Volume 5, Issue 8 p. 371-379
Research Article
Open Access

Measuring Seafloor Strain With an Optical Fiber Interferometer

Mark A. Zumberge

Corresponding Author

Mark A. Zumberge

Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, USA

Correspondence to: M. A. Zumberge,

[email protected]

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William Hatfield

William Hatfield

Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, USA

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Frank K. Wyatt

Frank K. Wyatt

Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, USA

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First published: 26 July 2018
Citations: 24

Abstract

We monitored the length of an optical fiber cable stretched between two seafloor anchors separated by 200 m at a depth of 1900 m, 90 km west of Newport, OR, near the toe of the accretionary prism of the Cascadia subduction zone. We continuously recorded length changes using an equal arm Michelson interferometer formed by the sensing cable fiber and a mandrel-wound reference fiber. A second, nearly identical fiber interferometer (sharing the same cable and housing), differing only in its fiber's temperature coefficient, was recorded simultaneously, allowing the separation of optical path length change due to temperature from that due to strain. Data were collected for 100 days following deployment on 18 October 2015, and showed an overall strain (length change) of −10.7 με (shorter by 2.14 mm). At seismic periods, the sensitivity was a few nε; at tidal periods the noise level was a few tens of nε. The RMS variation after removal of a −79 nε/day drift over the final 30 days was 36 nε. No strain transients were observed. An unexpected response to the varying hydrostatic load from ocean tides was observed with a coefficient of −101 nε per meter of ocean tide height.

Key Points

  • Seafloor strain is measured with an optical fiber
  • Laser interferometry provides high precision
  • Deployed at 1900-m depth in Cascadia subduction zone

1 Introduction

Earth strain is a fundamental geotechnical measurement useful for studying tectonics, earthquake dynamics, volcanoes, and slow slip events. It is defined as the ratio of a change in length Δl over a baseline length l. The unit “microstrain” (με) or “nanostrain” (nε) is assigned to the unitless quantity ε = Δl/l. In most places on Earth, secular strain accumulates more slowly than 100 nε per year. Solid Earth tidal strain has a typical peak-to-peak amplitude around 50 nε, and slow slip events on subduction zone faults may cause strains observed on the surface as large as 50 to 100 nε in a time scale of hours to weeks.

On land, strain is recorded by arrays of GPS receivers, by electromechanical borehole strainmeters (Gladwin, 1984; Sacks et al., 1971), and by vacuum laser strainmeters (Agnew, 1986). GPS signals do not penetrate seawater [although in conjunction with acoustic ranging, great progress has been made by Chadwell and coworkers (Spiess et al., 1998) tying GPS reference signals to seafloor acoustic arrays], and boreholes or vacuum pipes required for other land-based methods are impractical or very expensive on the seafloor. An optical fiber strainmeter is an alternative means to sense Earth strain on the ocean bottom, where some unique challenges are presented. The subseafloor material is normally sediment whose mechanical characteristics would not seem to be advantageous for geodesy. On the other hand, unlike the land surface, the deep ocean bottom does not experience weathering (wind erosion, frost action, or rainfall, leading to rock decomposition) which affects subaerial geodetic benchmarks. It is possible that, once embedded in the sediment, seafloor benchmarks are quite stable. Hundreds of concrete benchmarks have been placed on the bottom of the North Sea for geodetic monitoring of deformation associated with natural gas production and, at least at the 5-mm level, their vertical positions are quite stable over many years (Eiken et al., 2008; Stenvold et al., 2006). It remains to be seen how stable the endpoints of a long-baseline strainmeter can be when attached to deep ocean sediment. As will be shown below, a noise level at periods up to about a month of better than 50 nε was achieved in a 200-m-long instrument, indicating the prospects for attaching a strainmeter to the seafloor are fairly good (the associated displacement noise in the band from 0.004 to 2 × 10−7 Hz was about 10 μm after removal of tides and a linear trend). And, for a given noise in Δl, the noise in ε will be lessened as l is made longer—easily accomplished with optical fiber.

