Natural Seismic Event Analysis Based on Signal and Source Characteristics from two Experiments in Antarctica

Abstract

This study presents geophysical data from two passive seismic measurements conducted at two different sites in Antarctica. We analyzed the signals mainly in the frequency domain through the multitaper method to extract some spectral characteristics of the signals that would have been out of reach through the usual FFT approach. The power spectral density of the signals carries information about the processes that generated them, allowing its correlation with their source origin and type, either natural or anthropogenic. We deal with three different source types: calving, wind, and anthropogenic origins. The former is closely related to glacier dynamics, being modulated by the prevailing atmospheric processes. At both locations the wind noise is prevalent, complicating the analysis of other events like calving. We have used data classification, estimation of the source azimuth, and seismic apparent velocity to demonstrate the viability of using geophysical methods to study glacier elastic parameters and dynamics. Moreover, the calving rate can yield a wider and more independent understanding of glacier hydrodynamics and may help to estimate the future response of the polar areas to a changing environment.

Key words
Passive seismic; beamforming; multitaper method; calving event; anthropogenic sources

Introduction

Glaciers play a crucial role in the climate system, and understanding the factors that influence their dynamics is essential for studying global-scale climate change (Haeberli et al. 2017, Oerlemans 2001, Shakun & Carlson 2010). The relationship between these two phenomena is so intricate that a comprehensive analysis of one cannot be conducted without considering the other. As the average temperature of the planet increases, glaciers respond by undergoing accelerated melting. This, in turn, impacts the energy balance of the global climate system turning the analysis of glacier dynamics into an important parameter for understanding the ongoing global processes.

The geophysical methods are an important tool for studying glaciers, offering a non-invasive and safe approach to investigating these fragile ecosystems. For instance, the Ground Penetrating Radar (GPR) method has been utilized in mapping the internal layers of a glacier, enabling the identification of features such as layers of ancient ice, fissure structures, and water accumulation zones (Martins & Travassos 2015, Travassos et al. 2018, Bohleber et~al. 2017). Another technique used is passive seismic monitoring of teleseisms, microseisms, ambient noise, and glacier calving. For instance, valuable information about preferential flow paths within the glacier mass can be obtained through the monitoring of the microseisms caused at the interface between ice and the bedrock (Hammer et al. 2015). By monitoring the occurrence of the seismic signals generated during glacier calving events, where masses of ice detach from the glacier, one can infer information of glacier dynamics at its terminus and correlate them with other information, e.g., local meteorology, which may influence these occurrences (Aster & Winberryba 2017, Podolskiy & Walter 2016, Thomas et al. 2011).

This study presents two sets of passive seismic data obtained at two different sites in Antarctica. The first data were obtained in the interior of the Antarctic continent in which the seismic sources were ambient noise generated by the energy transfer from the winds to features on the snow surface. The second data were obtained in Admiralty Bay, King George Island (KGI). The seismic signals at KGI are a melange of meteorological, calving events from the surrounding glaciers, and anthropogenic origins. Both anthropogenic and natural signals can be harnessed as seismic sources (Diaz et al. 2022, Li et al. 2020, Okada 2003), such as road traffic, aircraft, wind gusts, rainfall, water bodies waves, wind turbines, etc.

We present here the seismic time and spectral characteristics of each signal group and correlate them with their sources. The preliminary results presented in this study are of great importance for planning the next stages of this research, which has been divided into two distinct lines of investigation. The first involves monitoring microseisms resulting from the ice interface, which provides information on the physical and mechanical properties of the glacier. The location of those microseisms and their focal mechanisms are crucial for understanding the internal processes of the glacier and its response to environmental changes. The second line of research focuses on the location and monitoring of glacier-calving events, which can provide insights into melting dynamics and the behavior of glaciers concerning climatic conditions.

The data obtained from these two research lines may be subsequently compared with climate and environmental data to identify possible cause-and-effect relationships. By doing so one may achieve a more comprehensive understanding of the factors that influence glacier hydrology, and how environmental changes affect their dynamics and their role in global climate change.

Methods

Assume a subsurface that is both laterally uniform and vertically heterogeneous, where seismic velocity increases with depth. There is a seismic array with $N_s$ sensors, with the largest distance between two sensors defining its aperture $a_a$. $a_a$ defines the resolution for small wavenumbers, the longest wavelength that can be resolved is ${\lambda }_{max}\sim a_a$, for $\lambda \gg a_a$ the array behaves like a single station. Conversely, the mean distance between contiguous sensors $\overline{g_i{g}_{i\pm 1}}$ defines the smaller wavelength ${\lambda }_{min}$ of a resolvable seismic phase.

Figure 1 schematically shows an elastic plane wave originated at a remote SW source reaching the array from below with an incidence angle $i$ in the vertical plane with a mean, or effective, crustal (mean) phase velocity ${𝐯}_c$. The array records the onset of a horizontal wave traversing the horizontal plane with an apparent velocity $v_h$ and a BAZ $\theta$, with a horizontal slowness.

Two techniques can be employed to determine the apparent phase velocity within narrow frequency bands: cross-correlation and frequency-wavenumber (f-k) analysis. In the former, seismic interferometry can be used to estimate the Green’s Function between two sensors, with one acting as a virtual source for the other (Tsai & Atiganyanun 2014, Wapenaar et al. 2010). We use here the latter, known as beamforming, which enhances the signal-to-noise ratio (SNR) by delaying and coherently summing signals from different sensors in a seismic array (Rost & Thomas 2002). Beamforming also allows for estimates of the source azimuth, known as backazimuth (BAZ), and the apparent velocity of the seismic signals. These parameters are needed for source localization, signal identification, and classification. The analysis requires the array to be placed far enough from the potential source to avoid the curvature of the wavefront, ensuring a plane wave incidence. Another requirement is a simple velocity model since the medium inhomogeneities affect the wave propagation and cause inaccuracies in the estimated BAZ and slowness.

