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  • Yuqiao Chen1,2,
  • Peng Yan3,4 and
  • Yuande Yang1,2
  • et al.

Reviewer 1: Jean-Jacques Royer Reviewer 2: Vladimir Cheverda Reviewer 3: Dimitrios Nikolopoulos

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Please check the attached PDF detailed review.

Review of the paper entitled

Wind-induced Seismic Noise and Stable Resonances Reveal Ice Shelf Thickness at Pine Island Glacier

By Yuqiao Chen, Peng Yan, Yuande Yang, David M. Holland  and Fei Li

This paper presents a structured, step-by-step HVSR resonance-peak methodology for inferring the floating ice-shelf thickness from passive, low-cost, non-destructive natural seismic noise generated by ocean waves. The HVSR technique, independent of meteorological variability, relies on tracking stable resonance peaks whose fundamental frequency equals half the S-wave velocity divided by the ice thickness. The resulting thickness estimates agree with those obtained from classical remote sensing, radar, and radio-echo sounding available in the Bedmap2 database at the same location. A key advantage of the proposed methodology is its ability to continuously monitor ice-self thickness.

When ice thickness is known, this framework can also be used to estimate the S-wave velocity of ice, and thus infer porosity, density, and temperature, although this potential application is explored here.

Overall, the paper is scientifically sound, well executed, and presents valid conclusions. However, several scientific and language improvements are required before publication:

  1. No error estimate is provided for the thicknesses inferred using the HVSR resonance-peak method. This must be included (see detailed review). An uncertainty estimate for the Bedmap2 thicknesses should also be provided.
  2. The uncertainty in the HVSR-derived thickness arises from (i) the uncertainty in the measured resonance frequency f (Df) (typically Df/f ≈ 2%-4% for HVSR peaks), and (ii) uncertainty in the S-wave velocity of ice Vs, which varies with fabric, temperature, and porosity (Vs = 1800-1950m s-1; DVs/Vs ≈ 3%-5%). Applying Eq. (1) yields Dh/h = ((Df/f)2 + (DVs/Vs)2)½ ≈ 4%-6%, corresponding to Dh ≈ 18-26 m with h = 440 m.
  3. Conclusions: Although the advantages of the HVSR method are clearly discussed, its limitations should also be explicitly addressed.
  4. Editing:

- Remove blank space at the bottom of pages 2 and 6.

- Figure 1: increase font sizes for all labels, axis titles, and scale markings to ensure readability.

- The second instance of figure 4 is mislabeled; it should be Figure 5.

  1. Language: The manuscript would benefit from a thorough editing to improve clarity, conciseness, and overall readability. A detailed set of suggested edits is provided below.

Despite these issues, the study offers a robust methodology and valuable findings. With careful English revision and attention to the points above, the paper has strong potential to contribute meaningfully to the evaluation and real-time monitoring of ice-shelf thicknesses, an important challenge in a warming climate.

Detailed Review

Some instances of plagiarism (21%) have been identified and must be addressed (see attached report).

Detailed comments

Suggested Title: Ice Shelf Thickness at Pine Island Glacier Revealed by Wind-induced Seismic Noise and Stable Resonances Reveal Ice Shelf Thickness at Pine Island Glacier

p.1 line 12: Antarctic ice shelves regulate ice-sheet discharge and global sea-level rise, yet their rapid retreat underscores the need calls for new, and low-cost monitoring tools. Here We analyze ambient seismic noise recorded by seismometers deployed on the Pine Island Glacier ice shelf to characterize wind-induced signals and detect identify persistent structural resonances. First, Power spectral analysis shows that wind sensitivity is strongly damped compared with bedrock sites: noise increases only 5–7 dB from 0 to 25 m s-1 winds, versus against a 42 dB increase at an inland bedrock station, reflecting the contrasted This less sensitive response results from different coupling environments of floating and versus grounded substrates. Second, The horizontal-to-vertical spectral ratio (HVSR) spectrograms reveal two temporally stable peaks at ~2.2 Hz and ~4.3 Hz that persist across stations and remain independent of environmental forcing. Forward modeling indicates that these peaks are correspond to S-wave resonances within the ice shelf. The inferred observed frequencies imply an ice-water interface depth of (~440 m) agrees consistent with the Bedmap2 thickness estimate (466 m). This work demonstrates that validates HVSR provides as an effective passive, single-station method for measuring ice shelf thickness measurement.

p.1 line 29: Antarctic ice shelves act as buffers that regulate control the flow of inland ice to the ocean [1]. Their stability is a key control on future global sea-level change, and many- are undergoing rapid retreat, such as Pine Island, Thwaites, Smith, and Kohler glaciers-are undergoing rapid retreat [2]. This rapid change makes floating ice shelves critical some of the most important environments on Earth, requiring continuous monitoring of their structure using with robust, low-cost, and non-invasive geophysical methods [3,4].