In an Optical Fiber Strainmeter (OFS), a cable housing an optical fiber is stretched between two endpoints and its length monitored continuously with a laser interferometer (DeWolf et al., 2015). The elastic cable (and optical fiber) follows the separation between the endpoints as long as any accumulated negative strain (i.e., contraction) does not exceed the initial stretch (typically 0.1% or 1000 με). In October of 2015, we deployed a 200-m-long OFS in an east-west direction on the toe of the accretionary prism of the Cascadia Subduction Zone, 93 km west of the Oregon coastline. Using the ROV Jason the instrument was installed between two ~100-kg anchors, tensioned, and operated continuously for 101 days until the batteries were exhausted.

2 Design of the Instrument

Figure 1 is a drawing of the instrument. The “active anchor,” built around a 2.5 cm (1 inch) thick steel plate 0.61 m (24 inches) square with a mass of 75 kg, holds the optics pressure case beneath it, from which emerges the strain sensing cable. On top of the plate a frame with a lifting bail holds an electronics pressure case, containing the signal processing and data recording electronics, two battery pressure cases, and an acoustic modem to allow communication with the system after it has been installed. The “passive” anchor is built around a similar steel plate, on the bottom of which is a fixture to hold the end of the tensioned strain sensing cable. The top-side frames on both anchors hold spools that are used during the installation.

Details are in the caption following the image
Two anchors, one passive, the other active, marked the baseline of the optical fiber strainmeter. They were held in place both by their weight and half-meter-long “tent stakes” that were pushed into the mud in an attempt to add stability.

Deployment of the system, at 44°28.164′N, 125°15.869′W, 1910 m deep, relied on the ROV Jason. The main difficulty is that the 4-mm-diameter strain sensing cable (a 1-mm stainless steel hollow tube, overcoated with polyethylene, holding two optical fibers) requires ~135 N (30 pounds) of tension to increase its length by 0.3 m, the desired pretension of the sensing cable, but it has a breaking strength of only 450 N (100 pounds). To tension the cable correctly without breaking it we proceeded in steps. First, the two anchors were prepared on deck in the following fashion: the 200.0-m fiber sensing cable was wound onto a spool temporarily attached to the active anchor with one end of the cable connected to the optics pressure case and the free end on the spool. On the other (passive) anchor, a 200.3-m length of wire-rope was wound onto a second spool fixed to the passive anchor. After both anchors were separately placed on the seafloor next to each other, the ROV latched the free end of the wire-rope onto the active anchor and carried the passive anchor away in a straight line to the east, spooling off the wire-rope until it became taught. In this way a 200.3-m separation between the two anchors was established precisely. (Later the wire-rope was detensioned so it would not affect the measurement.) Next the ROV collected the sensing cable spool from the active anchor and carried it to the passive anchor, the sensing cable paying out as it went. The final step was to stretch the sensing cable by 0.3 m and attach it to the bottom receptacle beneath the passive anchor. This was achieved using the ROV manipulators by turning the passive anchor on its side, pulling on the sensing cable, placing the mating cable termination into the passive anchor's latch, and finally righting the anchor.

The intent had been to bury the strain sensing cable in the sediment by excavating a shallow trench using suction from the ROV's water pump. This proved to be impractical. As an alternative, ROV drop-weights (1.4 × 20 × 30 cm weighing 7 kg each) were laid atop the sensing cable every 10 m or so along its length to hold it down to the relatively flat bottom. As a result, the sensing cable was buried about 10 cm below the surface at both ends but was exposed on the seafloor over about half its length. It also did not follow a perfectly straight path; rather, it underwent vertical undulations of about ±20 cm.

Figure 2 shows the internal workings of the sensor. A pair of interferometers is formed to sense the length changes of two different fibers in the strain sensing cable. The optical configuration of nearly equal-arm interferometers permits the use of a low-power 1310-nm diode laser and relaxes the requirements of narrow line width and high wavelength stability (we used an NEC model NDL7673_092W operating with an output of 0.7 mW). Polyimide-coated reference fibers are wrapped on an 80.2-mm-diameter fused silica mandrel held within the optics pressure case. The interferometers are sensitive to changes in the length of the strain sensing cable relative to the fixed lengths of the mandrel-wrapped fibers. A thermistor provides a correction for small temperature changes encountered by the mandrel fibers.

