Antarctic ice sheet thickness estimation using the H / V 1 spectral ratio method with single-station seismic ambient 2 noise 3

The horizontal-to-vertical spectral ratio (H/V) method implemented at single stations using seismic 11 ambient noise waveforms is a fast, noninvasive, efficient method to investigate the subsurface velocity 12 structures of the shallow crust. In this study, we report on a successful application of the H/V method to estimate 13 the Antarctic ice sheet thickness for the first time. Using three-component, five-day long, seismic ambient noise 14 records gathered from more than 60 temporary seismic stations located on the Antarctic ice sheet, the ice 15 thickness at each station was reliably measured. Preliminary analysis revealed that 60 out of 65 seismic stations 16 on the ice sheet obtained clear peak frequencies (f0) related to the ice sheet thickness in the H/V spectrum. Thus, 17 assuming that the isotropic ice layer lies atop a high velocity half-space bedrock, the ice sheet thickness can be 18 calculated by a simple approximation formula. About half of the calculated ice sheet thickness were consistent 19 with the Bedmap2 ice thickness values. To further improve the reliability of ice thickness measurements, 20 two-type models were built to fit the observed H/V spectrum through non-linear inversion. The two-type models 21 represent the isotropic structures of single and two-layer ice sheet, and the latter depicts the non-uniform, layered 22 characteristics of the ice sheet widely distributed in Antarctica. The inversion results suggest that the ice 23 thicknesses derived from the two-layer ice models were highly consistent with the Bedmap2 ice thickness 24 database, and their ice thickness differences were within 300 m at almost all stations. Our results support 25 previous finding that the Antarctic ice sheet is stratified. Extensive data processing indicates that the time length 26 of seismic ambient noise records can be shortened to 1—2 hours for reliable ice sheet thickness estimation using 27 the H/V method. This study extends the application fields of the H/V method and provides a complementary and 28 independent way to measure ice sheet thickness in Antarctica. 29


Introduction
The Antarctic ice sheet is the largest on the Earth, covering over 98 % of Antarctic continent.As a fundamental parameter of the Antarctic ice sheet, ice sheet thickness is significant for dynamic ice sheet modeling of mass The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-164Manuscript under review for journal The Cryosphere Discussion started: 11 September 2017 c Author(s) 2017.CC BY 4.0 License.needed to perform PRF; it usually takes at least a one-year period of data collection, thus greatly limiting the application of the PRF method in harsh environments such as those found in Antarctica.
In order to improve the reliability, accuracy, and efficiency of ice thickness investigation, we selected the horizontal-to-vertical spectral ratio (H/V) method to determine ice thickness.As a noninvasive and passive seismic method, the H/V technique has been extensively used in seismic exploration as a tool to detect sediment thickness, which suggests its powerful effectiveness in subsurface structure investigations (Konno and Ohmachi, 1998;Ibs-von Seht and Wohlenberg, 1999;Bonnefoy-Claudet et al., 2006;Bao et al., 2017).Considering that the sediments and ice sheet layer are both low shear-wave velocity (Vs) layers atop the high velocity bedrock, the H/V method should be suitable for determining ice sheet thickness.
Jean-Jacques (2010) applied the H/V method to four stations in the Dome C region of Antarctica for inferring the uppermost snow layer thickness and its corresponding ice properties a few meters depth.Picotti (2017) recently adopted the H/V method to detect glacial ice thickness ranging from a few tens of meters to ~800 m in Italy, Switzerland, and West Antarctica.The H/V method has been validated for its reliability to measure glacial thickness comparing with the radio-echo sounding, geoelectric, and active seismic methods implemented at or near the same study sites.The great advantage of the H/V method over other approaches is that there is no need to record earthquakes or active sources, since it utilizes seismic ambient noise.Moreover, the H/V method requires only a few tens of minutes of seismic ambient noise recordings at single portable three-component seismometers.This greatly enhances efficiency and reduces cost and logistical support requirements.
Since the shear-wave velocity of an ice sheet is ~1900 m s -1 , and generally much higher than a snow layer (~700 m s -1 ), therefore the velocity contrast of the ice sheet-bedrock half-space is not as high as that of the snow-ice sheet layer.Moreover, the H/V spectrum may be more complicated than that of a glacier or snow layer given the complex subglacial environment since there might be subglacial lakes and sedimentary layers.In addition, the internal ice structure might affect the H/V spectrum given the variations in seismic velocities induced by changes in density, and temperature, as well as the ice crystal size and orientation of an ice sheet.
Whether the H/V method can be used to estimate the ice sheet thickness or not remains an open question.
Although the H/V method has been successfully applied to study snow and shallow glacial thickness (Jean-Jacques et al., 2010;Picotti et al., 2017), to our knowledge, the H/V method has not been performed to estimate Antarctic ice sheet thickness yet.In this study, we present estimated ice thickness results from 65 stations with a typical coverage deployed on the Antarctic ice sheet to verify the feasibility of using the H/V method as an effective complementary way to existing methods for measuring ice thickness.
Despite their relatively sparse distribution, these three arrays together effectively cover East, and West Antarctica as well as the Transantarctic Mountain region (Fig. 1).In these three arrays, all stations are equipped with the Güralp CMG-3T or Nanometrics T-240 broadband sensors with a sampling rate of 25 Hz or 40 Hz.
Most stations are buried 1-2 meters below the surface snow to guarantee data quality (Anthony et al., 2015).
Equipped with solar panels and rechargeable batteries, the GAMSEIS and POLENET/ANET stations work continuously year round except the TAMSEIS, and provide abundant seismic ambient noise waveforms for the H/V processing.To investigate the effectiveness of the H/V method for ice thickness measurements and the proper time length for H/V processing, we selected seismic ambient noise records lasting about five days, which is much longer than that used in usual H/V data processing (only a few minutes' records for sedimentary investigations with tens to hundreds of meters thick).In total, 65 stations deployed on the Antarctic ice sheet were used in this study.