     Passive seismology based on using earthquake signals and the Earth's ambient seismic noise field has been evolving as become a powerful tool in cryospheric studies [5,6]. Because Antarctica is relatively aseismic The relative aseismicity of the Antarctic continent compared with to tectonically active regions, makes ambient seismic noise provides an important source of continuous signal for to inferring ice properties and structure [7,8].

     The Antarctic ambient noise field is known to be complex [9]. Noise sources are diverse and varied, originating from include oceanic processes such as infragravity waves and swell [10,11], but also from atmospheric wind forcing [12,13]. It is important to Understanding these sources characteristics in order to is essential for interpreting the noise field and monitoring environment conditions.

     On the other hand, Ambient noise also carries subsurface information from subsurface, and allowing for structural properties to be inferred using with techniques such as the horizontal-to-vertical spectral ratio (HVSR) method [14,15] and noise cross-correlation method [16]. The HVSR method has been successfully applied used to estimate the thickness of grounded glaciers and ice sheets [17–19], while other noise-based studies have focused on shallower structures such as probing near-surface firn properties [20–22] or the presence subglacial water cavities [23]. At present, However, the use of stable HVSR peaks to determine the full thickness of a floating ice shelf has not yet been demonstrated.

     In this study, we analyze study ambient seismic data records collected on the Pine Island Glacier (PIG) ice shelf. First, we characterize the high-frequency noise field at PIG and quantify its direct relationship with atmospheric wind forcing, and comparing it with an inland bedrock site. Second, we identify stable, low-frequency HVSR peaks and show . We demonstrate that they peaks are independent of environmental forcing and represent the structural resonance associated with the full of the entire ice shelf thickness above it’s the underlying ocean.

p.2 line 60: Our study site is located on the PIG ice shelf, a major outlet of the West Antarctic Ice  Sheet (WAIS) that flowing into the Amundsen Sea (Figure 1a). A seismic array consisting of five broadband seismometers (Nanometrics Trillium 120 Sec Response, 100 Hz sampling rate) was deployed near the ice shelf centerline from 2012 to 2013 [24]. The array (inset, Figure 1a) consists of includes seismic stations spaced with inter-station spacing ranging from 0.82-2.10 km apart. All The stations are positioned on the floating ice shelf, which features a complex surface topography of marked by longitudinal ridges and troughs [25]. A Bedmap2 cross-section derived from the Bed-map2 model [26] (Figure 1b) shows that at the approximate array location the ice thickness is ~466 m (surface elevation ~65 m, bed elevation ~810 m).

Comments: Blank space at bottom page 2 requires reediting.

Give an error estimate of the thicknesses provided by the Bedmap2 database, along with the methodology used (radar, radio-echo sounding, remote sensing, etc.). Bedmap2 thickness values are derived primarily from airborne and ground-based radio-echo sounding (RES) surveys, complemented by satellite remote sensing (surface elevation, surface velocity) and mass-conservation modeling in data-sparse areas. Reported thickness uncertainties vary spatially from ±30–60 m in regions of dense radar coverage to ±200–400 m where interpolation dominates. At Pine Island Glacier, the Bedmap2 ice-shelf thickness uncertainty is approximately ±100–150 m.