Details are in the caption following the image
A schematic drawing of the two interferometers that make up the OFS. Two fibers in the strain sensing cable, having disparate temperature coefficients, allow the separation of apparent length change from temperature and real length change from strain. Records of the optical phase changes from the two fibers are recorded and processed later to resolve temperature and strain (Det. is an abbreviation for photodetector). The power consumption of the instrument is laser, 0.8 W; detectors, 0.4 W; and signal processor/data logger, 3.4 W.

Each of the two interferometers is a Michelson-type. Laser light injected into 3 × 3 splitters is coupled into the sensing fibers and the reference fibers (the remaining outputs are unused). The interferometer arms are terminated by Faraday mirrors to circumvent polarization fading from uncontrolled birefringence in the fibers. When the reflected beams recombine in the 3 × 3 couplers, each interferometer generates two interference fringe signals ≈120° out of phase. These are digitized via photodetectors and processed in real time.

The method of quadrature fringe resolution described in Zumberge et al. (2004) and called the “femto” system is used to record bidirectional variations in the lengths of the sensing fibers. The two fringe signals from each interferometer are not exactly in quadrature; when plotted against one another, they trace out an eccentric ellipse which depends on the exact phase shifts in the 3 × 3 couplers. The outputs from the two pairs of photodetectors that receive the fringe signals are sampled 50,000 times per second. For each sample pair, a microprocessor calculates the instantaneous optical phase angle (the position of the sample on the ellipse) based on a theoretical ellipse fitted to a subset of 500 samples collected during the preceding few minutes. Tidal and microseismic activities provide a natural length modulation, causing a good distribution of samples around the ellipse that allow the system to update the ellipse parameters frequently and automatically. This is necessary because these parameters can change with time if the laser output power varies or other temperature-related factors affect the fringe signal amplitudes.

The rapidly sampled optical phase values are filtered and decimated to a 20 sample per second rate and stored in flash memory. The conversion from optical phase change Δϕ in radians to strain ε is given by
urn:x-wiley:23335084:media:ess2206:ess2206-math-0001(1)

where l is the length of the tensioned fiber (200.3 m) and λ is the laser wavelength (1310 nm). The factor of 1.17 in the denominator above comes from the slight gain in the sensing fiber resulting from the combined effects of physical length change and the fiber's index of refraction change (Zumberge et al., 1988). These values result in an optical phase to strain conversion coefficient of 0.445 nε per radian of optical phase shift (i.e., fringe shift). As the femto fringe signal processor can split a fringe to better than a thousandth of a radian, this is indeed a highly sensitive strainmeter.

The fiber used in interferometer #1 is normal telecommunication single-mode fiber. The fiber in interferometer #2 is specially doped with germanium and boron, giving it a temperature coefficient different by about 17%.

Consider the two strain sensing optical fibers shown in Figure 2 as having different thermal responses but identical strain responses. Define ε as the true strain experienced by the two fibers, ΔT as the average temperature change along the fiber path, b1 and b2 as the optical temperature coefficients for fibers 1 and 2 respectively, and ε1 and ε2 as the apparent strain from the two strainmeters, derived from their optical phase changes as given in equation 1 (including the thermal contamination). Then,
urn:x-wiley:23335084:media:ess2206:ess2206-math-0002
Knowing the coefficients b1 and b2 allows the solution for both ΔT and ε. These are given by
urn:x-wiley:23335084:media:ess2206:ess2206-math-0003(2)
urn:x-wiley:23335084:media:ess2206:ess2206-math-0004(3)
Both the results for the temperature and the strain require forming the difference between the two observed series. In general, if the contrast between the two temperature coefficients b1 and b2 is not substantial, the temperature will not be well resolved and noise will be added to the strain solution.

3 Results

The data are shown here in three different time scales: first the entire data set, then a short segment showing the observed strain during a teleseismic event, and finally the monthlong segment at the end of the experiment at which time some settling-in effects had apparently decayed away. In the last plot we show the efficacy of the temperature correction.

Figure 3 is the entire, unedited strain record from interferometer #1 beginning a day after the deployment period ended (on the scale of this plot, interferometer #2's record looks identical). The spikes in the record are of uncertain origin, although we suspect it is interaction with animals either with portions of the cable that remained exposed on the seafloor or with the anchor frames that extended above the seafloor by 90 cm. Soon after the deployment was completed we happened to observe on the Jason camera a large stingray fly next to active anchor: its wake produced a spike in strain of 160 nε. A persistent signal of amplitude varying between 50 and 150 nεat about a 2-s period exists in the record, also of unknown origin. We suspect this to be the interaction between ocean current and the anchor frames as it varied in amplitude from week to week.

