Geophysical research Letters

Supporting Information for

Characterization of the sub-mesoscale energy cascade in the Alboran Sea thermocline from spectral analysis of high-resolution MCS data

V. Sallares1, J. F. Mojica1, B. Biescas2, D. Klaeschen3, E. Gràcia1

1Barcelona-CSI, Institute of Marine Sciences - CSIC, Barcelona, Spain, 2Istituto di Scienze Marine - CNR, Bologna, Italy, 3GEOMAR Helmholtz Centre for Marine Research, Kiel, Germany.

Contents of this file

Text S1 to S5Figures S1 to S7Tables S1 to S2

Introduction

This supporting information contains five text files describing respectively the characteristics of the MCS acquisition system, the lateral resolution of the MCS data, the synopticity of the MCS data, the methodology used to estimate the signal-to-noise ratio of the MCS data prior to reflector tracking, and the data used to calculate the local oceanographic variables used in the work. Additionally, there are six figures illustrating different aspects of the text files referred to above, which include the sound speed model used to depth-convert the MCS profiles, the band-pass filtered MCS data used to calculate S/N, the individual kx slope spectra for the two MCS profiles, the MCS images with the tracked reflectors superimposed, a map of the MCS lines superimposed with a geostrophic velocity map, and buoyancy vs. depth, Richardson number, Turner angle, and RMS current and shear velocity diagrams within the targeted depth range. Finally, we have also included two tables; one with the definition and values of the different parameters and variables used throughout the manuscript, and the second with the S/N values obtained in the different frequency bands.

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Text S1.MCS acquisition systems are composed of an acoustic source and an array of hydrophones, or streamer, towed behind the vessel, which record the signal that is reflected at the medium's acoustic impedance contrasts. In the case of IMPULS, the high-resolution source consisted of by eight air guns with a total volume of 4.75 liters that was towed at a depth of 2 m and worked at a pressure of 138 bars. The source’s peak frequency was 150-200 Hz. The streamer was a GeoEel solid state digital one by Geometrics, with 6 active sections of 50 meters each towed also at 2 m deep. Each active section was constituted by 8 channels (hydrophone groups), resulting in a total of 48 channels with a spacing of 6.25 m. The distance from the center of the source array to the first active section was 7 m. The sampling rate was 1 ms, and the acquisition window for each shot was 5 s. The shot interval was 15 m along IMPULS-2 profile and 25 m along IMPULS-3, giving a Common Mid Point (CMP) fold of 6 for IMPULS-2 and 10 for IMPULS-3.

Text S2.An important step towards the calculation of the slope spectra is to suppress the random noise from the data and concentrate the analysis in the frequency bands where signal is clear. This can be efficiently done by: (1) estimating the signal-to-noise ratio (S/N) in the different frequency bands, and (2) selecting and applying a band-pass frequency filter that maximizes the signal-to-noise ratio. To estimate S/N we have applied a cross-correlation-based analysis that consists of the following steps:

i) Band-pass filtering the data;ii) Calculate the cross-correlation (CC) between each seismic trace

and all its neighbors within a distance equal to the length of the shortest reflectors used in the spectral analysis, dCC=1,250 m. This is first done in the upper part of the profile (30-120 m), hence the section that we consider to contain the signal.

iii) Calculate the maximum value of the CC within a time window corresponding to the mean separation between contiguous reflectors, tCC =10 ms, for each couple of traces (MaxSigij);

iv) Calculate the average value of MaxSigij for each seismic trace along the whole profile (AvMaxSigi);

v) Repeat steps ii) to iv) for the bottom part of the profile (120-240 m), which we consider to be noise, to obtain AvMaxNoisei;

vi) Calculate the ratio S/Ni=AvMaxSigi/AvMaxNoisei for each seismic trace;

vii) Calculate the average value of S/Ni for all the seismic traces: < S/Ni>=S/N;

viii) Repeat steps i) to vii) for the next frequency band.

Text S3.The lateral resolution of MCS images is limited by the width of the first Fresnel zone, 2Rx≈(λd)1/2, where d is the source-target-source distance and λ

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is the source wavelength [Sheriff and Geldart, 1995]. Conventional MCS systems with peak frequencies at around 40 Hz have been previously used to perform spectral analysis of targets deeper than 250 m [Holbrook and Fer, 2005; Krahmann et al., 2009; Sheen et al., 2009], so that Rx>50 m. Optimal data processing and depth migration could potentially improve this resolution to a limit of ~λ (i.e., 38 m for a 40 Hz source), but for imperfectly processed data the improvement is actually lesser. Our target (i.e. the stratified thermocline) is located between 35 m and 120 m depth; whereas the peak frequency of the source is 150-200 Hz (λ≈7.5-10 m), so the nominal lateral resolution of the resulting seismic images, Rx, is 8-17 m (table S1). The vertical resolution Rz is given by the Rayleigh criterion of ~λ/4, so ~2 m in our case (table S1).