Figure 1. Map and cross-section of the Pine Island Glacier (PIG) ice shelf study site. (a) Map of the PIG ice shelf. Seismic stations (black triangles) were deployed near the ice shelf centerline. The satellite image is from the Landsat Image Mosaic of Antarctica [27]. The top-left inset shows the detailed station array. The blue line represents the grounding line during the observation period. Locations of Automatic weather stations (AWS) locations Evans Knoll and NYU are shown as green squares. are shown for Evans Knoll and NYU. The top-right inset marks the study area's location within Antarctica (yellow star). (b) Cross-section along profile A-B, derived from the Bedmap2 model. At the PIG station location (marked), the model ice thickness is 466 m, the surface elevation is 65 m, and the bed elevation is -810 m (?).

p.3 line 78: In this study, we analyzed continuous seismic records from 1 February 2012 to 30 November 2013. Data from stations PIG1, PIG2, PIG3, and PIG4 were used; . Data from PIG5 was excluded due to poor data quality issues (Figure S1). Meteorological data, including wind speed and air temperature, were obtained from two nearby automatic weather stations (AWS) shown in Figure 1a: the Evans AWS [28], located ~22 km from the array, and the NYU AWS [29], collocated with the seismic array. As Because the Evans dataset from Evans is more complete than that from NYU and the fact that air temperatures recorded by both stations show Evans and NYU reveals no difference in their during overlapping periods (Figure S2), we used adopted the Evans record for all analyses in this study.

p.3 line 88: To quantify the relationship between wind velocity and the seismic noise field, we followed adapted the methodology of Frankinet et al. [13]. We first computed Hourly power spectral densities (PSDs) were computed for station PIG2 , which describe how the power of a seismic signal is distributed across different frequencies, for PIG2 station using the ObsPy package [30,31] describing how seismic signal power is distributed across frequency. The PSD was calculated with A smoothing parameter of 1/40th of an octave was applied at each central frequency. Also, its Probabilistic PSDs were also calculated to capture account for the statistical distribution of PSD values [32].

p.4 line 95: Following Frankinet et al. (2021), we sorted the hourly PSDs were shorted into bins based on average hourly wind speed (from 0-25 m s-1) using with 0.25 m s-1 intervals wide bins. To define the base noise level for each wind speed bin, we extracted the 5th percentile of noise power, which better represents the background noise floor than . This statistic is preferred over the mean because it is less affected by sensitive to transient outlier events (e.g., icequakes) and better reflects the background noise floor.

  We then quantified measured the change in noise power changes as a function of wind speed for each discrete frequency in the vertical-component data. We linearly fit the For every frequency, noise power was fit to with wind speed using for every frequency. This was done using a weighted linear regression, with weights defined as equal to the inverse of the within bin standard deviation within each bin (only bins with fewer than 10 or more observations were excluded considered). We found that A single linear model relationship provided a robust fit to our data across the 0-25 m s-1 range: wind speeds. This relationship is described by the function y=ax+b, where y is the 5th-percentile noise power (dB) at a given frequency, x is the wind speed (m s-1), and a (slope) and b (intercept) are the regression parameters for that this specific frequency.

  To investigate the structural signals, daily HVSR curves (0.1–40 Hz) were computed from three-component seismic data recorded by at the PIG stations using hvsrpy [33], with Processing employed 60-s non-overlapping windows, Konno-Ohmachi smoothing method (b=40) [34], and geometric averaging mean combination of the horizontal components [35].

  Finally, to show the evolution of the ice shelf's resonant properties over time, we created HVSR spectrograms were then generated by stacking the daily HVSR curves in chronological order to track changes in resonant properties over time. To test the hypothesis idea that the observed low-frequency HVSR peaks correspond to are structural resonances, we computed synthetic HVSR curves using the OASES, a seismo-acoustic modeling package [36] that OASES can solves wave propagation equation for horizontally in layered mediums consisting of fluid-solid media layers.

  We constructed A simplified 1D structural model of the PIG ice shelf, underlying water cavity, and bedrock was constructed with  system. The model parameters are listed in Table 1 and based on . These parameters are similar to those used by Diez et al. [37]. To examine investigate the sensitivity of the HVSR response to the ice-water interface depth of ice-water interface, we performed a suite ran a series of forward models in which the ice thickness was varied while , and fixed the total depth to bedrock was held constant.

p.4 line 126: Synthetic seismograms were generated by computing frequency-domain solutions across the bandwidth of interest and applying an inverse Fourier transform to obtain time- domain signals. The HVSR curves were then calculated determined from the synthetic horizontal and vertical component seismograms.

p.4 line 132: Figure 2a shows the PSDs for all three components at station PIG2, binned by wind speed from 0 to 25 m s-1 and averaged within each bin. The results clearly demonstrate a frequency-dependent relationship in which noise power increases with wind speed across the full frequency range, with a stronger And the effect is stronger at higher frequencies (mostly above 1 Hz). This correlation is consistent with observations by Frankinet et al. [13] at the Belgian Princess Elisabeth Antarctica Station (PEAS). However, a direct comparison with the PEAS reference noise models (shown as dashed (0 m s-1) and dotted (25 m s-1) lines in Figure 2a, representing 0 and 25 m s-1 winds respectively) reveals demonstrates differences in both the overall noise levels and the wind sensitivity to wind.