Details are in the caption following the image
The raw strain (displacement) signal with no corrections or edits applied. The series is low-pass filtered with a corner frequency of 1.6 Hz.

While the temperature coefficients were established beforehand, in practice we find that a least squares fit of the raw strain difference between the two fibers (which is a constant factor times the integrated temperature) and the time series of the mandrel thermistor is an effective means to remove the thermal contamination from the data. Apparently, temperature variations affected the observed strain in additional ways—this is discussed in the section on instrumental artifacts.

The record from a teleseism (magnitude 7.1, Vanuatu, 9450 km away), fortuitously occurring early in the record while we were still on site and able to examine data, confirmed that the cable was properly tensioned and reliably sensing strain. In our previous deployments on land and in boreholes we have always had a means to manually change the cable length while observing the optical length to confirm the in situ calibration coefficient (equation 2). We had no practical means for such a check in this installation. However, we can infer the local strain, recorded on a seismometer 12.3 km away (from station HYSB1 on the Ocean Observatory Initiative cable node at the slope base), by dividing the east component of the ground velocity by the nominal Rayleigh wave velocity. Figure 4 displays the result. The records from both the seismometer and the strainmeter have been band-pass filtered between 0.04 and 0.06 Hz. We have not accounted for the Rayleigh wave dispersion (noticeable in Figure 4 as the varying ratio of strain to ground velocity). Nevertheless, the observation confirmed that the strainmeter's cable was tensioned properly and we could reliably use a previously confirmed calibration.

Details are in the caption following the image
East-west strain from the OFS and ground velocity, determined from a seismometer 12.3 km to the west. The seismometer's record has been divided by 4 km/s to give an approximate prediction of strain in a bandwidth centered at a period of 20 s.

Finally, Figure 5 shows two results—the efficacy of the temperature corrections and an apparent strain response to ocean tide height. First the raw data, with a slope of −79 nε/day removed and low-pass filtered with a corner frequency of 0.004 Hz (250 s), is plotted. The RMS variation over this one-month segment of uncorrected (but detrended) strain is 130 nε. Next the two temperature records (shown in the lower panel) are least squares fit to the strain and subtracted, yielding the trace labeled “temperature corrected.” A clear tidal signature becomes visible following the temperature correction. Pressure data, collected from a bottom pressure recorder sited 280 m away, scaled with least squares to fit the strain signal (with the resulting coefficient of −101 nε per meter of equivalent water height), is plotted beneath the temperature-corrected strain record. When the measured tidal signal is subtracted, the resulting residual, labeled “fully corrected,” has an RMS variation of 36 nε, a reduction by a factor of 3.6 relative to the raw data.

Details are in the caption following the image
The final one-month segment of data, corrected for drift and temperature, revealing a tidal strain response to hydrostatic pressure variation.

The two temperature series are shown in the lower portion of Figure 5. The upper trace, labeled “mandrel temperature,” is derived from a thermistor attached to the reference mandrel on which the reference optical fibers were wound and therefore is known absolutely. The lower temperature trace is derived from the difference between the strain records with the two temperature-coefficient-contrasting fibers, as given by equation 3. Note that this only gives the temperature change with time (averaged over the length of the sensing cable), not the absolute temperature, so there is an unknown offset between the two (chosen arbitrarily here for display purposes).

There are some noteworthy aspects to the temperature correction. First, the two temperature records are quite similar, as one would expect. The mandrel temperature is made at a point inside a pressure case buried about 10 cm beneath the sediment surface and housing electronics that dissipate about 1 W. Apparently, this did not elevate the internal temperature significantly because the 2 °C ambient temperature was confirmed with a CTD cast done around the time of deployment. The fiber temperature is averaged along the length of the sensing cable, some of which is directly exposed to ambient seawater. As is apparent in the plot, the average fiber temperature contains some higher-frequency variations but, in general, the two temperature records are in good agreement.

