Distributed acoustic sensing of microseismic sources and wave propagation in glaciated terrain

Records of Alpine microseismicity are a powerful tool to study landscape-shaping processes and warn against hazardous mass movements. Unfortunately, seismic sensor coverage in Alpine regions is typically insufficient. Here we show that distributed acoustic sensing (DAS) bridges critical observational gaps of seismogenic processes in Alpine terrain. Dynamic strain measurements in a 1 km long fiber optic cable on a glacier surface produce high-quality seismograms related to glacier flow and nearby rock falls. The nearly 500 cable channels precisely locate a series of glacier stick-slip events (within 20–40 m) and reveal seismic phases from which thickness and material properties of the glacier and its bed can be derived. As seismic measurements can be acquired with fiber optic cables that are easy to transport, install and couple to the ground, our study demonstrates the potential of DAS technology for seismic monitoring of glacier dynamics and natural hazards.

Along the northern cable section a total of 28 explosive charges (125 g of Riodin HE) were drilled through the snow and set off ca. 30 cm within the ice to investigate the performance of the DAS system in active seismic experiments. (A) Explosion seismograms of all channels along this segment are shown for a single shot. Green and red curves indicate the expected arrival times of direct and reflected P-waves traveling at 3800 m/s and the dominant phase is the Rayleigh wave. The lack of a clear reflection is likely related to the poor ice-cable coupling resulting from the damping snow layer. (B) Shot seismograms recorded on Station RA51 with x-axis indicating source-station distances and y-axis indicating time relative to direct P-wave arrival. Each time series represents a single shot and all shots are located along the northern cable section connecting RA51 with RA52. In contrast to the shot gather of Panel A, a small secondary arrival is visible (red line) in Panel B, which we interpret as the basal P reflection. For wavenumbers above 0.04 m -1 (wavelength below 160 m) and frequencies above 10 Hz, the frequency-wavenumber peaks lie near a straight line whose slope describes the propagation velocity of a Rayleigh wave. In contrast, at lower wavenumbers, this linear relation between frequency and wavenumber is no longer apparent which we suggest is a manifestation of the 220 m length limit of the cable segment. Notice that at all stations, the first P-wave break is suddenly interrupted by a downward motion after approximately 1 sample (2 ms). This is the results of a "ghost", i.e. reflection off the ice surface, which reaches the borehole seismometer slightly later than the direct wave. Prior to the first P-wave break, acausal precursory oscillations at the Nyquist frequency of 250 Hz are visible, which may mask weaker refracted arrivals.  Figure 12 that the DAS and acceleration pulse shapes are practically identical up to frequencies of 50 Hz. The pulse shapes start to differ substantially only for frequencies above 100 Hz, which corresponds to a wavelength of 15 m, i.e., 1.5 times the gauge length.

Supplementary Notes
In these supplementary notes, we derive the phase and amplitude of plane waves recorded by DAS. This has implication for our ability to measure traveltimes in DAS waveforms, depending on the frequency range that we consider. The major conclusion is that DAS recordings of strain rate are practically identical to a scaled acceleration recording for wavelengths exceeding the gauge length. Only for wavelengths shorter than about half the gauge length, pulse shapes start to differ more substantially, potentially leading to biased traveltime measurements.

Supplementary Note 1: Plane waves recorded by DAS
We consider a plane wave displacement at position x in the frequency domain, where A is the polarisation vector, k is the wave number vector of length |k| = k, and ω is the circular frequency. In the time domain, Equation (1)  DAS measures strain rate averaged over a certain length, the gauge length. So, we first compute the strain tensor related to the displacement in (1): The optical fibre is oriented in a certain direction, specified by the unit vector e. The strain in that direction is = e i ij e j = −i (e T A)(e T k) e −i(k T x+k∆) . (3) More generally, the orientation is position-dependent, i.e., e = e(x). Here, for simplicity, we consider e constant. In the next step, we average the strain over a certain distance along the fibre. For this, we parameterise the position x as This means, we consider a gauge length , half of which is left of the measurement location x = 0, and the other half is right of it. Carrying out the averaging integral, we find = 1 Taking the time derivative of (5) in the frequency domain (multiplication by iω), we finally obtain the stain rate averaged over the gauge length: Equation (6) holds for both P and S waves, as we have not specified the polarisation direction.

Supplmentary Note 2: Amplitude spectrum
It is clear from Equation (6) that the measurement of strain rate and the act of averaging over the gauge length has modified the amplitude spectrum from the constant in the displacement Equation (1) to where is the effective wave length, and n is the unit-length propagation direction parallel to k. (This is the wavelength seen by the fibre. When the propagation direction is exactly along the fibre, we have n e and λ a = λ. In the other extreme case we have n ⊥ e, and the apparent wavelength is infinite.) The averaging over the gauge length acts to eliminate certain frequencies from the spectrum. In fact, the spectral amplitude vanishes for all frequencies ω for which an integer multiple of λ a fits into the gauge length, that is, = nλ a , n ∈ N .
Interestingly, Equation (11) also implies that the contributions of frequencies with are added to the complete time-domain DAS recording with reversed amplitude. Obviously, this is only something that happens at high frequencies.

Supplementary Note 3: Phase spectrum and traveltimes
Since the amplitde spectrum is obviously complicated, we consider the special case of low frequencies. For this, we express (6) in terms of ω: where we introduced the apparent velocity For frequencies that are low in the sense of we may approximate the sin in (11) Equation (14) shows that the spectrum of the DAS recording is identical to the spectum of displacement acceleration (i.e., proportional to ω 2 ), just scaled by the inverse apparent velocity c a and the orientation term e T A. In this long-wavelength scenario, the DAS measurement will look like a displacement acceleration recording at x = 0.
In any case, we see that the phase of the DAS response (6) is exactly the same as the phase of the displacement (1) measured at x = 0, namely e −ik∆ . Thus, the whole prodecure of computing strain, averaging over the gauge length, and taking a time derivative has not changed the phase. As a consequence, we still observe a pulse centred at an arrival time of t = ∆/c. What has changed is the pulse shape in the time domain. However, since the frequency-domain amplitude (7) is real-valued, it is still symmetric around the arrival time, meaning that we do not expect any picking error due to a skewed pulse shape.

Supplementary Note 4: Examples
To illustrate the above developments, we consider a specific case where the gauge length is =10 m, and the apparent velocity is c a =1700 m/s. Supplementary Figure 12 shows the amplitude spectrum of a DAS recording compared to the aplitude spectrum of an acceleration recording. The latter also corresponds to the low-frequency approximation of the DAS response. Supplementary  Figure 13 contains a collection of pulse shapes as a function of frequency. The main conclusion is that the DAS recording is practically identical to a scaled acceleration recording for frequencies up to around 50 Hz. Only above 100 Hz the pulse shapes start to differ more substantially. Still, up to around 150 Hz, the traveltime picking error (based on picking the maximum) is exactly zero.