Figure 2. Wind-induced seismic noise at station PIG2 (2012–2013) on the PIG ice shelf. (a) Power spectral densities (PSDs) for the east-west (E), north-south (N), and vertical (Z) components, PSDs are binned and averaged by wind speed and averaged. with The color bar indicates wind speeds from 0 m s-1 to 25 m s-1. The black dashed and dotted and dashed lines show the lower (0 m s-1) and reference upper (25 m s-1) and lower (0 m s-1) reference PSD limits, respectively, obtained at from PEAS. (b) Parameters obtained from a Linear regression parameters for model fit to the vertical component data, for which where y is the noise power (PSD) and x the is wind speed. Top: panel: slope a (orange). Bottom panel: intercept b (green), both plotted as a functions of frequency. The vertical red dashed line indicates the 5 Hz frequency. (c) PSD as a function of wind speed, extracted at the 5 Hz (as marked in panel b). Black dots show represent the mean noise power with one-standard-deviation error bars showing one standard deviation. Red triangles show represent the 5th percentile of the noise power. The red dashed line is the linear function fit to the 5th percentile data at the 5th percentile of noise.

Comment: Figure 1 requires larger font sizes for all labels, axis titles, and scale markings to ensure readability.

  1. 5 line 153: First, the dynamic range of wind-induced noise at PIG is much dramatically smaller. Frankinet et al. [13] reported a 42 dB noise increase at 10 Hz between 0 and 25 m s−1 wind speeds for at PEAS, whereas In contrast, our PIG data at PIG (Figure 2a) shows only a 5–7 dB a much more subdued increase of only 5–7 dB for over the same frequency range. Second, the noise power limits are essentially differ substantially between , reflecting the two sites. The PEAS station, located on bedrock, is significantly quieter during calm conditions: its lower noise limit (0 m s-1, dashed line) is more than 20 dB lower (e.g., at 10 Hz) than the quietest noise observed at PIG. Conversely, during Under high winds, however, the PEAS site becomes much louder, with its upper noise limit (25 m s-1, dotted line) is approximately ~15 dB higher than that of the loudest conditions measured at PIG.

For these measurements, To quantify wind-driven noise variations at PIG, we developed a synthetic noise model based on linear regression of noise power wind speed at each frequency.  to quantify noise changes at each frequency relative to the wind speed at PIG ice shelf. Figure 2b shows the regression parameters a and b. Also Figure 2c illustrates shows the fit linear regression at 5 Hz (dashed red line in Figure 2b) where wind-induced noise increases by approximately ~6 dB from 0 to 20 m s-1. Figure 3a further shows that the noise power for across multiple frequencies, from (2-20 Hz) which can be well described by linear regression each fitted by a linear regression function.

Figure 3. (a) PSDs as a function of wind speed for multiple various frequencies. Triangles show the 5th percentile of the noise power, with different colors representing for frequencies from 2 Hz to 20 Hz. (b) Synthetic model of wind-induced seismic noise increase at PIG, showing . The plot shows the modeled increase in PSD increase in decibels (dB) as a function of wind speed and frequency.

p.6 line 174: With all the linear parameters determined, we can obtain produced a synthetic PSD spectrum. Figure 3b shows the modeled PSD increase (in dB) across the range of frequency and wind-speed. We also computed the RMS (root mean square) ground velocity in the 1-40 Hz band, where cryoseismicity is expected to happen, from these synthetic PSDs. Even at a high wind speed of 25 m s-1, the resulting ground velocity is only 0.07 μm s-1. This noise level is far below much smaller than typical icequake amplitudes signals (0.3 μm s-1) [38], suggesting that wind-induced noise is not a primary factor limitation for icequake detection here at on the PIG ice shelf.

p.6 line 182: Having characterized the high-frequency, wind-driven noise, we now analyze the temporal behavior characteristics of the HVSR. The HVSR spectrograms, which stack HVSR curves  over time (shown for station PIG2 in Figure 4), exhibit three distinct features phenomena.

