Distributed acoustic sensing (DAS) turns an ordinary optical fiber, such as an unused strand in a telecommunications cable, into a line of thousands of vibration sensors. An instrument called an interrogator sends laser pulses down the fiber and listens to the faint light that scatters back. When a vibration stretches or squeezes a section of fiber, the light scattered from that section changes, so the interrogator can tell where along the fiber the ground moved and how.

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Click the map to strike the ground with a hammer. Click the fiber (or the waterfall below) to choose which channel to plot. The fiber is colored by how fast each part of it is being stretched or squeezed.

Waterfall: strain rate along the fiber over time
squeezingstretching
One channel

Reading the waterfall

Each column of the waterfall is one channel, a short section of fiber, and each row is one moment, with the newest at the bottom. A hammer strike makes a V: the wave reaches the nearest part of the fiber first and then spreads both ways, and the slope of each arm is the wave speed. A passing car makes a diagonal streak whose slope is the car's speed. An earthquake wave from far away arrives as a nearly straight line, tilted by how much the wave travels along the fiber.

A fiber feels only stretching along its length. A wave that crosses the fiber at angle $\theta$ to it is felt with a factor of about $\cos^2\theta$, so a wave arriving broadside ($\theta = 90^\circ$) is nearly invisible. Try sending the earthquake wave from different directions to see this.

Inside the interrogator

How the interrogator measures distance and strain

Glass is not perfectly uniform: tiny variations frozen into the fiber scatter a little of the light backward, which is called Rayleigh backscatter. The interrogator sends a short laser pulse and records the light that returns. Light scattered at distance $z$ returns after it has gone there and back, at time $$ t = \frac{2 n z}{c}, \qquad\text{so}\qquad z = \frac{c\, t}{2 n}, $$ where $c$ is the speed of light and $n \approx 1.47$ is the refractive index of the fiber's core. So the return signal over time is a map of the fiber over distance: a 1 km fiber is read in about 10 μs, and the next pulse can go out right after. The animation above slows this down by a factor of about 400,000. Each pulse produces one row of the waterfall, which fills in from near to far as the light returns; real interrogators send thousands of pulses per second.

The returned light looks like random noise, because the scatterers are randomly placed, but it is the same from pulse to pulse while nothing moves. When a section of fiber of length $G$ (the gauge length) is stretched by strain $\varepsilon$, light has farther to travel through it, and the phase of the light scattered from its far end shifts relative to its near end by $$ \Delta\phi = \frac{4 \pi n \xi G}{\lambda}\, \varepsilon, $$ where $\lambda \approx 1550$ nm is the laser's wavelength and $\xi \approx 0.78$ accounts for how stretching also changes the glass's refractive index. Light from beyond a stretched section passes through it on the way out and back, so its phase is shifted too, and that shift carries on along the rest of the fiber (the first phase graph above). Taking the difference across each gauge removes this carried-over shift and leaves only the strain within that gauge, which is how DAS pinpoints where the fiber stretched (the second graph). Comparing this phase from one pulse to the next gives the strain rate of every section of fiber, thousands of times per second. That is one row of the waterfall.

Why measure phase rather than timing? Because the changes are far too small to time. A vibration might stretch a 10 m section of fiber by about 10 nanometers. That delays the returning light by only about $10^{-16}$ seconds, a million times shorter than an electronic detector can time. But the light itself oscillates about $2 \times 10^{14}$ times per second, and 10 nm is a noticeable fraction of its 1550 nm wavelength. So the delay shows up as a measurable shift in where the light is in its oscillation, its phase, which the interrogator reads by interfering light from the two ends of the gauge. In effect, the phase is timing measured with the light's own oscillations as the clock ticks. (Measuring Distance with the Phase of Light shows this with a simple interferometer.) The round-trip time is still what tells the interrogator where the light came from; the phase tells it how much that section stretched.

What is the light interfered with? In one common design, the returning light is interfered with itself. The receiver splits it into two paths, one longer than the other by the round trip across one gauge length, and then recombines them. That way, the light scattered at distance $z$ meets the light scattered at $z + G$ at the same moment. The two waves add, and how bright their sum is depends on the phase difference between them: in step they add to twice the brightness, out of step they cancel. The resting phase difference is random, because the scatterers are, but when the section between them stretches, it changes, and so does the brightness. (Real receivers split the light three ways, with different extra phase shifts, so they can tell which way the phase moved, not just how bright the sum is.) In the other common design, called coherent or heterodyne detection, the returning light is interfered with a copy of the laser's own light, slightly shifted in frequency. That recovers the phase at every point along the fiber, and the interrogator then subtracts the phases at the two ends of each gauge. Measuring Distance with the Phase of Light has interactive demos of both designs.

The gauge length sets the trade-off between sensitivity and detail: a longer gauge collects more phase change, so it is less noisy, but it averages over more fiber, so it blurs out waves shorter than the gauge. Try a long gauge length with the walker, whose footsteps make short waves.

This page simplifies the physics for illustration: each source makes a single wavelet that travels at one speed, the ground is uniform, and the strain rates are in arbitrary units.