Detecting changes at the leading edge of an interface between oceanic water layers

Many physical phenomena in the ocean involve interactions between water masses of different temperatures and salinities at boundaries. Of particular interest is the characterisation of finescale structure at the marginal interaction zones of these boundaries, where the structure is either destroyed by mixing or formed by stratification. Using high-resolution seismic reflection imaging, we present observations of temporal changes at the leading edge of an interface between sub-thermocline layers in the Panama Basin. By studying time-lapse images of a seismic reflector between two water boundaries with subtle differences, we provide empirical constraints on how stratified layers evolve. The leading edge of this reflector, which is characterised by a gradual lateral decrease in vertical temperature contrast (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|\Delta T|$$\end{document}∣ΔT∣), increases in length over ~3 days coupled with an increase in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|\Delta T|$$\end{document}∣ΔT∣. A critical mixing state, in which turbulent diffusion is gradually replaced by double-diffusion as the dominant mixing process, is thus revealed.

layering is also more disturbed. The undulating reflections reveal how the stratification is differentially disturbed by the internal waves over the basin and over the ridge, indicating possible changes in the process of mixing along the profile. Excluding the effects of wind-driven mixing beneath the thermocline barrier in the eastern equatorial region (Sprintall & Cronin, 2001;Liu et al., 2016), a potential explanation for the change in reflectivity could be the upward emission and energy cascade of the internal tides generated over the shallower and rougher ridge topography, which is negatively correlated to the sub-thermocline stratification. The same phenomenon is also seen on SAP_C (not shown).

Supplementary Figure 2:
The CTD cast (JC112-016) acquired on 22 Dec 2014 during cruise JC113 (~52 days prior to the seismic acquisition during cruise JC114) shows the general water properties at the intersection of SAP_A and SAP_B (Figure 1 and Supplementary Figure 1). (a) Potential temperature-salinity (T-S) diagram that is used to identify the water masses of the whole water column, with the colour scale denoting the water depth. The identified water masses are: STUW -Subtropical Underwater; AAIW -Antarctic Intermediate Water; and NPDW -North Pacific Deep Water. The thickened part shows the depth range between 300 to 1400 m, with the blue dot at the mean target depth of the reflector at ~560 m. Grey contours: potential density, 0 , referenced to the surface. (b) Measured and estimated curves of potential temperature (°C, black), salinity (psu, blue), potential density 0 referenced to 0 dbar (kg/m 3 , grey), density ratio (red), acoustic speed (m/s, green), and reflectivity (×10 -3 , purple). Two red dashed lines mark the range of Due to the time dependency of the finescale structure of the water, it is not possible to directly relate this CTD profile to the seismic images since they are not coincident in time. However, the hydrographic data do reveal the fundamental properties and stratification of the water column in the Panama Basin. For example, the T-S diagram shows the principal water masses from shallow to deep: STUW, AAIW, and NPDW (Fiedler & Talley, 2006); and the ≈ 5 at 560 m depth favours a double-diffusive stratification (Radko et al., 2014a). Reflectivity is calculated form the hydrographic parameters (IOC et al., 2010). Figure 3: Event tracking and AVO amplitude picking on the raw unstacked seismic data of common mid-point (CMP) super-gathers (Sheriff & Geldart, 1995;Paramo & Holbrook, 2005). The tracked events using the value 0.8 of the cosine of instantaneous phases (right column, black contours) of the corresponding data (left column) around the depths of the target reflections (red dashed lines). The AVO responses are then picked from the tracked events (black dashed lines). Examples from four representative locations of (a) 10 km, (b) 50 km, (c) 51 km, and (d) 65 km along SAP_B are presented. (a, e) The region with high reflectivity and coherent phase. (b, f) The end with weak reflectivity and still trackable phase. (c, g) The weak reflectivity but untrackable, bifurcated phase. (d, h) Neither the seismic events nor the phase are identifiable far from the end of the target reflection.

