator Crossover Distance Calculator Geophysics Calculator Calculator Formula Free Online

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What is seismic refraction surveying?

Seismic refraction is a geophysical technique that generates seismic waves at the surface and records their arrival times at a line of receivers (geophones) at varying offsets, using the differing travel times of direct and refracted (head) waves to determine subsurface layer velocities and depths.

How do you calculate depth to a refractor from a seismic refraction survey?

Using the intercept-time method, depth z = ti*V1*V2 / (2*sqrt(V2^2-V1^2)), where ti is the refracted wave's travel-time intercept at zero offset (read from a straight-line fit to refracted arrival times), and V1 and V2 are the upper and lower layer velocities.

What is crossover distance in seismic refraction?

Crossover distance is the offset at which the refracted wave's travel time becomes shorter than the direct wave's travel time, beyond this distance the refracted arrival is the first arrival recorded. It is calculated as xcross = ti*V1*V2 / (V2-V1).

What is the critical angle in seismic refraction?

The critical angle is the angle of incidence at which a seismic wave refracts along the boundary between two layers rather than continuing into the lower layer, given by thetac = arcsin(V1/V2). Waves hitting the boundary at exactly this angle generate the head wave that produces refracted arrivals at the surface.

Why must V2 be greater than V1 for this method to work?

Refraction seismology depends on a head wave forming, which requires the lower layer to have a faster velocity than the upper layer (V2 greater than V1). If the lower layer were slower, no critical refraction (and therefore no head wave or refracted first arrival) would occur, and this method cannot determine that layer's depth.

How is intercept time (ti) obtained from real field data?

Intercept time comes from fitting a straight line to the refracted wave's arrival times at multiple offsets (the far-offset portion of the travel-time curve) and extrapolating that line back to zero offset. The travel time where that fitted line crosses the time axis is the intercept time ti.

What causes errors in seismic refraction depth estimates?

Common error sources include a refractor that dips rather than lying flat, near-surface velocity variations, incorrectly picking the first-break arrival times, and hidden intermediate layers (the blind zone problem), all of which this simplified flat two-layer model does not account for.

What units does this calculator use?

Layer velocities V1 and V2 are entered in meters per second (m/s), and intercept time is entered in milliseconds (ms). Output depth and crossover distance are in meters, and the critical angle is in degrees.

How is seismic refraction used in practice?

Seismic refraction surveys are widely used for near-surface site investigation, including mapping bedrock depth for construction and foundation engineering, locating the water table, groundwater and mineral exploration, and characterizing soil and rock layers before excavation projects.

How does this differ from seismic reflection surveying?

Seismic refraction relies on head waves that travel along a layer boundary and re-radiate upward, best suited to shallow, near-surface layer depths. Seismic reflection instead records waves that bounce directly off boundaries and is used to image much deeper subsurface structure, including the reflection coefficient calculations covered by a separate calculator.

📌 Quick Tips

💡Seismic refraction surveys work because a wave hitting a boundary at exactly the critical angle travels along the interface at the faster layer's velocity, continuously re-radiating energy back up to the surface, this head wave is what produces the refracted arrival.
💡At short offsets, the direct wave (traveling straight through the upper layer) always arrives first, at long offsets the refracted wave, despite its longer path, arrives first because most of that path travels at the faster refractor velocity, the crossover distance is exactly where the two arrival times are equal.
💡This calculator uses the intercept-time method, reading the refracted wave's travel-time line back to its intercept at zero offset, a different but related crossover-distance method solves for depth using only the crossover distance and layer velocities.
💡This simplified two-layer model assumes a flat, horizontal refractor with V2 uniformly greater than V1, real subsurface geology often has dipping or irregular interfaces, which needs more advanced reciprocal or delay-time methods to interpret correctly.
💡Layer velocities are normally read as the reciprocal slopes of straight-line fits to real travel-time data, V1 from the direct wave's slope and V2 from the refracted wave's slope, this calculator takes those already-fitted velocities as inputs.