Comments: Bottom of page 6 required editing to avoid blank space.

Figure 4. HVSR spectrogram and meteorological data for station PIG2 (2012–2013). (a) The Three- component HVSR spectrogram for PIG2 station. Two stable HVSR peaks (F1 and F2) are identified and marked with dashed boxes (F1 and F2). The diverging color scale is centered at 1, with that red indicating HVSR peaks and blue indicating HVSR troughs. The White vertical lines indicate data gaps. (b) Wind speed  time. (c) Air temperature.

p.7 line 191: First, HVSR in the high-frequency HVSR band (e.g., > 7 Hz) is highly variable, as shown in (Figure 4a), with shifting and has changing peaks. Although a direct, simple quantification of this the relationship between HVSR variability and meteorological conditions change (Figures 4b and 4c) is complex, the variability in this band highly variable nature of this frequency band strongly suggests that it is dominance by environmental forcing and sensitivity to near-surface (firn) conditions. Second, the low-frequency band (e.g., < 7 Hz) is dominated by blue shading (Figures 4a), implying that the indicating HVSR values is consistently below less than 1 (HVSR troughs). This HVSR baseline pattern indicates that the vertical (V) component of motion exceeds is stronger than the horizontal (H) motion component in this whole frequency across the entire band. Third, and most importantly, two distinct features, labelled F1 (~4.3 Hz) and F2 (~2.2 Hz), are visible appear as clear HVSR frequency peaks across at all four seismic stations (Figure 5a). Although their peak amplitudes has vary over time during the observation period, their frequencies remain remarkably stable. These peaks show no correlation with fluctuations the variations in wind speed or air temperature data.

This contrast between the highly variable high -frequency HVSR band and the stable low-frequency  distinction in HVSR behaviour between the high-frequency band and lower frequency stable peaks strongly suggests that F1 and F2 are not atmospheric or firn-related signals. We hypothesize that their stability reflects points to a deeper structural origin, and refers to resonances of the ice-water-bedrock system.

Comment: Figure 4 below is erroneously labeled

Figure 5. (a) HVSR spectrograms for stations PIG1–PIG4 from (2012–2013) for the 1-10 Hz frequency band. The color scale represents the HVSR values, with red indicating HVSR peaks and blue indicating HVSR troughs. Two stable frequency peaks, observed consistently with across all four stations over time throughout the deployment period, are labeled as F1 (~4.3 Hz) and F2 (~2.2 Hz). White vertical bands indicate periods of missing data. (b) Synthetic HVSR models for the PIG ice shelf. Stacked HVSR values are shown as a function of frequency and to the ice-water interface depth. Each horizontal trace is a forward model computed with OASES. The observed spectral peaks (white triangles, F1 and F2) of the station data agree match with a modeled ice-water interface depth of approximately ~440 m.

p.8 line 219: To test our hypothesis that whether the stable F1 and F2 peaks represent are structural resonances, we used the OASES package to modeled the HVSR response of the ice-water-bedrock system using OASES. The modeling results, shown in (Figure 5b) provide strongly support validation for our this hypothesis.

The modeled matches HVSR curves reproduce resonance peaks at frequencies very closely matching to F1 and F2 at PIG ice shelf. The modeling shows that these peaks are sensitive to the ice-water interface depth: qs the ice layer becomes thins, in the model, the corresponding resonance frequencies shift higher. peaks shift to higher frequencies.

Nevertheless, The observed frequencies for F1 (~4.3 Hz) and F2 (~2.2 Hz) (indicated by the white triangles in Figure 5b) align coincide with a modeled ice-water interface depth of approximately ~440 m (Figure 5b).

p.8 line 230: Our investigation of the 0.1 - 40 Hz ambient noise field on the PIG ice shelf shows two types of signals: The characteristics of wind-driven noise power amplification driven by wind and stable HVSR peaks that persist independently of environmental forcing, reflecting the underlying ice-shelf structure.

p.8 line 235: Wind-noise analysis reveals a complex, two-part contrast between PIG and bedrock stations, such as PEAS [13]. First, during quiet calm wind conditions, the baseline noise at PIG is much higher (e.g., >20 dB higher at 10 Hz) than at PEAS the quiet bedrock station. Second, PIG is far much less sensitive to wind: whereas PEAS sees a massive exhibits a ~42 dB noise increase between low and high wind speeds, the noise increase at PIG shows only a is much smaller ~5-7 dB increase, meaning that even under strong winds, absolute noise levels during high winds are lower at PIG remain lower than those at PEAS. Frankinet et al. [13] used two linear functions to models seismic noise at PEAS because they observed a change in noise-wind two different behavior at of the noise for wind speeds larger and smaller than 6 m s-1. In contrast, our study, however, we find no such breakpoint at PIG, a single did not see this behavior and found that one linear regression fits the data very well, which is the approach consistent with work by Lott et al. [39] and Johnson et al. [40]. The reason for Explaining the behavior difference at PEAS is beyond the scope of this study.

