Geolocation of Distributed Acoustic Sampling Channels Using X-Band Radar and Optical Remote Sensing

Abstract

Distributed Acoustic Sensing (DAS) is a new oceanographic measurement technology that exploits the physical sensitivities of fiber-optic communication cables to changes in pressure, allowing time series measurements of pressure at meter-scale spacing for ranges up to 150 km. The along-cable measurement locations, called channels, are evenly distributed, but the specific locations of each are initially unknown. In terrestrial applications, channel locations are often found by the “tap test” where acoustic transients are created at surveyed locations along the cable. For submarine installations, tap tests are inconvenient or logistically impossible. Here we describe a new method for submarine channel geolocation by comparing DAS signals to ambient ocean wave time series using a variety of cross-spectral methods. Ground truth data were derived from two remote sensing sources: marine radar (X-band) and shore-based cameras. The methods were developed and tested at two coastal locations and showed an ability to geolocate DAS channels to within 10 m at ranges of up to 3 km (radar) or within 1.0 m at ranges up to 600 m (optical).

1. Introduction

Distributed Acoustic Sensing (DAS) is an emerging technology in oceanography that allows fiber-optic cables to be used to measure geophysical signals. A single DAS interrogator attached to one end of a fiber-optic cable can record cable strain and temperature at meter-scale intervals for up to 150 km, continuously and at kHz frequencies. This spatial and temporal resolution has made DAS a popular technology in a variety of terrestrial fields such as seismology, cryosphere and hydrosphere research, border security, mining, traffic control, and structural health monitoring [1,2,3]. Recently, there has been a significant increase in applications of DAS for recording ocean processes on both commercially available telecommunication cables and custom-installed cables. DAS has been used for acoustic monitoring of marine mammals and storms [4,5,6,7,8] and submarine seismology and stratigraphy [9,10,11,12,13,14,15,16]. There have also been significant advances in the use of DAS for measuring oceanographic processes including surface gravity waves [17,18,19,20], internal waves [21,22], turbulence [23], and tsunamis [24].

Fundamentally, DAS measures changes in the phase of the continuous Rayleigh backscatter of laser light from micro-impurities in the cable as a pulse transits along the cable from a shore-based interrogator. In the absence of environmental change, the phase of this reflected signal will be unchanging. However, optical fibers are sensitive to environmental change in two ways: there is a dependence of the refractive index of the glass, n, on pressure and temperature, and a sensitivity to along-cable strain (compression or extension) and changes in cable length [25,26,27], which in turn affect the phase of the reflected light. Strain can be generated by non-static pressure or vibrations. The change in phase resolves signals with nano-strain and milli-kelvin sensitivity [21]. In the following, we will focus on pressure sensitivities only. These measurements are computed over a reference length, called the gauge length, which is typically 2–20 m. Consequently, the spatial resolution of the measurements is always limited by this gauge length. As guiding rule, the gauge length should not be less than 3/2 of the length of the laser pulse [28].

The time-varying phase signal is discretized to a series of “channel” locations, which represent a discretization in the sampling time interval based on the two-way travel time of light in glass. The channel spacing is defined by the user at the time of data collection, based on the desired spatial resolution and data storage limitations. Thus, the instrument returns time series (one time sample for each laser pulse) at a set of along-cable channel locations. Geolocating these channels in a useful coordinate system is a significant challenge for any DAS application.

Traditionally, channel locations have been identified by providing a known strain signal at a known location, colloquially known as “tap testing.” For example, a hammer strike on a plate on the ground or beach surface can be used to generate an acoustic signal at surveyed locations adjacent to a buried fiber [29,30,31], allowing estimation of DAS channel locations based on signal arrival times at different parts of the cable [32]. Unfortunately, these methods generally require direct or nearly direct access to the cable to reduce uncertainty due to long distances [29]. It is not usually logistically or physically possible to conduct direct tap tests on submarine cables, even when the exact cable path is known.