Methods
The single-station H/V method, extensively used in sediment structure detection, acquires reliable sediment thickness and shear-wave velocities (Nogoshi andIgarashi, 1971；Nakamura, 1989).In this method, seismic ambient noise data are collected by a three component seismometer and the ratio between the horizontal (H) and vertical (V) Fourier spectra are calculated.The principle of the technique can be understood by assuming a low velocity sedimentary layer overlying a high velocity bedrock half-space.Due to the sharp impedance contrast at the interface between the two layers, the shear-wave energy within the sedimentary layer produces a prominent peak that can be observed in the H/V spectrum.
Extensive field experiments and numerical simulations have been carried out to verify the reliability of the H/V spectrum as derived from the H/V method.Although the amplitude value of the H/V spectrum peak frequency is not that robust since the contributing factors are complicated, the H/V spectrum peak frequency is commonly accepted as a proxy of the resonance frequency of a particular layer (Field and Jacob, 1993;Lachetl and Bard., 1994;Javier and Chávez-García, 1994;Delgado et al., 2000;Fäh et al., 2001;Lunedei and Malischewsky, 2015;Picotti et al., 2017).To calculate the H/V spectrum, a specialized GEOPSY program was developed by the European SESAME team, and widely used to investigate the sediment structures (Bard and The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-164Manuscript under review for journal The Cryosphere Discussion started: 11 September 2017 c Author(s) 2017.CC BY 4.0 License.SESAME team, 2005).Then an approximation equation or H/V spectrum inversion approach can be used to derive the sedimentary layer thickness with the H/V spectrum.
Under the assumption of one-dimensional velocity subsurface conditions, in cases of homogenous and isotropic sedimentary layers over a homogenous half-space, the observed peak frequency equals the fundamental resonant frequency of the sedimentary layer.Thus, the resonance frequency of the low velocity layer is closely related to its thickness h through the following relationship (Ibs-von Seht and Wohlenberg, 1999;Parolai et al., 2002;Picotti et al., 2017;Civico et al., 2017): Where Vs is the average shear-wave velocity of the sedimentary layer, and 0 f is the observed peak frequency.
Provided that a correct estimate of the average shear-wave velocity of the sedimentary layer is available, its thickness can be roughly estimated.
Complicated sedimentary internal structures, including anisotropy and low velocity layers beneath stations, will affect the H/V spectrum and consequently violate the assumptions of Eq. ( 1).Therefore, when inferring complex subsurface structures, an inversion of the full H/V spectrum can be used to explain more accurately the observed H/V spectrum.Based on different assumptions for the interpretation of ambient noise wavefield composition, several inversion approaches have been proposed and successfully applied to study sedimentary structures (Fäh et al., 2003;Arai and Tokimatsu, 2004;Herak, 2008;Lunedei and Albarello, 2009;Sánchez-Sesma et al., 2011).
The H/V method has been successfully applied in studies of sedimentary structures, such as studies of thickness and shear-wave velocities (Ibs-von Seht and Wohlenberg, 1999;Langston and Horton, 2014;Civico et al., 2017;Bao et al., 2017).However, applications in ice environments are rare.Jean-Jacques (2010) studied the snow layer thickness and the ice properties beneath four stations in Dome C region of Antarctica using the H/V method.Picotti (2017) measured ice thickness ranging from tens of meters to 800 m of six glaciers in Italy, Switzerland and West Antarctica.However, the impedance contrast between the ice sheet layer and the overlying bedrock is not as high as that of sedimentary-bedrock and snow-ice layers.Moreover, the complex subglacial environment and internal ice structure create other technical obstacles.Thus, there have been no investigations of ice sheet thickness incorporating the H/V method for measurements or estimations.
In this study, the H/V spectra of 65 stations deployed on ice were processed by using the GEOPSY software, which has been used for sedimentary structure investigations in many regions.Under the general assumption that the seismic properties are stable throughout the whole ice column, we calculated the ice thickness using Eq.
(1) as in most seismological applications to approximate the ice sheet as a homogeneous layer.Meanwhile, a non-linear H/V spectrum inversion method developed by García-Jerez ( 2016) was adopted to constrain the observed H/V spectrum to infer the ice structure, comprised of shear-wave velocity and thickness.Having acquired the resonance frequency of the ice sheet, we adopted Eq. ( 1) with a uniform average shear-wave velocity-1900 m s -1 of the ice layer to calculate the ice thickness.This velocity used here is reasonable given that it is in the general range of ice Vs determined by seismic experiments (Kim et al., 2010).
Moreover, this velocity has also been widely used in previous studies (Hansen et al., 2010;Wittlinger and Farra, 2012;Ramirez et al., 2016).Keeping the velocities set, the ice thickness at each station was calculated using Eq. (1).
In the H/V spectrum inversion procedures, Bedmap2 ice thicknesses were used as references to build the initial models, as along with the related seismic elastic parameters (Fig. 2, Wittlinger and Farra, 2012;Ramirez et al., 2016).We adopted two different models assuming the ice sheet is homogenous and inner ice stratified; respectively, as shown in Fig. 2 to perform H/V spectrum inversion.Model A is a simple homogeneous and isotropic ice structure with an ice layer overlying the half-space.In this model, the ice thickness varies from 0.7 to 1.3 times the Bedmap2 ice thickness for each station.Model B is constructed following Wittlinger (2012Wittlinger ( , 2015) ) as a two-layer ice structure in which a low shear-wave velocity lies in the lower ice layer.In this model,