Supplementary
AVO attributes are widely used to characterise physical properties across reflective boundaries in the solid Earth (Sheriff & Geldart, 1995). To date, the work by Paramo & Holbrook (2005) is the only study extending the AVO technique to quantify the temperature contrasts on seismic oceanography data. Here we improve this technique using an inversion procedure and apply it to a time-lapse seismic reflection to see the spatial-temporal temperature variations across a water sheet. Three steps are necessary to extract the AVO response (Methods): (1) true amplitude processing, (2) amplitude calibration, and (3) automatic amplitude picking. Four examples of event tracking are shown above. The contour of ( ) = 0.8 loses its lateral coherent at 51 km, where we define the tip of the reflector on raw unstacked CMP gathers. The trackable tips on CMP gathers are different than on the stacked seismic images (Figures 4 and 5) because of the enhanced signal-to-noise ratio on the stacked image. Figure 4: An example at 9 km on SAP_C showing the derivation of the temperature contrast and its uncertainty using a Markov Chain Monte Carlo (MCMC) scheme based on Bayesian statistical inference (Tarantola, 2005). (a) Distributions of the rejected (grey dots) and accepted samples (coloured dots, normalised probability density function (PDF) of the bivariate Gaussian distribution fit). (b, c) Marginal distributions of salinity and temperature. (d) AVO responses of the data (blue) and the prediction (red). The grey region is the 95% confidence interval of the fit. (e) Three runs of Markov chains with random initial starting models but showing the same convergence. The burn-in iterations (grey) are exaggerated in (f), showing the MCMC method has converged within 20 iterations. The contribution of salinity to the reflection coefficient is insignificant in the study region and hard to constrain, so we focus on the dominant temperature parameter as the primary cause of the observed reflectivity. Figure 5: Shipborne 75-kHz Acoustic Doppler Current Profilers (ADCP) data recorded on FS Sonne, which sailed ~9 km behind (~1 hour delay) the RRS James Cook that was acquiring the seismic data. (a) The time of ADCP track, which is enlarged in (b), starts from dark red and ended at blue. Red arrow: mean flow direction at 560 m depth. (c, d) Eastward and northward current components u and v, respectively. The colour time scale used in (a) is shown along the bottom of these plots, as well as the acquisition periods of SAP_A (green) and SAP_C (brown). (e, f) The current strength and current direction with respect to north. The ADCP data at the turns are removed (shaded region).

Supplementary
To evaluate the development, e.g., lengthening, erosion, or strengthening, of the time-lapse reflections; the lateral advection caused by water current needs to be compensated for. Hence the mean current during the seismic acquisition was derived from shipborne ADCP data.
The average current profile shown in Figure 1c is calculated from these ADCP data. It can be seen that the large variations of current in both strength and direction are mainly above 350 m (thermocline). And below this depth (sub-thermocline), the velocity is more stable (< 12 cm/s) and the direction is uniform at around 10° from north. The eastward velocity component is relatively small and its contribution is estimated in Supplementary Figure 6. Tsuchiya & Talley (1998) suggest that the water at the target depth is sourced by the NNE-ward current bringing well-stratified water with layers and sheets into the central Panama basin water over the saddle area of the central Carnegie Ridge to the south. The empirical parametrisation scheme for a double-diffusive system of salt fingering based on the modified four-thirds flux-law is used to infer the heat and salt fluxes across the interface (Turner, 1965;Schmitt, 1979;Shen, 1993;Radko et al., 2014b). Since ∆ is much better constrained than ∆ in our results, the parametrisation is modified using only ∆ to compute the buoyancy fluxes: where the notations are: , flux of temperature across an interface; , flux of salt; , buoyancy flux ratio of heat to salt ; , density ratio; and , heat expansion and salt contraction coefficients; , flux-law coefficient; , acceleration due to gravity; and , effective thermal diffusivity.