Text S4.A key difference between geological and oceanographic studies using MCS systems is that in the latter case the structures to be imaged move. This motion, which includes both displacement and oscillation, combined with that of the vessel, makes that the seismic images of the ocean are not synoptic. The water movement distorts the obtained images so that it can substantially modify their kx spectra if water velocity is significant compared to that of the seismic acquisition vessel (~2.5 m/s) [Klaeschen et al., 2009; Vsemirnova et al., 2009]. According to numerical simulations, the resulting effect is an increase of the the spectral slope when acquisition goes in the same direction as water displacement, and a decrease when the vessel moves in the opposite direction [Vsemirnova et al., 2009]. These are the trends observed at the smallest wavenumbers of the individual spectra of IMPULS-2 and IMPULS-3 profiles (kx<1-2x10-3 m-1 in fig. S3), which were acquired antiparallel and parallel to water movement, respectively (fig. S5). However, the resolution of the oceanographic model used in these simulations is of O(102 m), so it reproduces internal wave movements until kx≈2x10-3 m-1 only [Vsemirnova et al., 2009], but not between 2x10-3 m-1 and 10-1 m-1 (fig. 4 and fig. S3). Given that the group velocity of internal waves is limited by Nx, waves move slower as their x decrease (e.g. ~1 m/s to ~0.1 m/s for 1000 m- to 100 m-long IWs, respectively), so the effect on spectral slopes should reduce accordingly. On the other hand, the internal wave period must be longer than N-1≈724 ±210 s (table S1), whereas the time needed to image ~500-100 m of profile is ~4-10 times shorter. The similarity between the two individual spectra, including spectral slopes and scales of the slope changes (fig. S3), confirm that the effects of wave propagation and oscillation are insignificant above 2x10-3 m-1, so the images can be considered as quasi-synoptic at the scales analyzed.

Text S5.To calculate the local oceanographic variables shown in table S1 and figure S7, we have used two types of complementary data. The Coriolis parameter is fc=2sin, where =1.1606x10−5 s-1 is the rotation rate of the Earth and

is latitude. The buoyancy frequency, N (z )=(−gρ0

∂ρ( z)∂z )

12, where g is

gravitational acceleration, 0 is the average density between 30 m and 110

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is the density gradient with depth (fig. S7a), has been estimated using data from an XCTD deployed during the seismic acquisition (fig. 2a). The value of N in table S1 is the average of N(z) between 30 m and 110 m. The Root Mean Square (RMS) velocity, V, including the two components and the shear velocity corresponds to the average valueat the different depth ranges within the surveyed area. They have been estimated using Acoustic Doppler Current Profiler (ADCP) data acquired in the region during the SAGAS experiment in May-June 2010, which was averaged in 8 m depth bins (figs. S6d,e,f). Note that all the variables displayed in fig S7 are only indicative, and they have just been used to estimate an average within the studied depth range, because they are not simultaneous to the seismic acquisition. ΔV is the velocity fluctuation of V(z) with respect to the mean velocity between 30 m and 110 m; whereas the variance of the vertical shear of the horizontal flow used to calculate Ri, ∂V/∂z, is the the vertical gradient of V within the same depth range.

References.Sheriff, E.G. and L.P. Geldart (1995), Exploration Seismology (2nd ed.), Ed. Cambridge University Press, Cambridge, UK.

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Figure S1. (a) Detail of the transition between internal waves and turbulence possibly associated to shear instabilities as inferred from theory and numerical models (dashed line). Inset: Sketch of the power spectral density of kinetic energy as a function of the horizontal wavenumber (kx) as indicated by observations (solid line) [e.g. Ferrari and Wunsch, 2009]. Energy is injected by the Coriolis force (A), climatological forcing and tides (B) at the production range and then it cascades towards smaller scales (C) until the dissipation range. (b) Conceptual diagram of energy flow for the ocean circulation [Müller et al., 2005]. Possible routes: 1. Inertia-gravity-wave route. Governing processes: 1A. Storms, tides and currents generating inertial waves, 1B. Shear instability, internal wave breaking. 2. The instability route. Governing processes: 2A. Baroclinic instability, 2B. Unbalanced instability, 2C. Isotropic turbulence and dissipation. 3. The boundary route. Governing processes: 3A. Dissipation in boundary layers, 3B.

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Isotropic turbulence and dissipation. The grey rectangle shows the observational gap (OG) between 10-3 m and 10-1 m-1.

Figure S2. Processed and depth-converted HR-MCS images along IMPULS-3 profile, superimposed with the (a) temperature and (b) sound speed maps derived from coincident XBTs. See fig. 2a for XBT locations.

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Figure S3. Band-pass filtered data corresponding to the IMPULS-3 HR-MCS profile. The corresponding frequency bands are 10-40 Hz (a), 40-80 Hz (b), 80-120 Hz (c), 120-160 Hz (d), 160-200 Hz (e), 200-240 Hz (f), 240-280 Hz (g), 40-240 Hz (h).