Results
In this study, the H/V spectra of 65 stations were obtained.respectively.Following the general interpretation principles for H/V spectra (Bard and SESAME team, 2005), the peak frequency denoting the largest amplitude should be the resonance frequency of the ice sheet layer, while the peaks appearing with lower amplitudes at higher frequencies may indicate the shallower impedance contrast layers.The reasonableness of considering the first peak frequency with the largest amplitude as the resonance frequency of the ice sheet layer was verified through rough estimation based on Eq. ( 1), i.e., for station E012, the Bedmap2 ice thickness at that location is 1050 m, so the resonance frequency according to Eq. ( 1) should be 0.452 (the given Vs is 1900 m s -1 ), and as expected was observed in the H/V spectrum.However, there are exceptions such as station N148 displayed in Fig. 2 whose first peak amplitude is slightly lower than that of the following peak observed at higher frequency.At this station however, the location of the first peak correlates with the resonance frequencies through rough estimation.In addition, there are some stations that have no peak frequencies correlating with the ice sheet thickness, despite the existence of peak frequency with strong amplitude in the frequency band.Station ST07 seen in Fig. 3 is such a case, whose fundamental resonance frequency as calculated by Eq. ( 1) should be 0.191 (its Bedmap2 ice thickness is 2490 m).Nevertheless, no clear peak around this expected frequency is observed in the H/V spectrum.We therefore can group the results into three categories: 1) 42 stations with first peaks denoting the largest amplitude in the observed spectrum related to the ice sheet resonance frequency, like the E012, E018, GM02, N148, P071, ST01, ST02 stations in Fig. 3.
2) 18 stations with first peaks with slightly lower amplitude but also related to the ice sheet resonance frequency such as station N108.
3) Five stations without peaks correlating to the resonance frequency, such as station ST07.
Figure 4 shows the H/V spectra of stations along four profiles, together with the ice sheet and bedrock elevation extracted from Bedmap2 database for each station.As shown in Fig. 4, although the neighboring stations are 80 km apart for profile AA', 100 km for profile BB' and DD', and 20 km for profile CC', the shape of the spectra are similar along each profile.Also, along each profile, the peaks associated with the ice thickness are clear and the locations of the peaks shift towards lower or higher frequencies cohering with the variation of the corresponding ice thickness.There are four stations (N060, ST04, ST06, ST07) along the four profiles without peak frequencies related to their corresponding ice thicknesses.This may be caused by the bad coupling of the seismometer with the ice surface or possibly a complicated subglacial environment, for example clear evidence indicates the existence of sedimentary layer beneath station N060.Having identified resonance frequency of the ice sheet, we calculated the ice thickness using Eq. ( 1) with the average shear-wave velocity-1900 m s -1 .The results are listed in Table 1.We projected the calculated ice thickness and the reference Bedmap2 ice thickness for stations along the four profiles in the upper elevation panels in Fig. 4. It is clear that the calculated ice thickness for some stations along the four profiles are close to the reference ice thickness like the E012, P071, and ST01 stations, while there are large deviations at some stations such as E018, N148, and ST02.
The optimum shear-wave velocity models derived from H/V spectrum inversion are presented in Fig. 5 and supplementary Fig. S2.The observed H/V spectrum together with the synthetic H/V spectra using the two optimum shear-wave velocity models are plotted in Fig. 6 and shown in supplementary Fig. S3.As Fig. 6 and the supplementary Fig. S3 shows, the synthetic H/V spectra of the optimum inversion results for model A and model B at almost all stations, both fit the observed H/V spectra in peak frequency and spectrum shape.However, the inversion ice thickness from model A deviates substantially from the Bedmap2 thickness at most stations (such as N108, N148, GM02 and ST02 in Fig. 5), and the difference extends 1 km for some stations (Fig. 7).By contrast, the inversion thickness from model B is consistent with the Bedmap2 thickness as the differences between them are mostly within 200 m.The overall inversion ice thicknesses from model B are listed in Table 1.
We also projected the inversion thickness for stations along the four profiles in the elevation panels seen in Fig. 4, which depicts a high level consistency between the inversion and the reference ice thickness at these stations.
The results of four different length seismic ambient noise records (1 h, 2 h, 4 h, 8 h) used to obtain H/V spectrum are displayed in Fig. 8 (and in supplementary Fig. S4).These plots show that the shape of the spectra of the four tested record lengths are similar to the shape determined using a record five days long.The peak frequencies of the four different length records are all within the margin of error for the peak frequency as determined with the record five days long.We found that the longer the ambient noise record, the more stable the peak frequency is as there are slight shifts in the peak frequency when determined with 1 h and 2 h records; such as those from stations E018 (Fig. 8), E020, and E024 (shown in supplementary Fig. S4).Despite variation in ice thickness from 600 m to about 4 km at the study sites, the length for recording seismic ambient noise suited for H/V methods can be as short as 1-2 hours, in terms of stability and efficiency.