Also, The higher ambient noise baseline at PIG is consistent with expectations for compared to the bedrock PEAS site matches the expected behavior of floating ice shelves. As Baker et al. [11] showed for the Ross Ice Shelf, floating ice is strongly directly coupled to oceanic processes forcing, such as swell and infragravity waves, and provides producing a noisy seismic wavefield. These contrast with Inland bedrock sites, such as PEAS, which lack this direct oceanic coupling, naturally that are directly connected to oceanic forcing and therefore exhibit a much substantially lower noise floor.

Such The stark contrast in difference of wind sensitivity likely arises from the differences in near-surface coupling at each site. At PEAS, the sensors are directly coupled directly to bedrock [13], leading to a highly enabling efficient transfer of wind energy into seismic motion the solid earth. At PIG, sensors are installed within the rather low sensitivity is due to installation of the sensor in the ice shelf firn layer, which This firn layer acts as a mechanical insulator and reduces wind coupling that couples the seismometers inefficiently to have strong wind sensitivity. We use Our synthetic noise modeling further shows that, even under strong winds, lead to RMS ground velocities in the cryoseismic frequency band (1–40 Hz) that remain well below much smaller than typical icequake amplitudes signals. The opposite is true for PEAS, where wind noise can obscure mask events. Thus, site-specific coupling conditions (bedrock vs. firn) can therefore affect influence the completeness of icequake catalogs and should be considered when comparing cryoseismicity across locations.

p.9 line 263: The HVSR spectrograms (Figures 4a and 5a) show that in the low-frequency band (e.g., < 7 Hz), the baseline HVSR values are consistently below less than 1, indicating that the vertical (V) component of motion exceeds is stronger than the horizontal (H) motion component. This behavior result is consistent with observations from Amery Ice Shelf the phenomenon described by Zhan et al. [41] regarding the Amery Ice Shelf, who showed identified the sub-ice-shelf water layer acts as a strong low-velocity waveguide. The water column can traps P-wave energy, causing it to near-vertical resonance and propagate near-vertically to the surface, amplifying the vertical component of the ambient noise field.

  Emerging from Superimposed on this vertically-dominated baseline are the two stable HVSR peaks, F1 (~4.3 Hz) and F2 (~2.2 Hz). Unlike the highly variable high-frequency HVSR features values, these peaks show no correlation with environmental forcings (Figure 4) and appear are consistently across all stations (Figure 5a). We interpret them features as S-wave resonances within the solid ice layer.

  This interpretation is strongly supported by OAESE forward modeling strongly support this interpretation (Figure 5b). The modeled matches the resonance peaks match F1 and F2 closely and demonstrate that their frequencies are very close to the observed F1 and F2 And it shows that the frequency of each peak is sensitive to the ice-water interface depth. The modeling results show that the observed peaks, F1 (~4.3 Hz) and F2 (~2.2 Hz), correspond to a modeled ice thickness of -water interface depth of approximately ~440 m, in close agreement with the Bedmap2 estimate of . This modeled thickness agrees closely with the 466 m ice thickness at the station location derived from the Bedmap2 dataset. The ~26 m difference of ~26 m (< 6%) lies falls within the uncertainties of both the 1D passive-seismic model and the Bedmap2 dataset.

Comments: Please give the uncertainty associated with the Bedmap2 thickness along with a brief description of the methodology used. The estimated 440 m thickness also requires an error propagation analysis to establish the confident interval for this measurement.

The uncertainty in the estimated thickness arises from the uncertainty in the (i) measurement resonance frequency f (Df) (typically (Df/f ≈ 2%-4% for HVSR peaks), and (2) the S-wave velocity of ice Vs which varies with fabric, temperatures, and porosity (Vs = 1800-1950m s-1; DVs/Vs ≈ 3%-5%). Eq. (1) yields Dh/h = ((Df/f)2 + (DVs / Vs)2)½ ≈ 4%-6%, thus Dh ≈ 18-26 m with h = 440 m.