In the absence of tap testing, most submarine DAS studies have relied instead on approximations of cable channel location based on other signals such as the passage of a transiting vehicle, with accuracies of meters to tens of meters [17], or estimates based purely on the distance along fiber from some shore-based reference location. However, the along-fiber cable locations are usually derived from GPS surveys of the cable-laying vessel rather than the cable. These surveys can be spatially sparse and provide only an approximation of the bottom cable location. And again, the location of individual channels along the cable trajectory can only be known from some proximity measure. Without accurate channel geolocations, the locations of measured signals cannot be determined.

Here, we propose exploiting time series analysis methods to compare DAS strain at any channel with ground truth measurements of surface gravity waves recorded by in situ pressure sensors and/or remote sensing from shore-based radar and optical cameras. Our goal is to develop and test signal processing methods to allow meter-scale geolocation of a suite of DAS channels by comparison against non-transitory, natural signals like ocean waves. We demonstrate this method in three ways: first in comparisons against fixed wave sensors installed at known locations, second against wave signals from a shore-based radar located on an ocean beach, and third against optical time series from shore-based cameras, also overlooking an open ocean beach. For the natural beach cases, wave data were collected for waves arriving from different directions, and 2D DAS channel locations were found at intersections of lines of zero estimated time lag (explained in Section 2).

Section 2 describes the general signal processing methods used. Section 3 describes a series of tests, first with an analysis of a wave tank dataset—the most controlled of the three cases—and a demonstration of the cross-spectral methods. This is followed by the case of a pre-existing communication cable transiting from land to sea near Florence, Oregon, comparing against marine radar data. Finally, we discuss a short, cross-shore cable installation at a research site at Duck, North Carolina, comparing DAS signals with image time series data from shore-based cameras. We then close with Discussion and Conclusions.

2. Methods

The heart of geolocation methods, including the tap test, is the estimation of time lags between DAS signals from various channels and a ground truth that is well geolocated. Here we use fixed instruments, radar and camera data, as the ground truth. The signals to be compared are random-wave time series, and we use cross-spectral methods, which provide robust signatures of time lags.

Consider two time series, y₁ and y₂, which measure the same ocean waves, potentially with different imaging physics, but with a time lag, Δt, between the signals due to either a spatial displacement or a time sync difference in the acquisition systems. If we compute a cross-spectrum between the signals, we can estimate a coherence-squared (referred to hereafter as “coherence” for simplicity) that measures the similarity of the signals as a function of frequency, and a phase function, ϕ(f), representing the relative phase of the two signals as a function of frequency, f (example shown in Figure 1). This phase can represent geophysical differences in the way the instruments sense the same ocean waves. For example, if one sensor responds to sea surface elevation and the other orbital velocity, there will be a 90° phase difference at all frequencies. Here we assume that those phase relationships are constant throughout the ocean wave band. On the other hand, if there is a time lag, Δt, between the signals, the associated phase correction, ϕ’(f), will be

$${\varphi }^{\prime }=2\pi {\displaystyle \frac{∆t}{T}}=2\pi f∆t$$

(1)

where T = 1/f is the wave period. From this we see that a time offset causes a linear phase ramp with frequency. By inverting this relationship, the time lag can be found as the mean slope over the coherent wave band,

$$∆t={\displaystyle \frac{1}{2\pi }} {\displaystyle \frac{d{\varphi }^{\prime }}{df}}$$

(2)

Figure 1 illustrates this concept with an example cross-spectrum between a DAS channel (205) from the Florence cable and an ADCP wave-measuring instrument at a known location at a 20 m depth (field work details are explained below). The two spectra (upper panel) are qualitatively similar and are highly coherent (middle panel) at frequencies between around 0.06 and 0.135 Hz (red asterisks in the bottom panel). The phase shows a clear ramp through the 0.075 Hz wide coherent band with a total change of ~3.5π, equivalent to a time lag of 23.3 s. If the time series are re-aligned by this amount, the remaining phase ramp will have a near-zero slope, and the process can be repeated to find an accurate time lag to null the phase slope, after which the remaining sampling phase relationships can be found. For this method, the coherent band is defined based on the cumulative “excess” coherence, where the excess is defined as the coherence minus the 95% confidence level on incoherence (above which signals are more than 95% likely to be coherent), shown as a dashed line in Figure 1. This cumulative excess will build over the coherent band to a maximum—the coherent band is defined as the frequency locations of 10% and 90% of this cumulative maximum and is marked in the figure by two red asterisks, at frequencies of 0.06 and 0.135 Hz. The slope of the phase ramp is found from the mean slope of the unwrapped phase in this band. If the maximum cumulative coherence is less than a user-defined threshold, the analysis is aborted.