Discussion
Bedmap2 ice thickness were used as reference to verify the ice thickness derived from Eq. ( 1) and H/V spectrum inversion since we lacked actual ice thickness as obtained from the more direct and accurate ice-core drilling, RES and active seismic methods at or near each study site.Because of various factors contributing to the uncertainty in the Bedmap2 database such as data coverage, basal roughness, and ice thickness measurement and gridding error, however, the Bedmap2 ice thickness is not exactly accurate with uncertainty varying from site to site.We obtained the uncertainty of the Bedmap2 ice thickness at each station from the grids of ice thickness uncertainty (Fretwell et al., 2013, also, the uncertainty at our study sites can be roughly seen in supplementary A comparison of the inversion ice thickness from Model B and Bedmap2 database reveals that the differences in ice thickness at all the 57 stations are less than 400 m; there are 33 stations whose differences are within 200 m and 47 stations within 300 m; the maximum difference was 370 m at station ST03.Given that uncertainty of the Bedmap2 database can reach 300 m in some study sites (Fretwell et al., 2013), it is certain that the inversion ice thicknesses are adequately constrained at over 47 stations.
Based on the homogenous ice sheet layer assumption, most of the ice thickness estimations derived from Eq.
(1) are not compatible with Bedmap2 ice thickness (Fig. 4 and Fig. 7), as the differences at 26 stations can extend 400 m and at 10 stations are over 600 m; the maximum difference reaches 910 m at station N036.Moreover, most of the inversion ice thickness results based on the homogenous ice structure of model A also largely deviated from the reference Bedmap2 thickness (Fig. 7 and supplementary Fig. S2).These large deviations cannot be attributed to the uncertainty in the reference Bedmap2 ice thickness since they made minor contributions to the large differences.
The inversion ice thickness from model B, however were highly consistent with the Bedmap2 database.A close examination of the inversion thickness from model B shows that it refined the rough estimation results at 47 stations as calculated with Eq. ( 1) to varying degrees.As at stations E012 and N036, the calculated ice thicknesses using Eq. ( 1) deviate from Bedmap2 at 90 m and 910 m, while the inversion ice thickness from model B refines the gaps to 20 m and 320 m.
We compared our results with those found in Wittlinger (2012).Using the PRF method and a grid search stacking technique, he found that the Antarctic ice is stratified, possibly due to the preferred orientation of ice crystals and fine layering of soft and hard ice layers under pressure.In Fig. 9, we present the ice thickness results for 12 stations common to both studies.It is clear that the interface separating the upper and the lower ice sheet layers determined using the H/V method and the PRF method, is consistent for almost all stations.
The agreement of two-layer ice sheet thickness with the Bedmap2 database, and the consistency of our results to Wittlinger`s results, as well as the large deviation of ice thickness estimated using Eq. ( 1) and model A jointly support the thesis that the two-layered ice sheet models are more reasonable than an homogeneous ice sheet layer assumption.Moreover, the ice thickness of 28 stations derived from Eq. ( 1) were close to the reference Bedmap2 database.This consistency, however, does not strongly support the homogenous ice sheet layer assumption as it can be attributed to the fact that the Vs values adopted in rough estimation was coincidental with the average velocity of the two-layer Vs models.The examples presented in this work clearly show that the H/V method with seismic ambient noise can be effectively to measure ice sheet thickness.However, there are also some limitations that may affect the results.
Shear-wave velocity (Vs), as the key parameter for H/V spectrum inversion and rough estimation using Eq. ( 1), will significantly affect the effectiveness and uncertainty of the H/V method.We can see from Fig. 6 that the synthetic H/V spectra from the optimum Vs profiles of model A and model B for the N108, GM02 and N148 stations (Fig. 5), match the observed H/V spectrum.The inversion ice thickness from model A and model B at these stations however, are remarkably different as the results from model B are more closely match the reference Bedmap2 ice thickness than those from model A (Fig. 5).Also evident in these results is a directly proportional relationship between ice thickness and the Vs as expected from Eq. ( 1) in rough estimation.Given a ∼5 percent variation in the average shear-wave speed of the ice layer, then ice sheet thickness estimation will result in a similar variation such as 150 m for a station with 3 km thickness.Accurate known Vs profiles are therefore prerequisites when obtaining reliable H/V spectrum inversion results, as well as for rough estimations using Eq. ( 1).
It is evident that the longer the noise record, the more stable the observed peak frequency is as the sources of the seismic ambient noise are more evenly distributed, spatially and temporally.This is significant for stations with thin ice primarily due to the fact that thin ice sheet layers are excited by high-frequency waves such as winds and other sources (Picotti et al., 2017).Thus, a longer ambient noise record can improve the stability of the H/V spectrum.In our study, we found that the quality of the H/V spectrum are generally better for thick ice sheet layers than for thin ice sheet such as stations BENN, E012, E018, E024, E026, and E028 with relatively smaller ice thicknesses than other stations.The H/V spectra for these stations exhibited less stability when the lengths of noise records decreased (Fig. 8 and supplementary Fig. S4).Also, the peak frequency obtained from a one hour long record slightly deviates from the peak frequency determined with a five day record.These deviations consequently could lead to uncertainties in ice thickness estimation.The efficiency and the cost of noise record acquisition in Antarctica however, are equally important.In this sense, the proper record length in H/V method application is 1-2 hours.