  The physical origin of these peaks follows from the boundary conditions of frequencies could be explained by the ice shelf 's specific boundary conditions and its S-wave transfer function [42]. The system forms an extreme "stiff-over-soft" structure situation, where the solid with an elastic ice layer overlying seawater. Carcione et al. [42] showed derived from the S-wave transfer function that in such a configuration the fundamental S-wave resonance from the classic quarter-wavelength (f0= Vs/4h), typical a soft-over-rigid media, is suppressed. Instead, the fundamental S-wave resonance corresponds to at a minimum value, and the first resonance peak corresponds to the half-wavelength mode (f1= f0/2 = Vs/2h), with   These resonance peak frequencies given by:

 

where Vs is the S-wave velocity of the ice, h is the ice thickness, and n is the n-th frequency peak or higher modes.

  This physical model explains our OASES results. Using the parameters from our 1D model (Table 1; Vs=1900 m s-1) and the modeled ice thickness derived from the modeling (Figure 5b; h≈440 m), this formula predicts:

  • First resonance peak (n=1): f1≈2.16 Hz;
  • Second resonance peak (n=2): f2≈4.32 Hz;

These is twice the frequencies-double those that would be predicted by the standard f= Vs/4h formula used for grounded ice-align well the soft-over-rigid layers (used by researchers to investigate the thickness of glaciers [17,18]). These predicted frequencies are in good agreement with our observed peaks: F2 (~2.2 Hz) and F1 (~4.3 Hz), respectively. This confirms that the observed F2 peak represents the fundamental first S-wave resonance peak of the ice shelf and the F1 peak is its first overtone.

p.10 line 304: This study characterizes the ambient seismic noise field on the PIG ice shelf, revealing a wind-induced noise response that differs markedly from that at an inland bedrock site and , as well as identifying persistent structural signals using the HVSR method. We find that, Unlike the bedrock station, the ice shelf site exhibits higher noise levels for quiet wind during calm conditions and much lower is less sensitivity to strong winds speeds. This behavior most likely reflects the sensor coupling to seismometer with firn rather than rigid bedrock, underscoring the importance of need to get a good understanding of site-specific noise environments when interpreting cryoseismicity across different glacier settings.

Across all stations, we identify find two stable persistent HVSR peaks at ~2.2 Hz (F2) and ~4.3 Hz (F1), independent of changes in meteorological variability conditions. Our analysis confirms that these two peaks correspond to S-wave resonances within the ice shelf. Forward modeling gives an ice-water interface depth of ~440 m, in close agreement with the Bedmap2 thickness estimate (466 m), supporting validating the robustness of this resonance-based interpretation.

This work demonstrates presented a new application of the HVSR technique for estimating the thickness of a floating ice shelves. With further validation, continuously tracking of these stable frequencies of these HVSR peaks may enable real-time monitoring of ice-shelf thickness changes. This passive, low-cost approach offers a valuable powerful, low-cost complement to remote sensing and radar surveys and provides valuable information about important insights into ice-shelf stability in a changing climate.

Supplements:

Figure S1. Example of unnatural anomalous seismic data from PIG5. It may have been caused by result from instrument failure; therefore, we exclude the data from the PIG5 station.

Figure S2. Comparison of air temperature (panel (a) and wind speed (panel (b) data from the New York University (NYU) AWS (blue line) and Evans Knoll AWS (black line). The Gaps in the NYU AWS record indicate data highlight periods of missing data information.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Language: The manuscript would benefit from a thorough editing to improve clarity, conciseness, and overall readability. A detailed set of suggested edits is provided below.