The above method provides an estimate of time lag between a DAS channel and a single instrument but does not provide the direction of displacement if the time lag is due to spatial displacement. To estimate direction requires a 2D array of ground truth data, such as that provided by remote sensors like radar and camera imagery. Figure 2a shows an example tile of image pixels surrounding an initial-guess location of DAS channel 136 in Duck, NC. Cross-spectral estimates of time lag between the DAS time series and synchronized time series from each pixel location can then be found and a time lag array created (Figure 2b). The time lag array shows an apparent linear plane sloping from seaward to landward (right to left) with a slight rotation that aligns with the dominant wave direction. These data, [x_p, y_p, Δt], can be fit to a 3D plane, p₁x_p + p₂y_p + p₃Δt + p₄ = 0. The line of zero lag, defined as the line for which lag = 0, is then defined by the vector p_zero = [p₁, p₂, p₄] and is shown in Figure 2b by the black line. We know that the true channel position should lie on that line, although we do not know where because we can only find time lags in the direction of wave propagation, not along wave crests. If we analyze data from two days with different wave directions, the true channel location will be at the intersection of the two zero-lag lines. Multiple days can similarly be combined for more robust channel position estimates.

3. Results

3.1. Tests in a Wave Tank Environment

The geolocation method was first tested in the long wave flume at the O.H. Hinsdale Wave Research Lab at Oregon State University during the “Hybrid Flow-Sediment-Structure Interaction Analysis of Extreme Scour due to Coastal Flooding” experiment in 2024. The tank is 110 m long and 3.7 m wide. Concrete slabs were used to build a beach with a 15 m long, 1:12 ramp and a ~20 m flat section. The water depth was 4.6 m offshore of the beach and 0.55 m over the flat section. Geolocation tests were based on six fixed instruments attached to the tank wall over the flat section, three capacitance wire wave gauges at x = 36.12, 39.77 and 43.44 m from the wavemaker and three acoustic Doppler velocimeters (ADVs) at x = 35.91, 39.61, and 39.62 m (the latter two were at different water depths).

Two tests were conducted on 29 July 2024, using 12.3-min, 100 Hz time series of random waves with a significant wave height of 0.4 m and a peak wave period of 2.5 s. For each test, each of the six sensors was compared to each other sensor using cross-spectral analysis, and temporal offsets were computed. Spatial offsets were computed from the temporal offsets by multiplying by the finite amplitude wave celerity, c, as follows [33]:

$$c^2= g/k(1+f_1{\in }^{2}D) tanh\left(kh+ f_2\in \right)$$

(3)

where $\in =kH/2$, H is the wave height, k is the wavenumber (2π divided by the wavelength, L), h is the depth, g is the acceleration due to gravity, and

$$D={\displaystyle \frac{8+cosh\left(4kh\right)-2{tanh}^2\left(kh\right)}{8{sinh}^4\left(kh\right)}}$$

(4)

$$f_1\left(kh\right)={tanh}^5\left(kh\right),$$

(5)

$$f_2\left(kh\right)={\left({\displaystyle \frac{kh}{sinh\left(kh\right)}}\right)}^4$$

Estimates of each instrument position were found based on spatial offsets from the other five instruments. Since wave propagation was only in the x direction, only x locations of instruments could be estimated.

Figure 3 compares the geolocation estimates (y-axis) to surveyed wave gauge locations (x-axis) for all sensor pairs. The standard deviation of the estimation error is 0.42 m, supporting the validity of the method. It should be noted that the result is dependent on the merit of the finite amplitude celerity calculations. In subsequent applications, as discussed below, time lags are also a result of location offsets. But our main product will be lines of zero lag, so celerity estimates are not needed.