An elastic wave arriving at the seismic array can be characterized by its horizontal slowness, $u_h$, which is the inverse value of horizontal apparent velocity, $1/v_h$

$$u_h=\frac{1}{v_h}=\frac{\sin i}{\left|v_c\right|}$$(1)

and is related to: (i) the angle of incidence $i$, (ii) the true velocity $v_c$ and (iii) its azimuth with the North toward the epicenter, the BAZ, $\Theta$, refer to Figure 1 and Eq(1). These parameters are combined in a slowness vector ${𝐔}_0$,

Figure 1
(A) Snapshots of an elastic plane wave originated at a remote source at SW, reaching the Earth’s surface with a velocity $v_c$ at an incidence angle $i$. (B) The wavefront traverses the array horizontally with a horizontal velocity $v_h$ at a BAZ $\theta$. The point 0 is the reference origin for the array, and the position vector to sensor 5, ${𝐫}_5$, has an angle $\beta$ with the wave propagation.

$$\begin{array}{ccc}\hfill {𝐔}_0=& (u_x,u_y,u_z)=\hfill & \hfill (\frac{sin\theta }{v_h},\frac{cos\theta }{v_h},\frac{1}{v_{h}tani})=u_h(sin\theta ,cos\theta ,\frac{1}{tani})=\frac{1}{v_c}(sinisin\theta ,sinicos\theta ,cosi).\\ \hfill \end{array}$$ (2)

Beamforming Processing

The seismic signals’ onsets display relative time delays at each array receiver that have to be corrected to align them in time. Beamforming involves utilizing the precise combination of backazimuth and slowness to estimate time-shifts to a reference point. This allows the coherent summation of signals from various sensors, thereby enhancing the signal-to-noise ration (SNR).

The wavenumber vector ${𝛋}_h$ relates to the slowness at the horizontal surface as

$${𝛋}_h=\omega {𝐮}_h,$$(3)

where $\omega =2\pi f$, $f=\frac{2\pi }{T}$ is the angular frequency, and $T$ the period of the signal. Each of the $N_s$ array sensors is referred to with a position vector ${𝐫}_i,i=1,\dots ,N_s$, which has an angle $\beta$, in Figure 1A, with direction of propagation. All the spatial array parameters, $u_h$ and $\theta$, can be expressed by a single expression,

$$s_i(t;{𝐫}_i)=s_i(t-{𝐫}_i\mathbf{\cdot }𝐮)=s_i(t-{\tau }_i),$$(4)

where $s_i(t;{𝐫}_i)$ is the signal measured at the $i$-th sensor at time $t$, ${\tau }_i={𝐫}_i\mathbf{\cdot }𝐮$, the projection of the position vector onto the slowness vector, is the time delay.

The time delay can be rewritten in terms of the horizontal coordinates of site $i$ as,

$${\tau }_i=\frac{\left|{𝐫}_i\right|cos\beta }{v_h}=\frac{-x_{i}sin\theta -y_{i}cos\theta }{v_h},$$(5)

which is valid only for horizontal arrays, i.e., $z_i=0,\forall i$. In the case where a given sensor lies outside the horizontal plane, $z_i\ne 0$, equation (5) will have an extra term,

$${\tau }_i=\frac{-x_{i}sin\theta -y_{i}cos\theta }{v_h}+\frac{z_{i}cosi}{\left|{𝐯}_c\right|},$$(6)

which depends explicitly on the local mean crustal velocity $\left|{𝐯}_c\right|$, a clear hindrance in estimating ${\tau }_i$. Therefore elevation variations within the array should be avoided, maybe a good rule of thumb would be to use the Widess criterium to keep topographic changes $\le (\frac{\tilde{\lambda }}{4},\frac{\tilde{\lambda }}{8})$, $\tilde{\lambda }$ being the dominant wavelength (Knapp 1990).

The beamforming for the array is thus,

$$b\left(t\right)=\frac{1}{N_s}\sum _{i=1}^{N_s}{s}_i(t+{\mathbf{r}}_{\mathbf{i}}\cdot \mathbf{u})=\frac{1}{N_s}\sum _{i=1}^{N_s}{s}_i(t+{\tau }_i).$$(7)

Assuming $𝐮$ is the correct slowness at a given site, another slowness value $\hat{u}$ would have yielded another signal realization ${\hat{s}}_i(t-{𝐫}_i\mathbf{\cdot }\widehat{𝐮})$, the signal difference being

$$s(t+{𝐫}_i\mathbf{\cdot }𝐮-{𝐫}_i\mathbf{\cdot }\widehat{𝐮})=s(t+{𝐫}_i\mathbf{\cdot }(𝐮-\widehat{𝐮})),$$

we can input this in equation (7) to obtain the beam

$$b\left(t\right)=\frac{1}{N_s}\sum _{i=1}^{N_s}{s}_i(t+{\mathbf{r}}_{\mathbf{i}}\cdot (\mathbf{u}\mathbf{-}\hat{\mathbf{u}})).$$(8)

The seismic energy is calculated by integrating over the squared amplitudes,

$$E\left(t\right)={[\frac{1}{N_s}{s}_i(t+{𝐫}_i\mathbf{\cdot }(𝐮-\widehat{𝐮}))]}^{2}dt.$$ (9)

Apply Parseval’s and the shifting theorem to write the previous equation in the frequency domain,

$$E(\omega ,𝐮-\widehat{𝐮})=\frac{1}{2\pi }{\left|S\left(\omega \right)\right|}^2{|\frac{1}{N_s}exp(ı\omega r_i(u-\hat{u}))|}^{2}d\omega ,$$(10)

where $S\left(\omega \right)$ is the Fourier transform of the signal $s\left(t\right)$. As $𝛋=\omega 𝐮$, we can write

$$\begin{array}{c}E(\omega ,𝛋-\widehat{𝛋})=\frac{1}{2\pi }{\left|S\left(\omega \right)\right|}^2{\left|A(𝛋-\widehat{𝛋})\right|}^{2}d\omega \hfill \\ {\left|A(𝛋-\widehat{𝛋})\right|}^2={|\frac{1}{N_s}exp(ı\omega {𝐫}_i\mathbf{\cdot }(𝛋-\widehat{𝛋}))|}^2,\hfill \end{array}$$(11)

which is the array response function, ARF.