Conclusions
Given the vital role that ice sheet thickness plays in ice mass balance and global climate studies, many methods have been used to estimate ice sheet thickness, obtaining abundant results.However, new methods must be explored to enrich the database considering the vast area of the Antarctic ice sheet and the limitations of the existing methods.
In this study, the H/V method is proposed as a reliable, efficient method to investigate the Antarctic ice sheet thickness.The H/V method is effective for identifying the fundamental resonant frequency correlating with the ice sheet thickness.In this approach, the ambient noise recording length can be as short as 1-2 hours, reducing costs and increasing efficiency.Equation (1) can retrieve a fast and rough estimation of the ice thickness but Frequency (Hz) P 0 6 1 P 0 7 1 P 0 8 0 P 0 9 0 N 1 7 3 P 1 1 6 P 1 2 4 0.1 0.2 0.5 Cross section showing H/V spectra and the ice sheet thickness obtained from the H/V method at stations along the four profiles (Fig. 1).In the below H/V spectra cross section panels, the red circles denote the resonance frequencies correlating to the ice thickness for each station, and the spectra of the four stations without clear peaks are plotted with red lines.The upper panels show the variation of the bedrock and ice surface elevation along each profile obtained from Bedmap2 database.In these plots, the red dots indicate the reference Bedmap2 ice thickness, while the yellow and the blue dots represent the calculated ice thickness using Eq. ( 1) and the inversion ice thickness from model B, respectively.

