Ross Ice Shelf Displacement and Elastic Plate Waves Induced by Whillans Ice Stream Slip Events

Ice shelves are assumed to flow steadily from their grounding lines to the ice front. We report the detection of ice‐propagating extensional Lamb (plate) waves accompanied by pulses of permanent ice shelf displacement observed by co‐located Global Navigation Satellite System receivers and seismographs on the Ross Ice Shelf. The extensional waves and associated ice shelf displacement are produced by tidally triggered basal slip events of the Whillans Ice Stream, which flows into the ice shelf. The propagation velocity of 2,800 m/s is intermediate between shear and compressional ice velocities, with velocity and particle motions consistent with predictions for extensional Lamb waves. During the passage of the Lamb waves the entire ice shelf is displaced about 60 mm with a velocity more than an order of magnitude above its long‐term flow rate. Observed displacements indicate a peak dynamic strain of 10−7, comparable to that of earthquake surface waves that trigger ice quakes.


Introduction
The interactions between ice streams and ice shelves are highly important for the dynamics and stability of continental ice sheets and shelves.Ice shelves provide restraining forces to their associated ice streams and glaciers which act to resist their motion, commonly referred to as a buttressing effect (Dupont & Alley, 2005;Goldberg et al., 2009).Ice sheet models show that disintegration of ice shelves increases the velocities of the associated ice streams and leads to rapid ice sheet thinning and ice mass loss (Joughin et al., 2012;Martin et al., 2019).Collapse of ice shelves along the Antarctic Peninsula has resulted in increased motion and thinning of surrounding glaciers (Berthier et al., 2012;Scambos et al., 2004).These observations have brought increasing attention to the stability of ice shelves and to their interactions with upstream ice streams and glaciers.
Ice streams generally move at a relatively constant velocity over low friction basal surfaces from the ice sheet interior to their grounding lines, where they often terminate into ice shelves.Ice shelves similarly move smoothly over the ocean from the grounding lines to the ice shelf calving front.The motion of both ice streams and ice shelves is modulated by tides, but this occurs gradually in association with tidal cycles (Anandakrishnan et al., 2003;Brunt et al., 2010;Klein et al., 2020).The Whillans Ice Stream (WIS) in West Antarctica (Figure 1) represents an exception to this general rule, as it undergoes one or two tidally modulated phases of rapid stick-slip motion per day (Bindshadler et al., 2003).During these slip events, the WIS moves forward with ice velocities that are about 40 times faster than its average flow rate, translating up to 0.4 m over a time interval of about 10 min (Barcheck et al., 2021;Pratt et al., 2014).
As the rupture front of these basal slip events propagates across WIS, it encounters multiple regions with different frictional behavior, resulting in faster rupture propagation and more energetic slip (labeled as #2 and #3 on Figure 1).These "sticky spots" with rate-weakening friction (Goldberg et al., 2014;Lipovsky & Dunham, 2017) are similar to asperities in earthquake rupture mechanics, generating pulses of long period (15-150 s) seismic surface waves propagating in the solid earth that are observed at distances of greater than 1,000 km (Wiens et al., 2008).The far-field seismic signature of these slip events is thus characterized by two or three pulses each separated by 10-15 min (Pratt et al., 2014).Although the rupture velocity and thus the relative pulse timing varies from event to event, and the rupture onset is not always teleseismically observable, the surface wave pulses radiate from the same regions during all events.The WIS slip events seem to be unique, likely representing a particular phase of ice stream slowdown for ice streams in the Siple Coast (Winberry et al., 2014).Although stick-slip behavior has been documented at a small scale on many glaciers (e.g., Graff & Walter, 2021), there are no other observations of such large-scale stick slip behavior involving entire glaciers or ice streams.
Until now, the effect of transient ice stream or glacier acceleration on downstream ice shelves has not been documented.In this paper, we use seismic and Global Navigation Satellite System (GNSS) data from sensors deployed on the ice shelf to observe the effects of WIS slip events on the Ross Ice Shelf (RIS).We find that the WIS slip events produce elastic Lamb waves that propagate as guided waves within the RIS and are seismically observed on the shelf at distances up to 700 km.A permanent displacement pulse observed by GNSS receivers also propagates across the RIS in association with the Lamb waves, translating the entire ice shelf away from WIS.These results demonstrate that upstream disturbances in ice streams propagate across entire ice shelves, and could, in the case of large disturbances, produce strain rates that may affect ice shelf fracture and destabilization.