In the following sections, these cross-spectral methods will be applied to ocean field situations, first by comparing DAS signals to radar remote sensing images at Florence, Oregon (Section 3.2), and then by comparing against optical camera data at Duck, North Carolina. Each will rely on estimations of lines of zero lag and their intersections.

3.2. Radar Synch Testing at Florence, Oregon

Figure 4 shows a map view of the DAS cable and instruments from Florence, Oregon, from field tests in 2022. At the request of the cable owner and to protect the actual cable geolocation, all locations have been shifted to a reference origin at the estimated location of DAS channel 1. The fiber-optic cable (blue dots) was installed and surveyed in 2009, connecting Florence to Anchorage, Alaska. The shared survey data was sparse, with only nine points (black circles) defining the cable trajectory out to 5 km, the range of the radar used in 2022. The ground truth in 2022 included an ADCP wave sensor (red circle) installed in 20 m of water depth, approximately 30 m north of the cable that collected 2048 s long, 1 Hz records every hour. A marine radar (X-band) was deployed near the north jetty of the Siuslaw River, about 2.7 km from the ADCP. Radar data were recorded continuously but stored in 15-min files. The radar had a rotation period of 1.24 s and was sampled with an azimuth resolution of 0.5°, a range resolution of 3.0 m, and a maximum range of 5 km. DAS data were recorded using a Sintela Onyx interrogator recording at 1000 Hz with a channel spacing of 6.38 m. The strain time series were decimated to 2 Hz, and temporal samples were then interpolated to radar sample times.

The first objective was to find the DAS channel that was closest to the 20 m ADCP. While this is not a requirement for the method in general, it allowed a much-improved initial guess of all DAS channel locations based on this location estimate and the user-defined channel spacing. The analysis was complicated by the fact that the ADCP used an internal clock that could drift away from an initial UTC time synch set prior to deployment. Cross-spectral comparisons were used iteratively to estimate this time offset, Δt, adjusting the ADCP time shift until the phase ramp approached zero. The time lag and cumulative excess coherence were computed for each candidate DAS channel, and the channel with maximum cumulative coherence was selected as the closest channel (Figure 5), in this case channel 227, with an optimum Δt of −59.4 s.

This process was carried out for each hourly ADCP time series over eight days (Figure 6). The average closest channel was found to be 226 (Figure 6, second panel) with a stable average time lag of 59.1 s. From this estimate of the position of channel 226 and knowing the user-defined channel spacing and the approximate cable trajectory, the cross-shore and longshore locations for each channel could be estimated.

Knowing the approximate channel locations, DAS time series could now be compared to local radar time series to find planes of time lag and hence lines of zero-time lag, as described in the Methods Section. The nearest 30 radar pixels to the initial-guess locations were chosen to build the lag plane. However, since radar pixels at this distance were much more closely spaced in range, versus azimuth, the range data were first decimated by a factor of five. Two-hour-long radar datasets were used, representing days with dissimilar wave approach directions on 8 and 10 October 2022. Note that both radar and DAS were time-synced to UTC, a simpler case to analyze. Figure 7 shows an example of five DAS channel locations (218, 222, 226, 230, and 234) and the two intersecting zero-lag lines for each. Estimated channel locations (red asterisks at line intersections) are located close to expected guess locations (black asterisks). For the five illustrated channels, the average misfit was 6.5 m with a full range of 4.2 to 8.3 m.

Figure 8 shows the results for all 685 channels spanning from the shore to ~4 km offshore. The estimated locations generally match well with the initial-guess locations, confirming the surveyed path trajectory and providing all the DAS channel locations. Figure 9 shows the discrepancy, defined as radar-estimated minus initial-guess locations, with the x-component shown in panel a, the y-component in panel b, and the magnitude in panel c. The discrepancy is taken as a rough proxy for estimate errors since there is no actual ground truth for DAS locations. Panel a, the x-component of discrepancy, shows this component to be the largest source of discrepancy, with radar estimates shifted slightly landward from initial guesses close to shore (small x) but shifted to seaward by up to 60 m for offshore locations.