When the correct slowness is achieved,

$${\left|A(𝛋-\widehat{𝛋})\right|}^2=1,$$

the array is optimally tuned for that given slowness; all energy propagating with different values of slowness will be partly suppressed. The ARF is dependent on the frequency and is controlled by the array configuration, spacing and aperture. Equation (11) is the transfer function of the array, a function of slowness and wavenumber. Both slowness and BAZ can be computed from the wavenumber vector $𝛋={({\kappa }_x^2+{\kappa }_y^2)}^{\frac{1}{2}}$

$$\begin{array}{c}\left|𝛋\right|=\omega \left|{𝐮}_h\right|\hfill \\ \theta =arctan\frac{{\kappa }_x}{{\kappa }_y},\hfill \end{array}$$(12)

using the f-k analysis to obtain source location and surface wave phase velocities.

Figure 2 gives a summary of the processing flow of the beamforming.

Figure 2
Processing flow of beamforming.

Multitaper spectral estimation

The spectral estimates suffer from two sources of inconsistency, narrow and broad-band bias, and variance. The first arises from the fact the data length is finite causing signals at different frequencies, either nearby or distant, to be mixed and blurred. The spectrogram is proportional to the square of the spectral estimator, having an associated variance $\sim 100\%$ of the estimate itself (Bendat & Piersol 2011), a poor estimate of the spectral density function. The usual way of reducing the variance is resorting to band averages of the spectral estimates.

We deal with bias and variance by obtaining the spectral estimates using the multitaper method where a time series $y\left(t\right)$ is multiplied by a series of taper functions, the discrete prolate spheroidal sequence, DPSS, before computing the power spectrum $Y\left(f\right)$ by the Fourier transform (Percival et al. 1993, Thomson 1982). The algorithm produces several tapered versions of the data which are FFT transformed and averaged together to yield a spectrum with reduced bias and variance. As the DPSS tapers are orthogonal each single-taper estimate is uncorrelated to all others and then can be averaged together as if they were independent realizations of a given process, thus reducing the variance in the measured signal, and avoiding inconsistent spectral estimates.

The method also provides an elegant solution to the problem of bias errors, when signals of different frequencies become mixed, whether they are close together (narrow-band bias) or far apart (broad-band bias). With the control of variance and bias, we can produce more accurate and smoothed spectral estimates, far better than would be possible with the traditional time-frequency averaging approach in spectrograms.

Let a data series $y\left(t\right)$ with $N$ elements be $\Delta t\mathrm{\text{s}}$ long. Assume $W=\Delta f$ is a bandwidth over which we want to smooth the spectrum over. The bandwidth $W$ controls the spectral resolution, the smaller it is, the higher the spectral resolution, and the other way around; it is safer to set a smaller $W$ not to overlook any important spectral feature. The time-half-bandwidth product is

$$T_{\frac{W}{2}}=N\frac{W}{2}\ge 1,$$(13)

i.e., the product of the time series size and half the bandwidth of the main lobe $\frac{W}{2}$. The optimum number of tapers, $k_t$, should be less than the Shannon number, $2T_{\frac{W}{2}}$(Percival et al. 1993), or

$$k_t=\lfloor 2T_{\frac{W}{2}}-1\rfloor ,$$(14)

where $\lfloor \cdots \rfloor$ is the floor function.

For the k-th taper $w_k$, the Fourier transform of the time series $y\left(n\right)$ is

$$Y_k\left(f\right)=\sum _{n=0}^{N-1}y\left(n\right)w_k\left(n\right)e^{-2\pi ıfn}.$$(15)

The spectral estimate using the tapers $\hat{S}\left(f\right)$ is then obtained iteratively,

$$\begin{array}{cc}\hat{S}\left(f\right)=\frac{\sum _{k=0}^{K-1}{d}_k^2{\left|Y_k\left(f\right)\right|}^2}{\sum _{k=0}^{K-1}{d}_k^2};\hfill & \hfill d_k\left(f\right)=\frac{{\lambda }_k^{\frac{1}{2}}\left(f\right)}{{\lambda }_k\left(f\right)+(1-{\lambda }_k){\sigma }^2}\\ \hfill \\ \hfill \end{array}$$(16)

where ${\lambda }_k$ is an eigenvalue associated with $v_k$ and ${\sigma }^2$ the variance.

As the tapered data versions can be considered independent realizations of a given process, due to the orthogonality of the DPSS tapers, we can apply a harmonic F test on the multitaper spectral estimates. We assume the time series is a superposition of sinusoidal components of a background process with a continuous PSD (Ghil et al. 2002, Thomson 1982). Note that is not feasible with the usual spectral estimation via FFT. We use here a $99\%$ confidence cut-off for the F-test and the spectral power amplitude to avoid false positives (Mann & Lees 1996)

We can summarize the multitaper spectral estimation with the following steps:

1. Set the window size $N$ depending on the nature of the signal.

2. Set the desired frequency resolution $W=\Delta f$.

3. Compute the time-half-bandwidth product, relation (13).

4. For each of the DPSS tapers, estimate a single-taper spectrum, relation (15).

5. Sum over the single-taper spectra and obtain the mean, which is the multitaper spectral estimate.

The Datasets

The passive seismic data are from two different sites in Antarctica two sites $>2500\mathrm{\text{km}}$ far apart in the Antarctic Continent, the other in the South Shetland Islands. The first dataset was obtained at $({84}^{\circ }\mathrm{\text{S}},{79.5}^{\circ }\mathrm{\text{W}})$, hereinafter 84S. The seismic sources were ambient noise generated by the energy transfer from the winds on features on the snow surface such as sastrugi and the Cryosphere-I a scientific module, hereinafter C-I. Figure 3 gives an overview of the site locations, two views of the 84S site, and a glacier front in KGI.