Seismic and GNSS Data
The response of the RIS to WIS slip events was recorded by a network of broadband seismographs (Baker et al., 2019) and co-located GNSS receivers (Klein et al., 2020) (Figure 1) deployed on the ice shelf between 2014 and 2016.Twenty-seven broadband seismic stations were installed on the Ross Ice Shelf in late 2014 and operated continuously until late 2016 during the coordinated RIS (Mantle Structure and Dynamics of the Ross Sea from a Passive Seismic Deployment on the Ross Ice Shelf) and DRIS (Dynamic Response of the Ross Ice Shelf to Wave-Induced Vibrations) projects (Figure 1) (Baker et al., 2019; https://doi.org/10.7914/SN/XH_2014).Each station consisted of a Nanometrics 120PH posthole sensor buried to a depth of approximately 2 m below the snow surface, with data recorded at either 100 or 200 Hz by Quanterra Q330 dataloggers.The instruments were powered by solar panels during the summer and lithium batteries during the winter, so they recorded year-round.Instrument responses supplied by the Earthscope data center were deconvolved to provide three-component displacement or velocity records.
Thirteen of the RIS-DRIS stations had co-located GNSS receivers installed in November 2015, which remained in place for 1 year (Klein et al., 2020; https://doi.org/10.7283/58E3-GA46).Most of the receivers were powered by solar panels, so they did not record during the winter months.The GNSS receivers recorded at 1 Hz and were processed by Klein et al. (2020) using a precise point positioning (PPP) approach (Zumberge et al., 1997) to obtain daily time series for each station.The 1 Hz time series for each station was down-sampled to 0.0333 Hz to create a time series spanning the entire observation period.

Extensional Lamb Waves
The RIS seismographs record clear long-period signals on the horizontal components shortly after WIS slip events.We determine the times of WIS slip events independent of any signals recorded on the ice shelf by analyzing seismic signals propagating through the solid Earth to permanently installed Global Seismographic Network seismic stations in the Dry Valleys (VNDA) and at South Pole (QSPA), with known travel times to the WIS source region (Pratt et al., 2014;Wiens et al., 2008).The signals recorded by the seismographs on the RIS consist of a series of two or three arrivals, separated by 10-15 min (Figure 2), with timing that is consistent with arrivals observed at the permanent off-shelf seismic stations.The signals at the RIS seismic stations, at distances of 350-700 km, arrive only a few seconds prior to the signals at the permanent seismic station VNDA (distance about 990 km).Previous work identified the arrivals at VNDA as primarily fundamental mode Rayleigh waves (Pratt et al., 2014;Wiens et al., 2008), with elliptical particle motion and the largest amplitude on the vertical component.However, the arrivals on the ice shelf are observed only on the horizontal components, and so must Writing -review & editing: Douglas A. Wiens, Richard C. Aster, Peter D. Bromirski, Peter Gerstoft represent a different seismic phase with a velocity that is slower than the 3,000-4,000 m/s Rayleigh wave group velocity at 20-125 s period in this region (e.g., Shen et al., 2018).The seismic signals show particle motions that are approximately along the great circle path connecting the station and the WIS source region, with first motions oriented radially away from WIS.Following the initial arrival, the motion of the pulses become more complex (Figure S1).The maximum signal-to-noise ratio is observed at periods between about 20 and 100 s.This is because the WIS slip events produce little short period energy and the horizontal components of seismic stations on the ice become dominated by large-amplitude ocean-propagating infragravity waves at periods longer than several hundred seconds (Bromirski et al., 2015).To estimate the phase velocity of the arrivals, we computed the power of the stacked seismograms assuming different horizontal phase velocities and a source near the WIS (Figure 3).The estimated velocity of about 2,800 m/s is much slower than the P-velocity in ice (∼3,600 m/s) but much faster than the shear velocity in ice (∼1,900 m/s) or the P-velocity in water (∼1,500 m/s).We also estimated the group velocity, using approximate source times of the pulses from the Rayleigh wave arrivals at VNDA and the observed arrival times at stations on the RIS.The estimated group velocities are similar to the phase velocities, indicating there is no significant dispersion.We identify these arrivals as elastic plate waves, sometimes referred to as Lamb waves, propagating as guided waves in the ice shelf (Lamb, 1917).An elastic plate suspended in a vacuum gives a solution for longitudinal (extensional) waves with velocity: where V S and V P are the S and P wave velocities in the elastic plate.Press and Ewing (1951) derived a solution for an elastic plate overlying a liquid layer, arriving at the identical formula with a small imaginary term resulting in some attenuation.The equations have been rederived by many authors since that time, usually in the wavenumber domain, showing that long-period longitudinal waves in this system are a non-dispersive fundamental symmetric mode, often designated as S 0 (e.g., Chen et al., 2018;Graff, 1991).The predicted ratio of horizontal to vertical particle motion is approximately the ratio of plate thickness to the wavelength.For waves with 40 s period and the 350 m average thickness RIS (Das et al., 2020), this ratio is greater than 300, so this solution predicts longitudinal waves with particle motion that are almost perfectly horizontal and are radial to the source, consistent with our observations.Using a V p /V s ratio of 1.87 corresponding to the ice Poisson's ratio of 0.3 (Squire, 2007), and V s of 1,695 m/s derived by taking the time-weighted average V sv from the RIS seismic velocity profile of Diez et al. (2016), Equation 1 predicts a velocity of 2,865 m/s for the longitudinal wave speed, which is similar to the 2,800 m/s that best fits the propagation across the RIS.
Longitudinal Lamb waves excited by other processes have been previously observed propagating across ice shelves via array analysis in the time, frequency, or wavenumber domain.Chen et al. (2018) and Aster et al. (2021) noted that longitudinal Lamb waves were persistently excited by swell impinging along the RIS front and used array analysis to estimate the phase velocity as 2,940 m/s at 0.02-0.1 Hz, similar to the velocity observed in this study.Baker et al. (2020) also noted that long-period Lamb waves observed in the RIS interior were excited at the grounded margins of the RIS by teleseismic shear waves.