Figure 10 shows the mean (panel a) and standard (panel b) discrepancy statistics as a function of x, calculated in 100 m block averages (approximately 16-channel blocks). The bottom panel (c) shows the approximate bathymetry based on the original installation survey from 2009. Landward of about 30 m depth (x = 2000), mean discrepancies are typically 10–20 m, as are along-cable standard deviations, with the tightest performance for depths around 10–30 m. For deeper waters, standard deviations are larger, perhaps consistent with greater attenuation of pressure signal in the bottom-mounted DAS data. Overall, the radar geolocation method appears to be good to around +/−20 m, although data outside the surf zone and shallower than 30 m depths shows mean and standard deviation discrepancies around 10 m.

In the following section, these methods are tested using optical camera data from a 1600 m cable installed at Duck, NC. In this case, four data collections are used to provide a least squares estimate of each DAS channel location.

3.3. Camera-Based Testing at Duck, North Carolina

A 1600 m fiber-optic cable was installed in 2021 at the U.S. Army Corps of Engineers Field Research Facility (FRF), located on a long, straight beach on the Outer Banks of North Carolina, USA. The cable was a 9.4 mm OD Single Armor Umbilical with two single-mode and two multimode, tightly buffered fibers inside a gel-filled steel tube, covered in plastic and surrounded by a spiral of steel wire with a plastic sheath. The cable spool was attached to the stern deck of an amphibious LARC (Lighter Amphibious Resupply Cargo, a military surplus vehicle) while it drove straight offshore, following the y = 990 m transect across the narrow beach out to a 13.5 m depth (FRF uses a local coordinate system with x offshore from an origin behind the dune and y alongshore toward the north). GPS fixes were collected frequently during cable laying, defining the horizontal trajectory of the cable. Field notes reported a possible anomaly around x = 400 m as the LARC was thrown by waves while transiting an offshore sand bar. An inner bar was located at x = 235 and the shoreline around x = 105 m. The cable was buried across the dry beach but otherwise simply lay on the bottom sands, likely becoming buried over time due to its higher density. DAS data were collected with a Sintela Onyx at 500 Hz with 3.2 m channel spacing.

The first step was to identify the single closest channel locations using cross-spectral comparisons with each of three in situ AWAC wave sensors, none of which was time-synced to UTC, moored in 4.5, 6.0, and 11.0 m depths, ~47 m to the south of the cable. The process was the same as at Florence—cross-spectra were computed between each AWAC and a suite of plausible nearby DAS channels, and the most similar DAS channel was chosen based on the maximum cumulative coherence. Results appeared to be consistent among the three AWAC sensors to within a few DAS channels. Increased accuracy required comparison with data from a local Argus station [34] that collected camera image time series data over the region. The time series were part of the “cBathy” collection [35,36] that sampled a 0.8 by 1.5 km region with spatial resolution of 5.0 and 10.0 m in the cross- and alongshore directions, respectively. The time series were 1024 s long (~17 min), sampled at 2 Hz.

Prior to cross-spectral analysis, Argus data were adjusted in three ways. The Argus computer was found to no longer be synced to UTC but instead used an internal PC clock that was found to drift 10 s per day with an apparent reset every 10 days. Synchronizing Argus time series was accomplished by solving for the time offset for each dataset based on cross-spectral comparisons to DAS channel 152, the channel closest to the 4.5 m AWAC instrument. Since the location of this channel was considered to be well known by the above analysis and since DAS time series were UTC-synced, performing the same cross-spectral analysis to the closest pixel time series allowed time sync of all Argus time series in each cBathy collection. Second, the estimated x-y location of each Argus pixel had to be adjusted for the tide height. Pixel locations are found by mapping between desired 3D world coordinates and camera pixels. At the time of collection design, the z-level was taken as z = 0, for convenience. These locations were then adjusted for the accurate tide level for each run, measured at the end of the FRF research pier, with distance away from the horizontal camera location shifted by the fractional change in height between the camera and the water. These horizontal corrections could be up to ~5 m. Finally, the camera viewing geometry (the camera pointing angles, azimuth, tilt, and roll) is fixed at the time of camera installation but can still vary by hundredths of a degree due to wind, solar heating, and camera mount aging. These variations were measured by comparing locations of standard, fixed features in the view to initial reference values. Corrections were a few meters or less.