The C-I is the main landmark at 84S, a prismatic body $6.3\times 2.6\times 2.6{\mathrm{\text{m}}}^3$, weighting $\lesssim 3000\mathrm{\text{kg}}$, held at $1.5\mathrm{\text{m}}$ above the surface by four stilts, anchored with steel cables to the snow surface. There are four wind turbines and an automatic weather station, AWS, mounted on its top, which should affect the dynamic response of the prismatic body, a hollow prism. Those top fixtures, refer to Figure 3, and its free walls may imply the prism may be able to vibrate at higher frequencies than it would if fixtures were not there. Much like the wind-induced vibration on a yacht mast is amplified below decks, the hull acts as a sounding board. The crew reported annoying high-frequency vibrations on the module during fieldwork¹.

Figure 3
Panel A shows the location of the two experiments reported here on a map of Antarctica from the SCAR’s Antarctic Digital Database (https://www.add.scar.org). Panel B shows an aerial view of C-I aligned with the prevailing S$\to$N wind. Panel C shows a photo of the Ajax glacier front with a helicopter (circled in red) for the sake of scale. Panel D gives a closer view C-I with its four wind turbines and the AWS on its roof. The responsible for the data collection, Dr. Aquino, is standing in front of the module.

By its size and stance above ground C-I is by far the main obstacle to the wind and, most probably the main seismic source at 84S, Figure 3. Probably the tents pinched around should also be considered as relatively minor isolated sources. A myriad of sastrugi to be found everywhere around the C-I, refer to Figure 3, should constitute a diffuse and spatially uniform source, albeit secondary in terms of energy. It was observed elsewhere that those wavelike ridges of hard snow yield firn-trapped surface wave resonant signals of $\gtrsim 5\mathrm{\text{Hz}}$ in the immediate subsurface, $\lesssim 5\mathrm{\text{m}}$, a result of the interaction of wind with the superficial low velocities (Chaput et al. 2018). Based on empirical relations between body wave seismic velocities in firn (Albert 1998) and an ice density profile from a borehole dug at the site (Travassos et al. 2022), it is possible to estimate S-wave velocities in the immediate subsurface. We can estimate Rayleigh waves velocities in the range $[430-800]\frac{m}{s}$, assuming they are $\sim 0.9$ of the corresponding S-waves.

The second dataset was obtained in Admiralty Bay, King George Island, hereinafter KGI, the largest of the South Shetland Islands. The seismic signals at KGI are a mélange of meteorological, calving events from the surrounding glaciers, and anthropogenic origins.

The KGI is predominantly of volcanic origin, part of the Volcanic Arc Mountain Chain of the South Shetland Islands. All volcanic rocks on the Antarctic Peninsula are related to the Antarctic Peninsula Volcanic Group (Thomson & Pankhurst 1983), during the Jurassic–Palaeogene. Glacial sediments, including gravel, clays, and tillite deposits (compacted glacial sediments), are common on the island. The Quaternary geology of King George Island is affected by climate changes and glacial processes.

The ice cover of the KGI is characterized by an ice cap with three asymmetric, interconnected domes reaching $706\mathrm{\text{m asl}}$ (Braun et al. 2001). The average thickness of that ice cap along its glacial drainage divide is $\simeq 200\mathrm{\text{m}}$ (Macheret 1997). The precipitation at sea level is $800\frac{mm}{y}$ steady increasing with height, reaching $2480\frac{mm}{y}$ (Jiahong et al. 1998), an ice core study down to $15\mathrm{\text{m}}$, equivalent to $\simeq 73\mathrm{\text{y}}$ found a mean net accumulation rate of $0.59\frac{mweq}{y}$ (Simões et al. 2004).

The Admiralty Bay, the largest in KGI, is a fjord circumscribed by several glaciers with distinct physiographic expressions: highly crevassed with steep slopes tidewater (Ajax, Stenhouse, Goetel, Dobrowolski and Krak); hanging (Gdansk and Emerald) and discharge glaciers with land terminations (Dragon and Sphinx) (Arigony-Neto 2001). The average water depth at the Northern part of Admiralty Bay, in the Martel Inlet is $143\mathrm{\text{m}}$ becoming shallower toward the shore with $49\mathrm{\text{m}}$ (Perondi et al. 2022).

In both sites, we used a Geode ES-3000 seismograph operating in continuous recording, with Geospace GS-20DX vertical geophones, with a corner frequency of $f_c=10\mathrm{\text{Hz}}$. We used two distinct gather geometries, a linear, 1-D, at 84S and a circular 2-D array at KGI.

Results

We estimated the PSD with an adaptative multitaper method using $NW=3$ and $K=5$ tapers in tandem with the F-test with a confidence cut-off of $99\%$ using a multitaper package (Prieto et al. 2009, Prieto 2022). We processed the data within a Python framework with the ObsPy package (Beyreuther et al. 2010, Krische et al. 2015), with some limited use of the Seismic Unix system (Stockwell JR 1999).

