Final discussion

The previous chapters have shown that bubble-releasing seeps occur at different oceanographic and plate-tectonic settings, at different seafloor morphologies, at different water depths, in or outside of the gas-hydrate stability zone. Furthermore, bubble-releasing seeps are often associated with various kinds of chemosynthetic communities and authigenic methane-derived carbonates. Within this chapter an integration and comparison is made of the obtained results and of published data from other seep sites around the world which occur in similar or different geological settings. The comparison and integration allows a better understanding of the controls and the manifestations associated with bubble-releasing seeps

Extension of Information Geometry to Non-statistical Systems: Some Examples

Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a statistical manifold. An example of the former is the description of the Bose gas in the grand canonical ensemble. An example of the latter is the modeling of quantum systems with density matrices. Conditional expectations in the quantum context are reviewed. The border problem is discussed: through conditioning the model point shifts to the border of the differentiable manifold.Comment: 8 pages, to be published in the proceedings of GSI2015, Lecture Notes in Computer Science, Springe

Quantum and Fisher Information from the Husimi and Related Distributions

The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262 [1996]). In the former work, a metric (the Monge one, specifically) over generalized Husimi distributions was employed to define a distance between two arbitrary density matrices. In the Petz-Sudar work (completing a program of Chentsov), the quantum analogue of the (classically unique) Fisher information (montone) metric of a probability simplex was extended to define an uncountable infinitude of Riemannian (also monotone) metrics on the set of positive definite density matrices. We pose here the questions of what is the specific/unique Fisher information metric for the (classically-defined) Husimi distributions and how does it relate to the infinitude of (quantum) metrics over the density matrices of Petz and Sudar? We find a highly proximate (small relative entropy) relationship between the probability distribution (the quantum Jeffreys' prior) that yields quantum universal data compression, and that which (following Clarke and Barron) gives its classical counterpart. We also investigate the Fisher information metrics corresponding to the escort Husimi, positive-P and certain Gaussian probability distributions, as well as, in some sense, the discrete Wigner pseudoprobability. The comparative noninformativity of prior probability distributions -- recently studied by Srednicki (Phys. Rev. A 71, 052107 [2005]) -- formed by normalizing the volume elements of the various information metrics, is also discussed in our context.Comment: 27 pages, 10 figures, slight revisions, to appear in J. Math. Phy

The q-exponential family in statistical physics

The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the microcanonical ensemble belong to the q-exponential family.Comment: 18 pages, 4 figures, proceedings of SigmaPhi 200

The use of acoustic seafloor backscatter measurements for quantitative and qualitative characterization of methane seep areas

During the 2003 and 2004 cruises of the EC project CRIMEA almost 3000 active methane seeps were detected with an adapted scientific split-beam echosounder in the Dnepr paleo-delta area in the NW Black Sea (Naudts et al., in press). The seeps are widely, but not randomly, distributed over the transition zone between the continental shelf and slope, in water depths of 66 to 825 m. The highest concentration of seeps occurs on the shelf, in water depths of 80 to 95 m. Here, the location of the seeps is controlled by the underlying geology (filled channels) and seepage is characterized by the presence of pockmarks and high acoustic seafloor backscatter, visible on both multibeam and side-scan sonar data.Since seep detection during the CRIMEA cruises was performed independently but simultaneously with the multibeam and side-scan sonar recordings, these datasets possess a great potential for quantitative and qualitative analyses of acoustic seafloor backscatter in relation to the seep locations. Our analyses are further sustained by visual observations, high-resolution 5 kHz seismic data and sediment samples from gravity and multi-coring.For this study we selected an area of 37 km2 on the shelf.Within this area the normalized multibeam backscatter values ranges from -28.32 dB to 20.42 dB. After eliminating high-backscatter values caused by high topographic gradients, all seep positions within this area correspond to backscatter values of more than -2.89 dB and have a standard normal distribution. Furthermore, no seeps occur at locations characterized by the highest backscatter values. Within the area, 99.3 % of the seeps correspond to backscatter values ranging between -1.39 and 4.60 dB.These data indicate that actively bubbling seeps do not necessarily correspond to the highest backscatter values as would be expected; they rather surround the highbackscatter areas. This is also clear from visual observations in which bubbles are seen to emanate at the perimeter of white Beggiatoa mats. Since Beggiatoa mats are commonly associated with the precipitation of authigenic carbonates formed via AOM, these carbonates are very likely to be the cause of the higher backscatter values. Sediment samples and visual observation also indicated that areas corresponding to higher backscatter values are characterised by more shell material in the first 5-10 cm of the seabed.Also pockmarks are characterised by typical backscatter patterns. Better evolved, deeper, pockmarks are characterised by higher backscatter values and the seep activity is lower than at shallow pockmarks, which are often active bubbling. This could be explained by some sort of self-sealing of these seeps, as postulated by Hovland (2002).All these observations at the seafloor are clearly a result of the underlying geology where fluid migration is focussed to the sides of filled paleo-channels. The seismic data show the presence of a distinct “gas front” that locally domes up to the seafloor. These areas of gas front updoming on the shelf are characterised by seeps, higher backscatter values, Beggiatoa mats and pockmarks

