Geophysical research Letters
Supporting Information for
Submarine permafrost depth using ambient seismic noise
Overduin, P. P.1, Haberland, C.2, Ryberg, T.2, Ohrnberger, M.3, Kneier, F.1, Jacobi, T.3,
Grigoriev, M. N.4
1.
Periglacial Department, Alfred Wegener Institute Helmholtz-Center for Polar and Marine Research,
Potsdam, Germany.
2.
GFZ German Research Centre for Geosciences, Potsdam, Germany.
3.
Institute of Earth and Environmental Sciences, University of Potsdam, Potsdam, Germany.
4.
Siberian Branch-Russian Academy of Sciences, Mel’nikov Permafrost Institute, Yakutsk, Russia.
Contents of this file
Text S1
Figures S1 to S5
Introduction
Supporting information includes a description of instrument design, an explanation of the
data analysis and details on the derivation of shear wave velocity in the unfrozen
sediment layer.
1
Text S1.
Instrumentation
The underwater recording equipment consisted of a low-power digital recorder, a
standard short-period (4.5 Hz) 3-component geophone, and a battery pack (8x 1.5V Dcells) allowing for a deployment period of up to 40 days (Figure S1). These components
were enclosed in a watertight cylindrical container (diameter 15 cm, length 35 cm, 9 kg)
safe for operation down to 100m water depth (Figure 1a). The container was mounted
on a metal grid of 1 by 1m which was lowered to the seabed by a line from a boat and
connected to an anchor (sand-filled bag) and a buoy. The heart of the recorder was a
24-bit A/D converter continuously recording at 200 samples per second (sps). Digital
data was stored on a 16 GB SD card. The metal grid assured the approximately upright
position of the instrument (and the correct leveling of the sensors) on the sea floor.
However, some tilting could not be ruled out and the sensor was not automatically
leveled by a gimbal system. To correct for a possible tilt-influence on the 4.5 Hz sensors
(particularly of the horizontal components) we imposed a calibrating signal to the
geophones every 24 h, calculated the response function [Rodgers et al., 1995], and
corrected the time series using a restitution filter [Scherbaum, 1996]. This approach
proved to be capable of accounting for time-varying transfer functions due to tilting of the
recorders by varying water currents, storms, etc. Generally, we observed only minor
temporal changes in the tilt of the sensors, with the exception of a few stations for which
we observed small, but abrupt changes in the eigen-frequencies and damping factors of
the sensors possibly due to a change of the grid position.
Synthetic modelling
Figure S2 shows the results of our modelling, indicating the main low frequency H/V
peak associated with the unfrozen sediment overlying the frozen layer, clearly separated
from several higher frequency peaks which represent higher modes and water column
reverberations. Peak frequencies determined from model results (grey vertical lines)
containing the full wave field response and the λ/4 calculations (red lines) for pure
vertical incident SH-reverberations in the unfrozen sediment layer show a systematically
varying offset of not more than 20% which allows use of the λ/4 estimate as a first order
proxy measure of sediment thickness. A decrease in the thickness of the unfrozen layer
from 30 to 2 m beneath a constant water depth of 10 m results in a change in peak H/V
frequency from approximately 1.5 to 20 Hz.
Ambient noise analysis
To derive the actual thickness of the unfrozen, unconsolidated soft sediment layer
above the permafrost zone, the H/V method provides peak frequency values. With wave
propagation properties of that soft sediment layer, namely its shear wave velocity, these
frequencies can be used to estimate the thickness of the unfrozen layer. The data
analysis follows mainly the procedure of Bensen et al. [2007]. The originally continuous
data (vertical components) were split into one daily slices. After whitening the spectra,
the data was one-bit normalized, cross-correlations of station pairs were calculated in
the frequency domain and subsequently stacked. The correlation function, defined for
positive and negative correlation times, represents seismic waves traveling from station
1 to station 2 and vice-versa. The functions are generally dominated by surface or
interface waves.
Figure S3 shows the band-passed result of the cross correlations. The coherent
signals have a dominant signal period of 1.5 s. They represent interface waves probing
the upper part of the permafrost layer. The velocity of these waves is about 1.3 km/s.
2
Even given the widely distributed (in depth) sensitivity of surface/interface waves
(Scholte or interface waves), this velocity can be used to get a rough estimate of the
shear wave velocity in the permafrost layer. Thus we estimated the corresponding shear
wave velocity to be 1.5 km/s, assuming that V is approximately 0.85 Vs.