The 84S Dataset

The choice of the 84S 1-D seismic gather reflects the assumption that C-I is the prominent seismic source in the region. Two co-linear gathers ${𝐆}_1$ and ${𝐆}_2$ run S from C-I into the wind as shown in Figure 4. Both gathers are $L_{𝐆}=66\mathrm{\text{m}}$ buried in a $0.3\mathrm{\text{m}}$ deep trench in snow to protect the geophones and cable from wind-induced vibrations. Each gather has 12 geophones $g_i,i=1,\dots 12$, $6\mathrm{\text{m}}$ apart from each other. We have collected uninterrupted $\simeq 24\mathrm{\text{h}}$ worth of data at each gather, from Dec 15 to Dec 17, 2019, totaling 15804 data files. Each trace has a time window $\delta t=8\mathrm{\text{s}}$ and a sampling rate $\delta f=2000\mathrm{\text{Hz}}$, resulting in 16000 data points/trace.

Figure 4
Field layout at 84S, showing the two co-linear gathers, ${𝐆}_1$ and ${𝐆}_2$, running southward from the C-I. The circles are the geophones $g_i$, laid along a length of $L_G$. The first geophone $g_1$ is at $L_0=200\mathrm{\text{m}}$ from C-I baricenter. There is a gap of $L_g=40\mathrm{\text{m}}$ between geophones $g_{12}$ of $G_1$ and $g_1$ of $G_2$.

Some limited insight on the wind-induced vibrations on C-I can be gathered from a wind tunnel study performed on rectangular prism models with several aspect ratios $𝒜$, the ratio of the along-flow to cross-flow dimensions, and masses (Garrett 2003). Garrett’s prisms were supported by an axis parallel to its greatest length, free to vibrate in a direction transverse to the wind direction. Garrett’s prisms had $f_{lo}=[6,10]\mathrm{\text{Hz}}$, a range within the expected frequency range reported elsewhere in wind-induced seismic activity in cryospheric studies: $f_w=10\mathrm{\text{Hz}}$ (Podolskiy & Walter 2016). The C-I anchoring cables probably act to restrict the vibration amplitudes of C-I.

We choose geophone 6 of gather ${𝐆}_1$, file 4600, at $230\mathrm{\text{m}}$ S of C-I to illustrate the signal characteristics in a day with a strong breeze, wind force 6 on the Beaufort Scale, with gusts reaching $v_{w,\mathrm{\text{max}}}\le 12\frac{m}{s}$. The data is notched at $60.62\mathrm{\text{Hz}}$ as well as its even harmonics up to $606.2\mathrm{\text{Hz}}$. Those spectral lines are due to the AC-DC converter used to power the field laptop. All the data is band-passed within the range $[5,800]\mathrm{\text{Hz}}$; we refer to that filtered version of the data herein as the original data. The spectrogram of geophone 6 in Figure 5 shows low-amplitude isolated clusters of energy over the entire time window, being more energetic at $\lesssim 400\mathrm{\text{Hz}}$.

The adaptative multitaper method shows the signal has important spectral contributions throughout the whole frequency range, which are better shown using the spectral lines from the multitaper F-test. Figure 6 shows a complicated pattern of spectral lines, the most energetic at $(6.0,34.37,212.06,688.92)\mathrm{\text{Hz}}$, the latter being the most statistically significant throughout, a very high frequency indeed we find difficult to understand. Note that there is what appears to be a densification of more energetic spectral lines from the F-test in the range $(200,400)\mathrm{\text{Hz}}$, coinciding with the energy bands running the time window in the spectrogram, Figure 5.

Figure 5
Spectrogram of geophone 6 of file 4600, showing the energy well distributed over the entire time window and limited to $\lesssim 400\mathrm{\text{Hz}}$.

Figure 6
Spectral lines from the F-test on geophone 6 of file 4600. Panel A shows the spectral lines for the whole frequency range. Panel B shows spectral lines for $f\le 45\mathrm{\text{Hz}}$. In this figure and all F-Test plots herein, the dashed red line shows the 99% critical threshold.

The longer wavelengths of the surface waves, which correspond to the lower frequencies probe deeper into the subsurface. We can produce a lower frequency version of the data by decimating them by 4 and applying a band-pass of $[5,45]\mathrm{\text{Hz}}$. The six F-test lower frequency spectral lines above the 99% critical threshold are shown in . We can also reshape the multitaper PSD to these lines to display an energy distribution with three conspicuous spectral peaks at 6.0, 17.7, and $34.4\mathrm{\text{Hz}}$, Figure 7.

Figure 8 shows a modulation in the low-frequency version of the trace probably associated with the module’s vibration modes excited by the wind. This can be shown differently by taking the difference between the original trace and its filtered version to assess the frequency components removed by the filter, see Panel B of Figure 8.

Figure 7
The multitaper reshaped PSD to the F-test spectral lines of geophone 6 in range $[5,45]\mathrm{\text{Hz}}$.

Figure 8
Panel A shows the trace of geophone 6 with a band-pass of $[5,45]\mathrm{\text{Hz}}$. Panel B shows the difference between the original data and the low-frequency version shown in A.

The KGI Dataset

The seismic gather is on a plateau on Ulmann Point at $({62}^{\circ }{4.83}^{\prime }\mathrm{\text{S}},{58}^{\circ }{20.42}^{\prime }\mathrm{\text{W}})$ in the Martel Inlet, refer to . The seismic gather had a 2-D circular layout with 13 geophones, 10 along the perimeter of a circle, and 3 along its radius, the last one at the center of the circle, refer to Figure 9. The fieldwork lasted from November 14 to December 10, 2022, totaling uninterrupted $303\mathrm{\text{h}}$ worth of seismic data in 16102 data files with 13 traces each. Each trace has a time window $\delta t=65\mathrm{\text{s}}$ with a sampling rate of $\delta f=250\mathrm{\text{Hz}}$, resulting in 16250 data points/trace.

