GPR Hyperbola: Reading Pipe Position on a Radargram

What is a GPR hyperbola?

A GPR hyperbola is the inverted-U reflection that a compact buried object produces on a radargram. Ground penetrating radar (GPR) surveys image the subsurface by sending electromagnetic waves into the soil and timing each return signal. The beam of the receiving antenna is wide, so it picks up a pipe before reaching it and after passing it. The slant path is longer at those positions, the echo returns later, and the trace of arrival times forms an arch with its apex directly above the target.

The curve follows a simple rule: two-way time t = 2√(x² + d²) / v. Here x is the antenna's horizontal distance from the target, d its depth and v the radar velocity in the ground.

How do surveyors use the hyperbola in practice?

In three ways: the apex gives position, the apex time gives depth, and the curvature gives velocity. On site the operator stops the cart when an apex appears and sprays a mark directly over it. In the office, software fits a curve to each GPR hyperbola: a narrow arch means slow, wet ground; a broad one, fast, dry ground. That velocity then converts every time reading to depth, which is why our Dielectric Constant (Relative Permittivity) in GPR guide matters so much on mixed Indian soils. For the timing side of the same equation, read more on Two-Way Travel Time (GPR).

Scan lines should cross the service at right angles. An oblique crossing stretches the limbs and inflates the fitted velocity, while a line run along a pipe shows a flat band, not an arch.

A worked example

Suppose a hyperbola has its apex at 16 ns and the fitted velocity is 0.10 m/ns. Depth to the top of the pipe is 0.10 × 16 / 2 = 0.8 m. Half a metre to one side the same pipe should echo at about 18.9 ns, and at two metres away at about 43 ns, exactly the shape drawn above. If the measured limbs fall inside that curve, the ground is slower than assumed and the depth is shallower.

What can the hyperbola tell you about the object?

Some things clearly, others only as hints.

Every arch is picked along a measured scan line, and a survey is billed by those metres. To calculate the survey cost for your own route, enter its length and scope.

Rocks, tree roots and rubble also make arches, so each arch marks a candidate subsurface object, not proof of a pipe. Real examples are collected in the GPR Radargram Library.

Which misreadings of an arch cause the most trouble?

Picking the wrong point on the curve, and trusting a single arch. Most depth errors we see in other people's data come from a short list:

• Picking a limb instead of the apex. Any point off the top arrives later, so the pipe is reported too deep and slightly to one side.
• Treating ringing as a second pipe. Metal often produces a stack of repeated arches beneath the first; only the top one is real.
• Fitting velocity on an oblique crossing. The limbs look wide, the fitted speed comes out high and every depth on that line is inflated.
• Forgetting the radius. The echo comes from the top of the pipe, so the centre of a 600 mm main sits about 0.3 m below the apex depth.

A field scenario on a sector footpath

Five lines, two metres apart, are run across a footpath where a new duct is planned. Line 1 shows three arches with apexes at 9, 14 and 22 ns. Curve fitting gives 0.09 m/ns, so the depths are about 0.41, 0.63 and 0.99 m. Lines 2 to 5 show the shallow and deep arches at almost the same offsets, which marks them as continuous services. The middle arch appears on lines 1 and 2 only. It is most likely a buried kerb stone or a short abandoned stub, and it goes on the drawing as an unconfirmed feature, not a utility.

How do picked arches appear on our drawings?

Each apex becomes a surveyed point, and points that line up become labelled utility lines. For every pick we keep the line number, chainage, apex time, velocity used and calculated depth. In CAD the points join into a polyline on a layer for that utility type. Depth labels sit at intervals, with a confidence note where an arch was weak or broken. The data collected for those picks also feed the KMZ and shapefile, so the field team and the designer see identical positions.

No single code dictates how an arch is fitted. ASTM D6432-19 is the general guide to surface GPR practice, and ASCE 38-22 treats positions found this way as quality level B. PAS 128:2022 is the comparable UK specification for detecting buried services.

Related terms

Migration collapses each arch into a point. To detect and map crossings before digging, request a written estimate for your project.

Frequently asked questions

Why does a straight pipe appear as a curve on GPR?

Because the radar sees the pipe at an angle before and after passing over it. The slant distance is longer, so the echo arrives later, and the arrival times plot as an arch.

Can the hyperbola show the diameter of a pipe?

Only roughly. Large pipes give a flatter apex, and curve fitting can estimate radius, but the result is uncertain. A trial pit is the reliable way to measure size.

How do I learn to recognise hyperbolas on real data?

Start with clean examples and then move to cluttered urban scans; this walkthrough helps: How to Read a GPR Radargram.

Why does the same pipe give a different arch on another day?

Because ground conditions such as soil moisture change the radar velocity. Wetter ground slows the wave, so the arch narrows and the apex arrives later even though the pipe has not moved.

Can two pipes laid close together merge into one arch?

Yes. If they are closer than the antenna can resolve, their echoes overlap into one broad hyperbola. An antenna working at higher frequencies, or a test hole, separates them.

Does the apex give the top or the centre of the pipe?

The top. Radar reflects from the upper surface, so add roughly half the diameter to reach the centre line; on large water pipes that gap is significant.

Written by Saniya Parveen · Technically reviewed by Rahul Rai · Updated 8 November 2026