Methane Fluxes from a High Intensity Seep Area west of Crimea, Black Sea

Methane seepage is a wide-spread phenomenon in the Black Sea with an increase in density and intensity west of the Crimea in the Paleo Dnepr area between 70 and 250m water depth. Within the EU funded project CRIMEA we studied the impact of high intensity seeps on the methane distribution in the water column and its possible transport into the atmosphere. Here we present data which allow flux calculations of free methane from an area of 1 by 1.23 miles between 80 and 95m water depth. Our calculations are based on direct and hydroacoustic flux measurements of single seeps or small-scaled seep areas (several m2); the spatial extrapolation of these fluxes use the very strong correlation between the bubble seep occurrence and a high backscattering seafloor; the temporal variability of bubble release was detected via the lander-based hydroacoustic system GasQuant.More than 1000 bubbling seep sites were identified during two cruises in 2003 and 2004 by hydroacoustic water column surveys. The hydroacoustic detection of bubbles uses the strong backscattering of the free gas phase caused by the great impedance difference of bubbles in water (equivalent to the detection of fish and their swim bladder). In echograms, bubble streams or even single bubbles can be detected, traced and used for special analyses such as bubble rising speed, bubble size and shrinking rates. Because of the flare-like appearance of bubble streams in echograms we call these features ’flares’.Parallel multi beam mapping allowed the detection of the seafloor morphology together with the spatial backscatter intensity of the seafloor. The combination of flare occurrences with high backscatter areas provided a very good correlation. Normalized, the backscatter ranged from -12.5 to 7.1 dB for an area of 4.23 km2. All seep positions plott in areas with more than -2.7 dB, which is almost the entire area of investigation (95.8 %). However, 75% of the flares occur within only 20.1% of the area, half of the flares occur in only 9.2% and 25% even occur in only 3.8% of the area with backscattering values above 2.4 dB. This correlation allows to predict and extrapolate active bubble seeps even without direct or hydroacoustic observations.One reason for the high backscattering seafloor are patches of carbonate cemented seafloor (formed via AOM) which typically occurs just below bright white Beggiatoa mats. In addition, high resolution seismic studies with a 5kHz sub-bottom profiler clearly show a shallow gas front in normally 3m sediment depth. In those areas where strong gas front reflectors dome up and reach the seafloor surface the backscatter values and flare density are the highest. This clearly shows that the bubbles released are fed from shallow gas which also might have an impact on the physical properties of the seafloor and its backscatter behaviour. Seeps in lower or even very low backscatter areas possibly indicate a rather young or weak activity which did not (so far) cause a remarkable carbonate cementation detectable during multi beam surveys.However, the backscatter data are the base for our spatial flux calculations which use direct bubble trapping to distinguish the flux rate from one single seep hole and hydroacoustic methods for small seep areas of several m2. Direct bubble flux measurements were performed with the submersible JAGO by trapping the bubbles with a funnel. Fluxes vary between 0.55 and 1.44 ml/s (or 1.98 to 5.18 l/h at in situ volume; or 0.24 to 0.64 mmol/s). Subsequent GC-based gas analyses onboard confirmed that the gas phase consists exclusively of methane. Visual observations by JAGO and towed camera systems showed bubble diameters between 1 and 15mm with typical sizes between 3 and 7mm. Together with bubble rising speeds of typically 25cm/s both attributes are in very good agreement with detailed hydroacoustic measurements using a dual frequency scientific echo sounder EK500 (120 and 38kHz). Flux estimat