Figure 9
Panel A gives a depiction of the gather G on Ulmann Point. Panel B gives a map of Martel Inlet with the main landmarks addressed in this work. The location of the gather on Ulmann Point is marked G. E and S are the locations of the EACF Station and the ship position, respectively. Aj, Go, Do and Kr are Ajax, Götel, Dobrowolski, and Krak glaciers.

Here we concentrate on a few events from that dataset for the sake of signal characterization, based on its source. As before we begin by looking at the signal spectrogram and then analyze the PSD estimated with an adaptative multitaper method using $NW=3$ and $K=5$, in tandem with the spectral lines from the F-test with a confidence cut-off of 99%. We also notched the fundamental $60.62\mathrm{\text{Hz}}$ spectral line from the power inverter DC-to-AC. All the KGI data are band-pass filtered data within the range $[5,100]\mathrm{\text{Hz}}$; we refer to that filtered version of the data as the original data.

Wind Noise

The field site is subject to strong wind gusts, steep topography, and an ice cover to N and E. The stony ground constitutes a challenge to protect geophones from the wind. Besides the loose rock, several other structures may vibrate with the wind, becoming seismic sources: (i) The plastic box that protected the seismometer, the field computer, and the electrics; (ii) The guy cables that anchored the box to the ground, and (iii) Large rocks to be found everywhere in the field. Wind-generated seismic signals are reported in the literature at frequencies $[5,500]\mathrm{\text{Hz}}$ for wind speeds $⪆3\frac{m}{s}$ (Withers et al. 1996).

File 503 was collected during a storm, wind force 10 on the Beaufort Scale, with westerly gusts reaching $27\frac{m}{s}$, during the hour the file was recorded. The spectrogram of geophone 9 in Figure 10 shows significantly higher amplitudes than at 84S, spanning over most of the frequency range in repeating time bands of $\sim 5\mathrm{\text{s}}$. Those bands may be due to a superposition of processes of wind coupling with the inhomogeneities on the surface, producing what appears to be resonant signals. It was observed elsewhere that sastrugi yielded firn-trapped surface wave resonant signals of $\gtrsim 5\mathrm{\text{Hz}}$ in the immediate low–velocity subsurface, $\lesssim 5\mathrm{\text{m}}$, (Chaput et al. 2018). A proper understanding of the problem requires a knowledge of the mechanism of wind-ground coupling, which is well beyond the scope of this work.

The adaptative multitaper method shows the signal energy distributes along the whole frequency range, mostly concentrated in the range $[10,30]\mathrm{\text{Hz}}$. Figure 11 shows the reshaped PSD to the F-test spectral lines above the 99% critical threshold: $[13-29.3]\mathrm{\text{Hz}}$.

Band-pass all geophones within $[10,30]\mathrm{\text{Hz}}$ to obtain a seismogram for the entire gather. Figure 12 shows the seismogram limited to $t\le 30\mathrm{\text{s}}$ with two conspicuous and short duration wind events at $[5,10]\mathrm{\text{s}}$ and $[15,20]\mathrm{\text{s}}$, and a third longer one at $t>20\mathrm{\text{s}}$. Wind activity comes in bursts, a distinct behavior from a calving event seen in Figure 13. Those wind events have a characteristic S-shape in seismograms due to the relatively lower wind speed as compared to the rock velocities and to the 2-D gather geometry.

Figure 10
Spectrogram of geophone 9 of file 503, showing significantly higher amplitudes than at 84S, and repeating time bands of $\sim 5\mathrm{\text{s}}$.

Figure 11
Multitaper spectrum of file 503 reshaped to the spectral F-lines with cut-off values $\ge 99\%$. Note the effect of notching the influence of the power inverter at $\approx 60\mathrm{\text{Hz}}$.

Figure 12
Seismogram of wind activity of file 503. The event onsets at each geophone have a conspicuous S-shape due to the relatively lower wind speeds and gather’s 2-D geometry.

Figure 13
Spectrogram of a calving event at geophone 7 of file 1000. Most of the energy lies within the range $[10,40]\mathrm{\text{Hz}}$.

A Signal from a Calving Event

A calving event is a consequence of the propagation of fractures, or crevasses, in response to stresses, which isolate ice blocks from the main glacier mass away from the terminus. While fractures are generated and propagated entirely in response to unbalanced stresses at sub-aerial and/or sub-aqueous ice cliffs, calving is controlled by glacier margin geometry and ice rheology (Benn et al. 2007, Colgan et al. 2016). Seismic monitoring of calving activity, which generates energy across a broad frequency range with signals with low‐amplitude onsets, followed by higher‐frequency events followed by lower‐frequency narrow‐band codas (Richardson et al. 2010).

File 1000 has a conspicuous calving event, which appears in the spectrogram of geophone 7 as a $\sim 10\mathrm{\text{s}}$ band with most of its energy within the range $[10,40]\mathrm{\text{Hz}}$, Figure 13. That main band is preceded and followed by several bands of lower amplitude that can be due to wind or smaller mass falls. A closer look at the spectral content can be achieved by resorting to the multitaper approach.

The calving event appears conspicuously at all 13 geophones. Figure 14 shows a relative clustering of the spectral lines from the multitaper F-test $\le 30\mathrm{\text{Hz}}$. There are 97 F-test spectral lines with cut-off values $\ge 99\%$, which can be further subdivided into quantiles to reveal that 24 of those lines fall in the top tier of $99\%$, most of them clustered at $\le 30\mathrm{\text{Hz}}$, i.e., falling in the first cluster of lines seen in .

Figure 14
Panel A shows the spectral F-lines of file 1001 with cut-off values $\ge 99\%$, clustering at $\le 28\mathrm{\text{Hz}}$. Panel B shows the spectral F-lines after band-pass filtering with corners at $[5,25]\mathrm{\text{Hz}}$.