The coherence of the two temperature records might cause trouble when least squares fitting them to the raw data, yet this temperature correction method appears to be successful. The fitted temperature coefficients are different from those previously determined. The lab-determined values of b1 and b2 (11.7 and 9.7 με/°C, respectively) appear to determine the average fiber cable temperature well (as evidenced by the good long-period agreement with the thermistor record). However, the fitted value for b1/(b1b2) that best reduces the variance in the data is 3.2, smaller than the laboratory determined value of 5.8. Similarly, the fitted temperature coefficient for the reference mandrel fiber of 3.5 με/°C is smaller than the expected value of 10 με/°C. Partly, this is due to the compensating effect of the two temperatures; the interferometers are sensitive to the difference between the mandrel fibers and the sensing cable fibers so that, if the two temperature environments were identical, they would compensate each other and the temperature effect would cancel out. There is an additional temperature-related effect from the thermal-elastic coefficient of the tensioned cable housing the two fibers. This is discussed below.

4 Possible Instrumental Artifacts

The apparent relationship between observed strain and hydrostatic pressure of −101 nε per meter of tide height increase is somewhat surprising but not completely unexpected. Davis et al. (2017) observed anomalous tilt of 0.6 μrad per meter of tide height in the Cascadia subduction zone, and similar signals in the DONET array (Dense Oceanfloor Network System for Earthquakes and Tsunamis) have been recorded (personal communications, E. Araki, 2017). These are larger by an order of magnitude than anomalous tilts observed on land from ocean tide loading, and tidally driven strain signals on land are much smaller than what we have observed on the seafloor. In an infinite half space, there is theoretically no horizontal strain or tilt caused by uniform hydrostatic pressure—it comes about only if there are lateral variations in the load or in the rheology of the stressed structure. Our site is 90 km offshore, on the slope of the continental shelf, and there is a mapped splay fault only 2 km to the east (Goldfinger et al., 1992). It is therefore conceivable that the tidally driven strain record is caused by real deformation. Because it can be easily subtracted from the data, the signal is not relevant for the detection of longer-term deformation (from slow slip events, for example); however, it is important to address the possibility that the phenomenon is an artifact of the sensor rather than a geophysical effect. To this end, we consider several causes: a leak in the fiber cable, distortion of the sensor's pressure housing, and forces on the end anchors associated with hydrostatic pressure and temperature change.

The optical path length of bare optical fiber held at constant length responds to pressure with a coefficient of approximately 1 με per bar (100 kPa; Hocker, 1979), which is just the magnitude of the coefficient we observe, and is what would be expected if our strain sensing cable leaked, exposing the fiber to seawater pressure changes. However, the sign is opposite that of our observation so we discount this as the cause.

The pressure cases housing the interferometer optics at either end of the strain sensing cable distort slightly from varying hydrostatic pressure. For the dimensions of our pressure cases, however, the effect is smaller by a factor of 30 than our observation. The reference fiber wrapped on a mandrel inside the housing is isolated mechanically and was designed to be immune to pressure housing distortion.

The cable stretched between the two anchors was under tension by approximately 133 N (30 pounds), and changes in this tension must move the anchors slightly. It is difficult to model the force-displacement relationship of these anchors because we have little information on the stiffness of the sediment or the coupling between it and the anchors. The observed 101-nε strain for a 1-m tide change corresponds to a displacement of 20 μm. A very rough estimate of the force required to displace the anchor by this amount can be gotten from the characteristic scale of the anchors (d ≈ 1 m) and the near surface shear modulus μ, taken to be 1.5 × 105 Pa. This assumes a shear wave velocity of 10 m/s—a conservative estimate for this analysis [inferred values range from 0 to 100 m/s (Ewing et al., 1992; Ruan et al., 2014)]. These values lead to a force F≈3 N needed to move an anchor by Δx = 20 μm (F ≈ d Δx μ). While this estimate is somewhat speculative it is roughly in accord with our observation that initial 133 N of tension in the cable displaced the anchors 2 mm over three months, likely due to creep relaxation of an initial elastic deformation of the sediment by that amount. We therefore search for a mechanism that can generate a 3-N change in tension on the cable from a 10-kPa change in pressure (equivalent to a 1-m change in tide height).

The cable housing the optical fibers is air-filled at 1 atm and about 1 mm in diameter. The associated force on the ends of the cable for a 10-kPa pressure change is only 0.008 N. The plastic coating on the cable is polyethylene and shrinks slightly under pressure because of its bulk modulus. This shrinkage tends to increase the tension in the cable, but it amounts to only 0.1 N for 10 kPa of pressure.