The
Cryosphere Discuss., https://doi.org/10.5194/tc-2017-164Manuscript under review for journal The Cryosphere Discussion started: 11 September 2017 c Author(s) 2017.CC BY 4.0 License.During H/V spectrum acquisition using the Geopsy software, we remove the transient signals (earthquakes) from noise records with the STA/LTA technique and divide the records into 600 s length windows with an overlap of 5 %.Time series were tapered with a 5 % cosine function, and the FFT was calculated for each component.The spectra were smoothed with a Hanning window in a bandwidth of 0.1-2 Hz on a logarithmic frequency scale.The spectra of the two horizontal components (NS and EW) were merged to one horizontal component spectrum by calculating their geometric mean.The spectral ratios and corresponding standard deviation estimates between the horizontal component and the vertical component were calculated.
the thickness of the upper ice layer and the lower ice layer were set to occupy 60-75 and 25-40 percent of the Bedmap2 thickness, respectively.Using the non-linear Monte Carlo method(García-Jerez et al., 2016), we retrieved the optimum solutions for model A and B. These two solutions were best fitted to the observed H/V spectum.It usually takes a few minutes to about half an hour to collect seismic ambient noise waveforms in the investigations of sedimentary layers with thickness ranging from several tens to hundreds of meters.However, there is no experiences for the time length of recording seismic ambient noise in the Antarctic ice sheet with several kilometers thick.It is necessary to apply the H/V method with a much shorter recording time for seismic ambient noise, considering the harsh environment and logistical support difficulties in Antarctica.Therefore, we investigated the feasibility and reliability of H/V method by testing a range of noise record lengths; eight hour, four hour, two hour, and one hour intervals were tested.The processing strategies remained the same as in H/V spectrum acquisition except the window length was changed to 200 s when calculating the H/V spectrum using different length noise records.The Cryosphere Discuss., https://doi.org/10.5194/tc-2017-164Manuscript under review for journal The Cryosphere Discussion started: 11 September 2017 c Author(s) 2017.CC BY 4.0 License.
Figure 3 displays the H/V spectra of nine stations selected from three arrays.These examples are representative of all the results, and the remaining spectra are presented in the supplementary Fig. S1.It is clearly shown that in almost all H/V spectra there were two or three clear peaks in the frequency band.Generally, the largest amplitude appears at the first peak located around 0.2 Hz or below, and the second and the third peaks with lower amplitudes are located at ~0.5 and ~0.8 Hz,