Permanent Ice Shelf Displacement
GNSS receivers located at the seismograph sites during 2015-2016 record the permanent surface displacement and strain across the RIS.The GNSS signals contain low amplitude high frequency noise that precludes determination of the precise onset time of the displacement associated with the Whillans slip events, but it initiates simultaneously with or shortly after the arrival of the first large amplitude elastic plate wave and continues for 15-20 min (e.g., as shown at station RS18 in Figure 4).The total displacement is generally 50-60 mm and the average ice shelf velocity during the displacement episode is about 0.05 mm/s (5 m/day), compared to the approximate 2 m/day average velocity (Brunt & MacAyeal, 2014) at this station.However, the velocities are greater immediately following one of the extensional wave arrivals, reaching as high as 0.3 mm/s (26 m/day), or more than 10 times the usual ice shelf velocity.
The displacement is approximately in the direction away from the WIS but varies somewhat for the different slip subevents (Figure 5).For example, at station RS18, the first subevent occurring at the southernmost sticky spot produces more northward motion on the GNSS displacement record compared to the more southerly third subevent, which produces larger westward motions (Figure 5).This is consistent with the first motions from the seismograph records, which show the same trend (Figure S1).The ice shelf displacement returns to the average flow direction within a few minutes of the final extensional wave arrival.Overall, the GNSS records indicate that the WIS slip events displace the entire RIS, with area of about 500,000 square kilometers and mass of approximately 200,000 Gigatons, by about 60 mm over a period of minutes on an almost daily basis.Ideally, it would be useful to sample the displacement field continuously across the seismic spectrum to determine more precisely the relationship between the higher frequency elastic wave arrivals and the permanent displacement pulse.However, the seismic sensors (Trillium 120 posthole) have reduced sensitivity beyond the 120 s corner period and horizontal component signals become dominated by ocean infragravity waves at periods greater than about 150 s.The displacements recorded by RIS GNSS receivers also have high noise at these periods consistent with the infragravity wave background displacement field, which has rms amplitudes of several cm (Bromirski et al., 2015(Bromirski et al., , 2017)).Thus, we interpret the seismic and GNSS signals separately in high signal-to-noise and relatively bandlimited windows of about 20-125 s for the seismic data showing the elastic wave propagation, and at very long periods near zero frequency for the GNSS data constraining the permanent ice shelf displacement.