The energy is fairly evenly distributed along the entire frequency range so the overall shape of the signal remains recognizable after band-pass filtering with several sliding spectral windows: $([10,30],[44,50],[70,85],[88,98])\mathrm{\text{Hz}}$. The application of a band-pass filter with corner frequencies $[10,25]\mathrm{\text{Hz}}$ yielded the best result of all, indicating the clustered spectral lines may carry the most relevant signal information, a zoomed view of them is in Panel B of Figure 14. The reshaped multi-tape spectrum on the $\ge 99\%$ F-test spectral lines confirms that the main spectral energy lies in the range $[10,30]\mathrm{\text{Hz}}$, Figure 15.

The $[10,30]\mathrm{\text{Hz}}$ signal from the calving event lasts the entire trace duration $65\mathrm{\text{s}}$ as shown in Figure 16. Albeit we do not have a visual confirmation of that event we can speculate based on the Literature (Bartholomaus et al. 2012, Qamar 1988) that the event onset lies at ${\mathrm{\text{t}}}_0\gtrsim 0.5\mathrm{\text{s}}$, followed by a detachment or crumbing phase, the interaction of the main falling mass with the water, ending with some minor activity.

Figure 15
Multitaper spectrum of file 1001 reshaped to the spectral F-lines with cut-off values $\ge 99\%$. Note also the effect of notching the influence of the power inverter at $\approx 60\mathrm{\text{Hz}}$.

Figure 16
A calving event recorded at geophone 7 with a full trace duration. The event onset is at ${\mathrm{\text{t}}}_0$, followed by a detachment or crumbing phase ${\mathrm{\text{t}}}_1$. The fall of the main mass with the water is seen at ${\mathrm{\text{t}}}_2$, followed by some minor activity at ${\mathrm{\text{t}}}_3$.

$t\approx [7,37]\mathrm{\text{s}}$ and at $t\approx [37,45]\mathrm{\text{s}}$. That is followed by more at $t\approx [45,55]\mathrm{\text{s}}$.

Ship Signal

File 1700 was collected under a gentle breeze, wind force 3 on the Beaufort Scale, with gusts reaching $4\frac{m}{s}$ from SE recorded in the hour the file was recorded. There was an anchored ship shown with the letter S in Figure 9. Ship’s signal appears in the spectrogram of geophone 7 as a series of energy blobs due to the ship’s generator that runs in $1800\mathrm{\text{rpm}}$ ², see Figure 17. We choose not to notch the $60.62\mathrm{\text{Hz}}$ due to the AC-DC converter, showing it and the ship as well as their even harmonics.

The multitaper analysis of geophone 7 shows strong spectral lines from the F-test at 29.5 and $30.0\mathrm{\text{Hz}}$ due to the ship. Those two spectral lines conspicuously show in the reshaped PSD, $1000\times$ above the average energy, as seen in Figure 18. We can both band-pass in $[25,35]\mathrm{\text{Hz}}$ as well as notch the data $2\mathrm{\text{Hz}}$ around $f=30\mathrm{\text{Hz}}$ to obtain the signal from the ship, as well as a data version without the presence of the ship, Figure 19.

Figure 17
Spectrogram of geophone 7 of file 1700 showing the ship’s and AC-DC converter’s harmonic lines and their respective multiples.

Figure 18
The PSD of file 1700 shown in the range of $[25,35]\mathrm{\text{Hz}}$. The two peaks are due to the ship’s generator anchored at point S in Figure 9.

Figure 19
Trace of geophone 7 of file 1700. Panel A shows the ship’s signature after band-pass filtering in $[25,35]\mathrm{\text{Hz}}$. Panel B shows the same trace with the ship notched, i.e., without the ship.

Calving Events Localization

The KGI gather is suitable for beamforming as the coherent signals can be separated from surrounding uncorrelated noise, and because of the different onset times at each geophone of the 2-D gather. Beamforming corrects that time delay at each trace which depends on BAZ and slowness of a plane wave, to estimate the correct combination of BAZ and slowness (Rost & Thomas 2002). We perform beamforming in the frequency domain using FK analysis, where the best-fitting BAZ and slowness of a plane wave are estimated through a phase shift.

There are a couple of limitations inherent to the KGI field setup we need to be aware of: (i) The gather aperture $a$ imposes an upper limit of measurable wavelength is $\lambda \lesssim a$; (ii) The distances between geophones also define the position of side lobes of the ARF, equation(11), thus the largest wavenumber that can be resolved (Bormann 2013). Another limitation is the plane wave assumption, which may not hold as our sources, see below, are relatively close to the gather. While the aperture-related limitations cannot be overcome, the latter can be dealt with using spatial mapping by multi-array beamforming, based on the estimation of the cross-spectral matrix (Hayashi et al. 2022). Due to the small aperture $a$ we use short sliding windows along the seismograms where both the slowness and BAZ are to be estimated.

Geophone locations were converted to a local cartesian coordinate system with its center at the gather barycenter at $(429970,$ $3116132.5)$, UTM zone 21. We have set a square slowness grid of $3\times 3{\mathrm{\text{km}}}^2$ centered at the gather and a sliding window of $1\mathrm{\text{s}}$. We concentrate here on two events that originated in Ajax and Krak glaciers, refer to Figure 9.

The seismogram of file 1550 has a clear calving event within the time window $\delta t=[20,30]\mathrm{\text{s}}$, together with wind-related events, Figure 20. Records at EACF of wind speed revealed near gale wind, force 6 on the Beaufort Scale, with gusts reaching $15\frac{m}{s}$ from SE, during the hour where file 1550 was recorded. We use FK beamforming to obtain the polar plot of Figure 21, indicating the main energy comes from ${160}^{\circ }$ with the slowness of $u=0.9\frac{s}{km}$, or an apparent velocity of $v=1\frac{km}{s}$. In that plot, the relative power is summed and plotted in gridded bins, which are defined by the BAZ and slowness of the time window. The calving event probably originated in Krak glacier some $3000\mathrm{\text{m}}$ away, refer to Figure 9.