The tension in the cable varies with temperature. The stainless steel tube dominates (it provides 96% of the cable's strength). The thermal expansion coefficient of stainless steel coupled with the estimated force-displacement relationship for the sediment combine for an estimated impact of 43 nε/°C, significantly smaller than the other thermal effects mentioned above. The elastic modulus E of the stainless steel also has a temperature coefficient: E−1 dE/dT = −2.6 × 10−4/°C (Agnew, 1986). This contributes only 1.3 nε/°C.

Because none of the mechanisms above appears to be large enough to produce the observed tidally driven stain signal we conclude that it is the sediment's response to varying hydrostatic pressure. It could be associated with nearby faulting or local inhomogeneities in the sediment structure. Modeling these is beyond the scope of this work. Future experiments having several sensors oriented in different directions to resolve the full strain tensor are needed to unambiguously capture this phenomenon.

5 Discussion

It is likely that this type of instrument will prove useful for studying the rheological characteristics of seafloor sediment. Seismic compliance methods (Crawford et al., 1991; Doran & Laske, 2016; Ruan et al., 2014) do not normally extend to the very long tidal frequencies. Horizontal strain records, along with precise drift-compensated pressure measurements at the seafloor to provide vertical deformation records, and pressure measurements in boreholes to provide subseafloor volumetric strain (e.g., Davis et al., 2015), could provide new insight into shallow seafloor structure.

One of the main motivations to develop this instrument was to assess the capability of seafloor strain observations to detect slow slip events. The size of a static strain offset ε in the crust caused by an earthquake of moment magnitude M a distance R (in meters) away can be estimated from (Wyatt, 1988)
urn:x-wiley:23335084:media:ess2206:ess2206-math-0005(4)
With the current noise level of 36 nε we would have detected a M 5.5 event at 30 km or a M 6.6 at 100 km. For each factor of 10 improvement in the strain noise the detectable event magnitude at a given range is lowered by 0.67. Regular slow slip events downdip of the Cascadia seismogenic zone are estimated to have equivalent moment magnitudes of 6.2 to 6.8 (Gomberg & Cascadia 2007 and Beyond Working Group, 2010), and slow slip in updip regions elsewhere can be equally large (e.g., Araki et al., 2017; Wallace et al., 2016).

A number of steps are needed to lower the noise. First, better coupling between the end anchors and deeper sediment is needed to lower the creep caused by the tension in the cable. We have tested jetted-in anchor pipes and long anchor screws for this purpose. Next, it is important that the sensing cable be completely buried beneath the sediment and that the end anchors have very little expression above the seafloor to prevent noise from currents. Finally, the baseline length can be significantly longer for seafloor installations—1 km is not unrealistic. The efficacy of the temperature compensation is such that we expect to decrease the noise level at time periods of hours to weeks (appropriate for the detection of slow slip events) to a few nε.

6 Conclusions

The first seafloor optical fiber strainmeter operated for 100 days and demonstrated the capability of detecting strain with sensitivity of better than 50 nε for signals shorter than 1 month in duration. The sensor promises to provide new information on the distribution in space and time of slow slip events and, if operated in conjunction with a high-precision pressure gauge, on seafloor sediment rheology. A coupling between strain and hydrostatic pressure of −101 nε per meter of water at tidal frequencies was detected that is probably governed by local structure.

To realize its full potential as a marine geodetic sensor, several improvements are needed. These include complete burial of the sensing cable in the shallow sediment, better coupling between the end anchors and deeper, more consolidated material, lower power consumption to allow multiyear deployments operating from batteries, and, of course, greater length.

Acknowledgments

We appreciate the efforts of Don Elliott, David Horwitt, and David Price during the instrument construction. Successful deployment of the sensor would not have been possible without the skill and focus of the pilots of the ROV Jason. Duncan Agnew provided useful comments on a draft of the manuscript. This work was made possible by a grant from the National Science Foundation, award numbers 1235384 and 1617828. The strain data presented here are available from the UC San Diego Library Digital Collections (Zumberge et al., 2018). The seismometer data are available from IRIS, network name OO, station HYSB1, channel LHE.