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper examines one of the key processes influencing future global sea level change—the flux of continental ice into the ocean. This study draws on Earth's ambient seismic noise, which has recently become widely used in cryosphere studies. The Antarctic ambient noise field is known to be complex. Noise sources are diverse and varied, originating from oceanic processes such as infragravity waves and swells, as well as a number of atmospheric phenomena. It should be noted that ambient noise also carries information about deep processes and is used, among other things, to estimate glacier thickness. Here noise analysis would be helpful to analyze shallow cryostructures, such as layers of near-surface firn.
This publication explores the possibility of using ambient seismic records collected on the Pine Island Glacier (PIG) ​​ice shelf to study ice flux from the shelf into the ocean. The authors begin with the analysis of the high-frequency noise field at PIG and quantify its direct relationship with atmospheric wind forcing. Next, they identify stable, low-frequency Horizontal-to-Vertical spectral ratio (HVSR) peaks. They demonstrate that these peaks are independent of environmental forcing and represent the structural resonance of the entire ice shelf thickness above its underlying ocean. Next, they measure the change in noise power as a function of wind speed and search for linear correlation of the noise power with wind speed for every frequency. They are doing this by applying a weighted linear regression, which provided a robust fit to the data across the 0 to 25 m s-1 wind speeds. This relationship is described by the function y=ax+b, where y is the 5th percentile noise power (dB) at a given frequency, x is the wind speed (m s-1), and a (slope) and b (intercept) are the regression parameters for this specific frequency.
Finally, to show the evolution of the ice shelf's resonant properties over time, analyze HVSR spectrograms by stacking the daily HVSR curves in chronological order. To test the idea that the observed low-frequency HVSR peaks are structural resonances, they compare computed synthetic HVSR curves using OASES, a seismo-acoustic modeling package [36]. OASES can solve the wave equation for horizontally layered media consisting of fluid and solid layers.
Undoubtedly, the article deserves publication. However, taking into account given that it relies heavily on field studies, which are largely influenced by a number of random factors, I believe a study of Uncertainty Quantification (UQ) is essential here. I mean that auhtor should pay more attention on identifying, measuring, and reducing uncertainties in models and real-world systems, presenting in the paper. It would be also welcome if authors on this base characterize how unknown factors (like input variability or model limitations) affect outcomes, thereby making predictions, simulations, and decisions more reliable and robust (see wikipedia for introducing uncertainty quantification - UQ).

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

This paper utilises PSD approaches to study wind induced seismic noise in Antarctica. The key paper used is [13] but the methodology tools and way of application is unclear, especially when mixing a power-law (non-linear phenomena) with statistics and linear regressions (stochastic phenomena).  The authors should make an effort to explain the python scripts used and how precisely they derive figures 2c,3b,4a and  again 4 (which is 5) actually. Introduction need more details and as a general assessment more clear explanations. 

 

I have some specific comments below. To me it is a moderate revision, but I will click minor for now.

 

1.The Introduction is short and does not present the state of the art in detail. And this despite using 23 mainly modern references. Issues not well presented: a) The necessity of the study; b) Why seismology is significant; c) The noise fields; d) The HVSR and cross-correlation methods.

2.The term “complex” is used in Chaos, whereas publication 9 is different. Moreover publication 9 is from 2015. Avoid it everywhere. You may use complicated, multifaceted, composite etc.

3.Reference 27 on the Landsat image mosaic is not CC-BY. It has Figs 2,10,11 and 15 that may be related to Figure 1. Describe how precisely subplot a is related to reference 27.

4.Lines 78-86 should be moved to Section 3 (just below)

5.Since you imply python kindly give details for the ObsPy (https://github.com/obspy/obspy). How you installed it, computer that was used, verification of the software and validation of your model that uses this software. Python version utilised. That is more info on theory (PSD), more info on application. Describe what exactly 1/40th of an octave is. What do you mean by”probabilistic PSD” because PSD is a power-law (chaos) while statistics on stochastic phenomena (not Chaos). Please add details here.  For example lines 95-107.  There is a whole theory on PSDs. It is not only the certain reference. Hence, Explain better lines 95-107. The reader has to understand fully the methodology and you have to assist on that.

6.Figure 2: It is unclear from the methods but here: Two subfigures b (Need b1,b2). Show WS versus logF To derive (C) certain logF’s are needed. Why? What is the need then for a PSD (lines 100-112).  How precisely the error bars are created. As you may understand you have to be very precise in the methods and how you applied these (see also comment 5)

Author Response

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Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

3rd Review of the paper entitled

Review of the paper entitled

Wind-induced Seismic Noise and Stable Resonances Reveal Ice Shelf Thickness at Pine Island Glacier

By Yuqiao Chen, Peng Yan, Yuande Yang, David M. Holland, and Fei Li

This revised version shows significant improvement over the previous submission. It is now ready for publication. Overall, the paper is scientifically sound, well executed, and presents valid conclusions.