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Figure S4. Average horizontal spectrum of the tracked reflectors vertical displacement (Rx) scaled by the local buoyancy frequency at the reflector depth (N0/N) to eliminate stratification effects, and multiplied by (2πkx)2 to enhance slope variations (black line) obtained separately for the two analyzed profiles (solid line) and their corresponding 95% confidence interval (2σ) (shaded area) for IMPULS-2 (a) and IMPULS-3 (b). The vertical dashed lines indicate the changes of slope in both profiles, which occur at the same scales as in the combined spectrum. The colored lines follow the same code as in fig. 4. The dashed black line follows the original, unfiltered part of the spectra in the region affected by harmonic noise arising from repeated shooting. This is eliminated by applying a stop band of 0.024 to 0.019 Hz (IMPULS-2) and 0.027 to 0.021 Hz (IMPULS-3). See text for details.

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Figure S5. Processed and depth-converted HR-MCS images along profiles IMPULS-3 (a) and IMPULS-2 (b), with the tracked reflectors used in the spectral analysis superimposed (blue lines). The depth range of the tracked reflectors is 30-100 m. The two insets are zooms over the area encompassed by the dashed rectangles.

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Figure S6. Location of the IMPULS HR-MCS lines 1 to 4 indicating the direction of seismic acquisition (black arrows), superimposed with a geostrophic velocity map of the surveyed area at the time of the acquisition (May 17th, 2010, at 00:00AM) (red arrows). Note that the acquisition direction is approximately antiparallel to geostrophic velocity in IMPULS-2, whereas it is parallel in IMPULS-3. Geostrophic velocity data are taken from the Aviso database (http://www.aviso.altimetry.fr/duacs/).

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Figure S7. (a) Buoyancy frequency vs. depth diagram calculated with the temperature and salinity values obtained with an XCTD probe within the surveyed area (see XCTD location in fig 2a). (b) Richardson number for the studied depth range. The velocity measurements are not simultaneous; they were obtained with an ADCP during the SAGAS-2010 survey and averaged within 8 m depth bins. (c) Turner angle calculated using the same ADCP data. (d) Westward component of the RMS current velocity within the surveyed area using the same ADCP data. (e) Same as (d) but for the Northward component of the RMS current velocity. (f) Same as (e) but for the shear velocity. See additional details on the calculation in table S1 and supplementary text S5.

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Variable

Value Description

fc 1.36 • 10-5 s-1 Coriolis frequency at 36ºNN 1.38 • 10-3 + 5.6 • 10-4 s-

1Average local buoyancy frequency of the surveyed area between 30 m and 110 m

N0 8.33 x 10-4 s-1 Mean buoyancy frequency of the oceanu 0.2 + 0.01 m s-1 RMS velocity current (East-West) between 30 m

and 110 mv -0.07 + 0.01 m s-1 RMS velocity current (North-South) between 30 m

and 110 mV 0.2 + 0.01 ms-1 RMS velocity current (V2 = u2+v2) between 30 m

and 110 mΔV 0.02 + 0.002 ms-1 Mean variation of RMS velocity between 20 m and

120 mlc 9.172 m Horizontal scale of the Coriolis frequency

(lc=2π ΔV/ fc)lN 91 + 25 m Horizontal buoyancy scale (lN=2π ΔV/N)F 150 - 200 Hz Peak frequency of the HR-MCS source used in the

IMPULS-2006 experimentRx 8 - 17 m Lateral resolution of the HR-MCS system between

30 m and 110 m depth (2Rx=(λd)1/2)Rz 2 m Vertical resolution of the HR-MCS system (Rz=λ/4)

∂V/∂z 3.2 • 10-3 s-1 Variance of the vertical shear of the horizontal flow of the study zone between 30 m and 110 m.

Ri 0.2 + 0.1 Richardson number (Ri=N2/|∂V/∂z|2) of the study zone between 30 m and 110 m

ls 33 m Smallest scale of the internal waves-turbulence transition subrange

ln 15 m Scale of incidence of random noiselo 2 + 1 m Ozmidov length scale (lo=ε1/2 N-3/2)

Table S1. Description and values of the different oceanographic variables and parameters used in this work and referred to in the text. See also supplementary text S5 for details on the calculation of the different parameters and variables.

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Frequency band (Hz) AvMaxSig (·10-5) AvMaxNoise (·10-5) S/N

10-40 0.7 0.5 1.4

40-80 16 1.6 10

80-120 7 0.7 10

120-160 3 0.35 8.5

160-200 2 0.07 28.5

200-240 0.8 0.02 40

240-280 <0.1 0.01 6.5

Table S2. Values of S/N obtained in the different frequency bands applying the analysis described in the Methods section to the seismic images shown in fig. S2. AvMaxSig and AvMaxNoise are the average signal level and average noise level, respectively, for each frequency band.

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