The location of any DAS channel was then determined using the procedure described in Section 2. First, a local tile of surrounding pixels was found (Figure 2a). For each pixel, a cross-spectrum was computed between the pixel intensity and the DAS channel, and the time lag was recorded, until a tile of time lags was found (Figure 2b). These data were then fit to a 3D plane, and the fit parameters p(1, 2, 4) were saved as the equation of the line of zero lag. The process was carried out on multiple days when waves approached the beach from a variety of wave angles, thereby yielding lines of zero lag that intersected each other. Analyzing four days (10, 13, and 27 November and 17 December, 2022) yielded four such lines, creating six locations of intersection since each line can intersect with each of the others. A mean location was calculated as the weighted average of these six locations, where the weight for each intersection was

$$w_{ij}={\displaystyle \frac{sin\left({\alpha }_{ij}\right)\ast {\mathsf{\Gamma }}_i\ast {\mathsf{\Gamma }}_j}{max\left({rmse}_i,{rmse}_j\right)}}$$

(6)

where sin(α_ij) is the sin of the intersection angle between the ith and jth lines (near-parallel lines will yield poorly constrained intersection locations), Γ is the fraction of successful fits within each tile, and rmse is the rmse error of each tile fit. The standard deviation of these six estimates was used as a measure of spread of the estimates.

Figure 11 shows four example DAS channel locations, spaced 10 channels apart for clarity. For each DAS location, four lines of zero lag are shown. With one exception, the sixteen lines intersect over a small domain spanning one or a few meters for each DAS channel. The standard deviation of individual estimates is 0.6 m in x and 1.0 m in y (omitting the one stray line), a surprisingly tight estimate. All four estimates are consistently shifted ~5 m seaward of their estimated locations based on the AWAC sensor, well within the expected error from the initial analysis. The y locations are close to expectations for channels 136 and 146 but diverge to the north by around 10 m seaward of x = 400 where notes showed a potential installation anomaly.

Figure 12 shows the same analysis for all locations from channels 50 to 265, corresponding to x locations from 80 to 600 m. The geolocation estimates appear noisy inside the inner sand bar and surf zone (x < 235 m). Seaward of this, the estimates appear to be very consistent along the cable although they drift north and south of the surveyed track by up to 10 m. These trends are quantified in Figure 13, where the proxy error (Argus estimates minus survey track) is plotted in terms of x-deviations (panel a), y-deviations (panel b), and distance discrepancy (panel c). The errors appear to be primarily in the form of slight drift away from the expectation rather than methodology noise.

This is reinforced by Figure 14, which shows along-cable block means (panel a) and standard deviations (panel b) calculated over 25 m segments of cable. The standard deviations span a large range, so they are plotted in log-10 space. Outside of the surf zone, mean errors are typically 5 m, and along-cable standard deviations are typically 1–2 m but can be as low as 0.53 m. Note that in the region landward of the sand bar (x = 235 m), some channel locations are quite noisy and did not fit on the plot.

Overall, it appears that geolocation using shore-based cameras is typically accurate to 1–2 m outside the surf zone. Interpolation through estimates should yield a good map of DAS channel locations. Deviations from the intended path were mostly less than 10 m offshore from the sand bar.

4. Discussion

At the heart of the methods demonstrated here are cross-spectral analyses between DAS time series and data from geolocated sources, either fixed instruments or remote sensors. This technique is similar to a tap test in that both methods rely on ground truth data with high-fidelity locations, but the cross-spectral methods use signals that are passive and continuous, rather than active, transient signals. In many ways, cross-spectra of random-wave signals are preferred over time-domain approaches, since the phase ramp response to time or spatial shifts can be inverted to yield accurate lag estimates. This approach is also robust to phase differences in signal sensitivities, for example, if DAS data respond to pressure gradients, while the comparator ground-truth signals respond simply to pressure. The methods should work best for broad-band ocean waves rather than narrow-band swell, but the former are typical of natural oceans.