Figure 20
Seismogram of file 1550 for $\ge 10\mathrm{\text{s}}$ showing a calving event in $\delta t=[20,30]\mathrm{\text{s}}$ followed by wind-related events at $t>40\mathrm{\text{s}}$. Refer to Figure 9 for geophone positions.

Figure 21
Polar plot of event within time window $\delta t_w=[20,30]\mathrm{\text{s}}$ in file 1550. In this and the following polar plots, the BAZ is counted clockwise from N, the slowness is shown along the radial distance, and the color scale corresponds to the relative power.

The seismogram of file 1001 again shows a few events more or less entangled within $[15,25]\mathrm{\text{s}}$, Figure 22. Records at EACF of wind speed revealed NE gusts of $11\frac{m}{s}$ during the hour where file 1001 was recorded. We select a time window $\delta t=[20,23]\mathrm{\text{s}}$ to obtain the polar plot of Figure 23. The main energy comes from ${[331,350]}^{\circ }$ with slowness of $u=[1.0,2.3]\frac{s}{km}$, or an apparent velocity of $v=[0.5,1]\frac{km}{s}$. The sum of the relative power of this event is marginally less than of the corresponding for file 2372. The calving event probably originated in Ajax glacier some $1700\mathrm{\text{m}}$ away, refer to Figure 9.

Figure 22
Seismogram of file 1001 for $t\le 30\mathrm{\text{s}}$. Refer to Figure 9 for geophone positions.

Figure 23
Polar plot of event within time window $\delta t_w=[20,23]\mathrm{\text{s}}$ in file 1001.

Conclusions

We have analyzed in this work some seismic signals produced by natural and anthropogenic sources at two in two sites $>2500\mathrm{\text{km}}$ far apart in Antarctica: 84S and 2-D at KGI. The signals were analyzed both in the time domain and mainly in the frequency domain. We have used both the conventional Fourier analysis and the multitaper approaches, exploring in the latter the robustness in dealing with bias and variance, a great source of leakage in the conventional approach. In addition, there is the possibility of statistically perusing the periodic components of the data through the F-test, allowing one to show unequivocally the relative contribution of the spectral energy across the entire frequency range. The F-test and the PSD shaped with the spectral lines having F-test values above a confidence cut-off of $99\%$ revealed signal spectral contents that would not be seen clearly in the conventional approach.

At 84S we assume the main contribution originates from the vibrations on the top fittings on the C-I, four wind turbines, and an AWS, transmitted to the module structure. In a period of strong breeze, wind force 6 on the Beaufort Scale, the seismic energy was evenly distributed in the range of $[5,800]\mathrm{\text{Hz}}$, with two bands at 200 and $400\mathrm{\text{Hz}}$ throughout the time window. It is difficult to explain those but they may express modes of vibrations of the top fittings on the C-I. Notwithstanding this evenness in the energy distribution a low-frequency version of the signal, $[5,45]\mathrm{\text{Hz}}$, shows a frequency modulation in the data, which may express the module’s vibration only.

The wind-generated signals at KGI have amplitudes $250\times$ of those at 84S, due to the prevailing force 10 storm conditions. We observed repeating resonant signal bands in $\sim 5\mathrm{\text{s}}$ intervals across the time window. Probably those bands are due to a superposition of processes of wind coupling with features on the steep topography. Those features include loose and fixed rock and the box and its guy cables that protected the equipment from the elements. The energy distributes along the whole frequency range, but it is mostly concentrated in the range $[10,30]\mathrm{\text{Hz}}$. The wind activity comes as conspicuous bursts in the seismogram with a characteristic S-shape due to the relatively lower wind speed as compared to the rock velocities.

The calving events analyzed in this work generate seismic events with an energy distribution concentrated, as revealed by the clustering of spectral lines at $\le 30\mathrm{\text{Hz}}$. Nevertheless, they still display their energy distributed in $[5,100]\mathrm{\text{Hz}}$. We can replicate signal shape fairly accurately using $\simeq 10\mathrm{\text{Hz}}$ sliding spectral windows along the entire frequency range. Severe gales/storms generate seismic signals due to the coupling of the wind with the ground and other above-ground obstacles. Likewise, calving events energy is distributed through the entire frequency range, but with a clear concentration toward lower frequencies, $[10,30]\mathrm{\text{Hz}}$. The wind-generated seismic signals were present in most of the data analyzed, more or less intermingled with the calving events. An anchored ship some $2500\mathrm{\text{m}}$ to the W of gather G, generated two strong spectral lines at 29.5 and $30.0\mathrm{\text{Hz}}$.

We analyzed signals from two calving events with the beamforming technique to localize the sources as well as to estimate the slowness. We estimated wave slowness figures around $u=[1.0,2.3]\frac{s}{km}$, or apparent velocities $v=[0.5,1]\frac{km}{s}$. Some inaccuracy is expected on the higher end of the slowness range as one of the glaciers may be too close to meet the required plane-wave criterion adequately.

• 1
  Three people ran the experiment: Francisco Aquino and Isaias Thoen from UFRGS and Marcelo Arevalo. None of the present paper’s authors were in the field during data acquisition.
• 2
  The ship’s engine operates in $600\mathrm{\text{rpm}}$, personal communication.

ACKNOWLEDGMENTS

This work was fully supported by the Brazilian Antarctic Program (PROANTAR), through Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES). The two main sources come from the INCT da Criosfera (CAPES Proj. 88887.136384/2017-00) and PROANTAR/CNPq (Proj. 442755/2018-0).

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Publication Dates

• Publication in this collection
  22 July 2024
• Date of issue
  2024

History

• Received
  7 July 2023
• Accepted
  24 Nov 2023