Interface wave dispersion analysis
To estimate the shear wave velocity in the unconsolidated soft sediment layer
above the permafrost zone we looked at the dispersion curves of interface waves in the
cross correlation functions of vertical component data. Several station pairs showed
interface wave arrivals with a well-defined dispersion (some red traces between 200 and
600 m offset in Fig. S3). For the analysis of wave dispersion, the technique of frequencytime analysis of Dziewonsky et al. [1969] was used. Fig. S4 shows an example of the
dispersion curve analysis. Between 1.5 and 5 Hz signal frequency, a highly dispersed
interface wave can be seen. A non-uniform distribution of seismic background sources
led to the asymmetric (amplitudes) recovery of the cross correlation function. The
corresponding travel times of both interface waves (station 1 to station 2 and vice-versa)
are essentially the same.
The group velocity for higher frequencies approaches values of ~100m/s. Interface
waves at these frequencies propagate only in the uppermost layer, i.e. the unfrozen, soft
sediment layer. There is no simple direct conversion formula from group velocity
dispersion information to material velocities in the subsurface. However, for the high
frequency limit of the dispersion curve, the group velocities can be related to the shear
wave velocity of the shallowest layer using a simple factor. The factor depends slightly
(few percent) on the Vp/Vs ratio of the medium. Here we used a value of 0.85 as a proxy
conversion factor and thus estimated the shear wave velocity in the uppermost marine
layer to be around ~120 m/s, which is comparable to other observations (Stoll, 1977;
Dong and Hovem, 2011; Vanneste et al., 2011). The dispersion analysis of other station
pairs resulted in similar (±10%) group velocities. Finally we used the shear wave velocity
of 120 ±10% m/s as a regional value to convert the H/V peak frequencies to layer
thicknesses.
References
Bensen, G. D., M. H. Ritzwoller, M. P. Barmin, A. L. Levshin, F. Lin, M. P. Moschetti, N. M. Shapiro,
and Y. Yang (2007), Processing seismic ambient noise data to obtain reliable broad-band surface
wave dispersion measurements, Geophys. J. Int., 169, 1239–1260, 10.111/j.1365246X.2007.03374.x.
Dziewonski, A., S. Bloch, and M. Landisman, M. (1969), A technique for the analysis of transient
seismic signals, Bulletin of the Seismological Society of America, 59(1), 27-444.
Rodgers, P., A. Martin, M. Robertson, M. Hsu, and D. Harris (1995), Signal-Coil Calibration of
Electromagnetic Seismometers, Bull. Seis. Soc. Am., 85(3), 845 – 850.
Scherbaum, F. (1996), Of poles and zeros: Fundamentals of digital seismology. Kluwer Academic
Publishers, Dordrecht, The Netherlands, 257 pp.
Vanneste, M., Ch. Madshus, V. L. Socco, M. Maraschini, P. M. Sparrevik, H. Westerdahl, K.
Duffaut, E. Skomedal, and T. I. Bjørnar (2011), On the use of the Norwegian Geotechnical
3
Institute's prototype seabed-coupled shear wave vibrator for shallow soil characterization ¬ I.
Acquisition and processing of multimodal surface waves. Geophys. J. Int. 185, 221¬236 doi:
10.1111/j.1365-246X.2011.04960.x
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Figure S1. a) photograph of sensors on deck ready for deployment, including watertight
aluminum casing, metal grid for orientation, sand-sacks as anchors and buoys for
recovery; b) schematic of a deployed sensor.
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Figure S2. Modelled H/V intensity (grey lines mark the f0 peaks) vs. frequency for (a)
constant thickness of the unfrozen sediment layer (12 m) and varying water depths, and
(b) varying unfrozen sediment layer thicknesses and 10 m water depth. Red lines
indicate the λ/4 resonance frequency.
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Figure S3. Record section of the cross correlation data of all station pairs band-passed
between 0.5 and 5 Hz. The coherent event is dominated by the signal of ~1.5 s period.
The group velocity of that phase is ~1.3 km/s. Its dominant period corresponds to
surface waves probing the permafrost layer. Black traces are land-land station
correlations, blue are land-ocean and red are ocean-ocean station correlations.
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Figure S4. Positive and negative part of the cross correlation function for station pair
A3R-A44 (inter-station distance 288 m), right panel. The dispersion curve analysis is in
the left panel (red colors indicate high, blue colors low amplitudes). Traces are
normalized for frequency band. Note the presence of two surface wave phases, with
group velocities at higher frequencies (>5 Hz) going down to ~100 m/s.
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Figure S5. H/V ratios for the stations along profile BB’ (see Fig. 1b and 3a for profile and
station locations).
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