Discussion and Conclusions
These results demonstrate that large-scale stick-slip motion of an ice stream can transmit elastic waves and strain pulses across its downstream ice shelf, modifying and briefly dominating the motion of an entire ice shelf with lateral dimensions of nearly 1,000 km.Ice streams and their associated ice shelves thus constitute a single elastodynamical system, with persistent ice stream events possibly influencing ice shelf stability and deformation.The large number of recorded ice stream signals in this data set also show that ice shelf stick-slip events can be easily monitored and assessed using instrumentation placed on the ice shelf hundreds of kilometers away.
A particularly interesting implication is that dynamic strain from the extensional waves or the permanent strain pulse could trigger icequakes, thus facilitating deformation and fracture of the ice shelf.We estimate the peak dynamic strain experienced by the ice shelves during passage of the extensional waves and the displacement pulse using the relationship: where V is the phase velocity of the propagating wave and U r is the radial particle displacement (Gomberg & Agnew, 1996).The stress is given by (Bower, 2009): where E is Young's modulus and ν is Poisson's ratio (approximately 9.0 GPa (Schulson, 1999) and 0.3 (Squire, 2007), respectively, for ice).The largest WIS-associated ice velocities recorded at the GNSS receivers are about 0.3 mm/s, with the largest particle velocities inferred from the band-limited seismographs being somewhat smaller.Using the phase velocity of 2,800 m/s from the previous section gives a peak dynamic strain of about 10 7 and a radial normal stress of 1.2 kPa.
These dynamic strains and stresses are similar to or greater than those observed to trigger icequakes during the passage of seismic surface waves from giant earthquakes.Peng et al. (2014) and Li et al. (2021) observed icequake triggering in the Antarctic ice sheet and on mountain glaciers with peak dynamic strains as small as 10 8 .The peak dynamic stress changes of some of these events are smaller than 1 kPa, if the modulus of ice is used in calculating the stress change.Stresses triggering thermal icequakes are typically more than an order of magnitude larger than this (Podolskiy et al., 2019).However, thermal loading occurs over a much longer timescale than the passage of a seismic wave, likely allowing partial relaxation of thermal stresses.In comparison, Aster et al. (2021) examined swell-induced impact and/or fracture seismicity observed at stations within a few km of the RIS front and noted that such events become dynamically excited at a stress threshold between 1.2 and 3.8 kPa and at extensional strains near 10 7 .Overall, there is ample evidence of significant icequake triggering at the dynamic strains and stresses of the extensional waves from WIS.
These observations suggest that extensional waves and strain pulses from WIS stick-slip events could mobilize fractures in the ice shelf interior and contribute to its destabilization.However, up to now there are no documented cases of icequakes in the ice shelf that are clearly triggered by WIS slip events.Olinger et al. (2019) located more than 2,500 icequakes along rift WR4 near the intersection of the two lines of RIS seismic stations (Figure 1) but did not detect any greater seismicity during the passage of waves from Whillans slip events.This may be due to the fact that rift WR4 is deforming in tension, with icequakes likely confined to the upper few meters of snow and ductile deformation at deeper levels (Huang et al., 2022), whereas the strain pulses from the WIS slip events exert dominantly compressional stress across the entire thickness of the shelf.
The WIS is the only location worldwide where such large-scale stick-slip events have been documented and it is unclear how typical the current activity is over longer time intervals.The WIS flow rate has been decreasing, likely due to increased friction due to decreased subglacial meltwater (Stearns et al., 2005).This velocity decrease has resulted in fewer slip events, with some of the normal twice-daily slip events being skipped and larger slip then occurring during the next slip event (Winberry et al., 2014).If the dynamics of the slowing ice stream reach a point where larger slip events occur, it is possible that the extensional waves and strain pulse from larger slip events could have a greater effect on the deformation and stability of the RIS.

Figure 1 .
Figure 1.Geography of the Ross Ice Shelf region with seismic stations shown as blue circles.Seismic stations used in this study are labeled, with sites also equipped with Global Navigation Satellite System receivers denoted by asterisks.The grounding line, denoted by a red line, and background image are from Scambos et al. (2007).The locations of Whillans Ice Stream slip asperities (Pratt et al., 2014) are shown as red circles.

Figure 2 .
Figure 2. Broadband three-component seismic record showing extensional Lamb waves produced by the WIS slip event on 8 December 2014 recorded at station RS15 (Figure 1), a distance of about 390 km.Traces are rotated into radial and transverse directions relative to the WIS, with positive radial motion away from the source.The instrument response has been deconvolved and the seismograms filtered to produce velocity from 20 to 125 s.

Figure 3 .
Figure 3. (a) Record section from the 27 November 2014 (19:03) Whillans slip event showing the N-S component from seismographs deployed across the Ross Ice Shelf.Seismograms were filtered with a 20-67 s band-pass filter.The first subevent is not visible for this event.(b) Slant stack of the NS components for the 27 November 2014 event, showing the stack power as a function of stacking velocity.A velocity of 2,800 m/s fits the data best and is also indicated by a dashed line in the upper figure.

Figure 4 .
Figure 4. Comparison of displacement records of the co-located broadband seismograph and Global Navigation Satellite System (GNSS) receiver at station RS18 for the Whillans slip event of 7 December 2015 (16:19).Both records have been rotated into the back-azimuth of the WIS to give radial displacement records.Seismic data are filtered with a causal bandpass filter between 0.05 and 0.008 Hz to remove noise.GNSS data have been detrended to remove the long-term ice flow and filtered with a causal low pass filter at 0.005 Hz.Signals from the first and third subevents are visible on both records; the second subevent is absent at this station due to obstruction by the northernmost extent of WIS and Crary Ice Rise.

Figure 5 .
Figure 5. Map view of the displacement trajectory of station RS18 (Figure 1) during 7 December 2015, determined by Global Navigation Satellite System, showing the changes in speed and direction caused by Whillans slip events.The displacements have been smoothed using a 900 s causal low-pass filter.Open circles denote positions every 30 s. 15-minute time stamps are shown as red x's.The average annual flow velocity determined by Klein et al. (2020) has been subtracted from the motion, but some background motion remains due to seasonal and tidal fluctuations.