Markov Chain Monte Carlo inversion of temperature and salinity structure of an internal solitary wave packet from marine seismic data

Abstract

Marine seismic reflection technique is used to observe the strong ocean dynamic process of nonlinear internal solitary waves (ISWs or solitons) in the near‐surface water. Analysis of ISWs is problematical because of their transient nature and limitations of classical physical oceanography methods. This work explores a Markov Chain Monte Carlo (MCMC) approach to recover the temperature and salinity of ISW field using the seismic reflectivity data and in situ hydrographic data. The MCMC approach is designed to directly sample the posterior probability distributions of temperature and salinity which are the solutions of the system under investigation. The principle improvement is the capability of incorporating uncertainties in observations and prior models which then provide quantified uncertainties in the output model parameters. We tested the MCMC approach on two acoustic reflectivity data sets one synthesized from a CTD cast and the other derived from multichannel seismic reflections. This method finds the solutions faithfully within the significantly narrowed confidence intervals from the provided priors. Combined with a low frequency initial model interpreted from seismic horizons of ISWs, the MCMC method is used to compute the finescale temperature, salinity, acoustic velocity, and density of ISW field. The statistically derived results are equivalent to the conventional linearized inversion method. However, the former provides us the quantified uncertainties of the temperature and salinity along the whole section whilst the latter does not. These results are the first time ISWs have been mapped with sufficient detail for further analysis of their dynamic properties.

A Locally Generated High‐Mode Nonlinear Internal Wave Detected on the Shelf of the Northern South China Sea From Marine Seismic Observations

“…The acoustic impedance contrasts derived from two concurrent XBTs correspond well with the seismic reflectors (Figure a) which is calculated assuming an empirical T‐S relationship (Tang et al, ). To relate the seismic image to the water properties, we assume that these undulating reflectors are the water‐layer interfaces that are a proxy for the isothermals or isopycnals of the water column (Ruddick et al, ; Tang et al, ). From the seismic image, at least three types of internal waves can be identified as follows: (1) the ubiquitous background waves with amplitudes less than 20 m and wavelengths of ∼1 km; (2) the tide‐like or bore‐like waves with long wavelength fluctuations of ∼10 km and amplitudes greater than 50 m; and (3) the occasional nonlinear waves with amplitudes greater than 30 m and wavelengths of ∼1–2 km (Figures b and c).…”

“…The first step consists of recovering the “full” acoustic impedance field ( ) by adding the high‐frequency component impedance from seismic data ( , >15 Hz) and the low‐frequency component impedance from hydrographic data ( , <15 Hz; Biescas et al, ): where is the reflectivity (Figure ) at depth and is the impedance at depth . Figure shows the how is derived and the result is compared to acquired at 72.5 km along the section (Figure ) which is calculated assuming an empirical T‐S relationship from a neural network (Tang et al, ). The second step involves searching the T/S pairs following the principle of minimization of the impedance difference: …”

“…Figure shows the how is derived and the result is compared to acquired at 72.5 km along the section (Figure ) which is calculated assuming an empirical T‐S relationship from a neural network (Tang et al, ). The second step involves searching the T/S pairs following the principle of minimization of the impedance difference: where is the salinity associated with at each given pressure through the nonlinear T‐S relationship constructed using the neural network ( ; Tang et al, ) and and are the equations of state of seawater for the in situ density and sound speed, respectively (Roquet et al, ). Figure shows the comparisons between the inverted results and the in situ XBT (eXpendable Bathy Thermographs) measurements at 102.5 km along the section.…”

“…where R h ð Þ is the reflectivity (Figure 3) at depth h and Z 0 is the impedance at depth h 0 . Figure 5 shows the how Z inv is derived and the result is compared to Z xbt acquired at 72.5 km along the section (Figure 2) which is calculated assuming an empirical T-S relationship from a neural network (Tang et al, 2016). The second step involves searching the T/S pairs following the principle of minimization of the impedance difference:…”

“…The conventional marine multichannel seismic (MCS) imaging technique used for studying the Earth's lithospheric structures is a preferential approach that has been proven to be suitable for detecting NIWs (Tang et al, 2014(Tang et al, , 2015(Tang et al, , 2016. Seismic oceanography (SO) was first proposed by Holbrook et al (2003) and has been widely employed to investigate a variety of oceanic phenomena including eddies (Biescas et al, 2008;Pinheiro et al, 2010), currents (Tsuji et al, 2005), internal waves (Holbrook & Fer, 2005), staircases (Biescas et al, 2010;Fer et al, 2010), Kelvin-Helmholtz (KH) instability , and turbulence (Holbrook et al, 2013;Sheen et al, 2009).…”