The
Fig.S5).A close examination of the uncertainty of the Bedmap2 ice thickness reveals that the uncertainty at 52 stations ranges from 59 m to about 200 m, and the uncertainty at 57 stations is below 300 m.As the accuracy of the H/V method is at the same scale with the uncertainty of the Bedmap2 ice thickness at the 57 stations, the Bedmap2 ice thicknesses are adequate to verify the results derived from the H/V method.The remaining three stations including ST09, ST13, and ST14 are excluded for validation as the uncertainty of the reference ice thickness at these stations reaches 1000 m.

The
Cryosphere Discuss., https://doi.org/10.5194/tc-2017-164Manuscript under review for journal The Cryosphere Discussion started: 11 September 2017 c Author(s) 2017.CC BY 4.0 License.Table 1 Ice thickness results obtained from this study (Thickness I, II are ice thickness values obtained from Eq. (1) and model B, respectively)

Figure 1 .
Figure 1.Locations of the three seismic arrays used in this study.Some stations are lined to four profiles marked with AA', BB', CC' and DD'.TAMSEIS：TransAntarctic Mountains Seismic Experiment; GAMSEIS：Gamburtsev Antarctic Mountains Seismic Experiment; POLENET/ANET：The Polar Earth Observing Network/Antarctic Network.Ice sheet thickness data in this plot come from Bedmap2 database.

Figure 2 .Figure 3 .
Figure 2. Sketches of the two ice layer models used for H/V spectrum inversion.Model A comprises a single ice layer, while model B is a two-layer ice structure with low shear-wave velocity in the lower ice layer.The parameters used in the two models are referred to Wittlinger (2012).
Figure 4. Cross section showing H/V spectra and the ice sheet thickness obtained from the H/V method at stations along

Figure 6 .
Figure6.The synthetic H/V spectra and the observed H/V spectrum for the nine stations.The synthetic H/V spectra are

Figure 7 .Figure 8 .
Figure 7. Ice thickness derived from the H/V method versus the reference Bedmap2 ice thickness.The blue squares in panel (a), (b), and (c) represent ice thickness estimations from model A, Eq. (1), and model B, respectively.The red circles in each panel denote the Bedmap2 ice thickness and each Bedmap2 value is marked with its corresponding error bar obtained from the uncertainty grids(Fretwell et al., 2013).