Comparisons are shown here between the guessed locations of DAS channels and improved spectral-based estimates. There is a tendency to think of mismatches as errors. It should be realized that there is no real ground truth for this study. We do not know the true locations of DAS channels. So mismatches cannot easily be interpreted, although along-cable scatter is likely a good measure of errors in the method (assuming the cable-laying process was actually smooth).

An advantage of the methods proposed here is that estimates can be continually improved as long as new data is collected, unlike tap testing which is usually carried out once. Once a remote sensor has been installed, it would be common to collect data for an extended period. The resulting estimates should continue to improve according to the central limit theorem. Moreover, if the DAS cable locations change, this could also be detected.

Method performance appears to decline when the ocean waves break in the surf zone. This makes sense since the response phase of Argus cameras (and perhaps radar) changes when waves break (the brightest response of cameras to breaking waves is at the wave front, while non-breaking waves are brightest on the wave back). Ideally, the analysis should be limited to non-breaking conditions, which implies a cross-shore span that varies depending on wave conditions. It would not be difficult to analyze multiple days that include those with small waves and a narrow surf zone.

The comparison between radar and optical imaging geolocation examples is interesting. Optical results appeared to be more accurate but were only usable over a shorter range up to 700 m. Radar showed larger variations, but the tests were at 2.7 km from the radar, and only two test days were available. Radar has the advantage that the range is well constrained by the speed of light, but initial tests show that azimuth can drift slightly over time, with typical magnitudes of up to 10 m at a 2.7 km range. In turn, camera data can drift in both tilt and azimuth in ways that can also be corrected post-collection and can have magnitudes of several meters at the range of interest. Overall, the results shown here demonstrate that both methods will provide excellent ground truth for DAS geolocation.

The accuracy of the technique was a pleasant surprise but raises the question of whether there are sensitivities in the method that can be optimized. The estimation algorithm relies on finding time lags over a tile of test pixels and then fitting to a plane from which the line of zero lag is found. Individual cross-spectra were based on either 30-min (radar) or 17-min (optical) time series, spectral-analyzed with 30 degrees of freedom. Each tile was composed of roughly 50 pixels spanning approximately two ocean wavelengths, so each estimated line of zero lag was based on a huge number of degrees of freedom (number of coherent frequencies times the number of pixels, typically 500 degrees of freedom). Fewer degrees of freedom could be used, but the computation time is short, being mostly dominated by the time to load data files. Finding intersections of lines of zero lag was simple for the radar case, since only two runs were available, but this required some decisions on a weighting scheme for the four optical data runs. The scheme used above was reasonable, but other weighting schemes could be investigated as more data runs are incorporated in the future.

5. Conclusions

Distributed Acoustic Sensing is an emerging ocean sensing technology that provides strain and temperature measurements along the length of fiber-optic cables at high spatial and temporal resolutions. The along-cable spacing of DAS channels is user-defined at the time of collection, but the specific location of each channel is not known. In most geophysical applications, this degree of freedom is solved by using a “tap test”, an artificial transient that can be detected by sensors and at locations found from the time of flight. We propose using continuous measurements of natural signals recorded by geolocated ground truths (in this case ocean waves) as an alternative, with time offsets found from cross-spectral phase ramp signals. This method is applied by comparing DAS signals to continuous time series from fixed instruments, including radar and optical camera data. For array sensors such as remote sensors, time lags can be computed by comparing a DAS channel with many pixels over a local tile and fitting the resulting time-lag data to a 2D plane from which the line of zero lag can be found that shows the true DAS channel location in the dominant direction of wave propagation. Sampling from multiple days with different wave directions yields multiple lines of zero lag whose intersection is a good estimate of the true channel location. Tests were performed with both radar and optical camera data, finding O(10 m) accuracies with radar at ranges up to 3 km (based on two datasets), and O(1 m) accuracies with cameras at ranges up to 600 based on four datasets.