Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.

Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.

Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological Survey, are confronted with actual traverses to test their validity.

It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.

A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.

Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed. populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (similar to 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.

Can carbon surface oxidation shift the pore size distribution curve calculated from Ar, N(2) and CO(2) adsorption isotherms? Simulation results for a realistic carbon model

Using the virtual porous carbon model proposed by Harris et al, we study the effect of carbon surface oxidation on the pore size distribution (PSD) curve determined from simulated Ar, N(2) and CO(2) isotherms. It is assumed that surface oxidation is not destructive for the carbon skeleton, and that all pores are accessible for studied molecules (i.e., only the effect of the change of surface chemical composition is studied). The results obtained show two important things, i.e., oxidation of the carbon surface very slightly changes the absolute porosity (calculated from the geometric method of Bhattacharya and Gubbins (BG)); however, PSD curves calculated from simulated isotherms are to a greater or lesser extent affected by the presence of surface oxides. The most reliable results are obtained from Ar adsorption data. Not only is adsorption of this adsorbate practically independent from the presence of surface oxides, but, more importantly, for this molecule one can apply the slit-like model of pores as the first approach to recover the average pore diameter of a real carbon structure. For nitrogen, the effect of carbon surface chemical composition is observed due to the quadrupole moment of this molecule, and this effect shifts the PSD curves compared to Ar. The largest differences are seen for CO2, and it is clearly demonstrated that the PSD curves obtained from adsorption isotherms of this molecule contain artificial peaks and the average pore diameter is strongly influenced by the presence of electrostatic adsorbate-adsorbate as well as adsorbate-adsorbent interactions.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (~ 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.

Vertical distribution of suspended aggregates at time series station DYNAPROC

Day/night variations in the size distribution of the particulate matter >0.15 mm (PM) were studied in May 1995 during the DYNAPROC time-series cruise in the northwestern Mediterranean Sea. Data on vertical distributions of PM (>0.15 mm) and zooplankton were collected with the Underwater Video Profiler (UVP). The comparisons of the UVP data with plankton net data and POC data from water bottles indicated that more than 97% of the particles detected by the UVP were non-living particles (0.15 mm) and that the PM contributed 4-34% of the total dry weight measured on GF/F filters. Comparison of seven pairs of day and night vertical profiles performed during the cruise showed that in the upper 800 m, the mean size and the volume of particles was higher at night than during the day. During the night, the integrated volume of the PM increased on average by 32±20%. This increase corresponded to a shift of smaller size classes (<0.5 mm) towards the larger ones (>0.5 mm). During the day, the pattern was reversed, and the quantity of PM >0.5 mm decreased. During the study period, the standing stock of PM (60-800 m) decreased from 7.5 to less than 2 g m?2 but the diel variations persisted, except for two short periods in the superficial layer following a wind event. The cyclic feeding activity induced by the diel vertical migration of zooplankton could be the best candidate to explain the observed diel fluctuations in the size classes of PM in the water column. However, our results also suggest that in the upper layer additional driving forces such as the increase of the level of turbulence after a wind event or the modification of the zoo- and phytoplankton community can influence the PM temporal evolution.

Vertical distribution of suspended aggregates in the equatorial Pacific

Marine snow (MS) distribution from the surface to 1000 m depth was determined in the equatorial Pacific using the underwater video profiler during the Etude du Broutage en Zone Equatoriale cruise in fall 1996. The latitudinal transect was carried out at 17 stations along the 180° meridian from 8°S to 8°N during a cold phase of El Niño-Southern Oscillation. Higher MS concentrations were found below the equatorial zone than poleward. At the equator the estimated integrated MS carbon/m**2 in the upper kilometer was 5.7 g/m**2, while both southward and northward (between 1° and 8°) the mean integrated MS carbon was about 2.7 g/m**2. In the upper 50 m the MS carbon was twofold lower than the combined carbon of autotrophic and heterotrophic protists and four times lower than the mesozooplankton carbon biomass, both measured concurrently during the cruise. Different water bodies had different MS content. The highest concentrations were found in the South Equatorial Current, the South Equatorial Counter Current, and the North Equatorial Countercurrent. Tropical waters at the south in the South Subsurface Countercurrents and the warm northern superficial waters had the lowest MS biomass. Mechanistically, a latitudinal "conveyor belt", a poleward divergence of upwelled waters that return to the equator after being downwelled at north and south convergent zones, may partially explain the vertical distribution of particulate matter observed during the studied period.

Vertical distribution of large particulate matter in the Western Mediterranean Sea

The relationship between mesoscale hydrodynamics and the distribution of large particulate matter (LPM, particles larger than 200 ?m) in the first 1000 m of the Western Mediterranean basin was studied with a microprocessor-driven CTD-video package, the Underwater Video Profiler (UVP). Observations made during the last decade showed that, in late spring and summer, LPM concentration was high in the coastal part of the Western Mediterranean basin at the shelf break and near the continental slope (computed maximum: 149 ?g C/l between 0 and 100 m near the Spanish coast of the Gibraltar Strait). LPM concentration decreased further offshore into the central Mediterranean Sea where, below 100 m, it remained uniformly low, ranging from 2 to 4 ?g C/l. However, a strong variability was observed in the different mesoscale structures such as the Almeria-Oran jet in the Alboran Sea or the Algerian eddies. LPM concentration was up to one order of magnitude higher in fronts and eddies than in the adjacent oligotrophic Mediterranean waters (i.e. 35 vs. 8 ?g C/l in the Alboran Sea or 16 vs. 3 ?g C/l in a small shear cyclonic eddy). Our observations suggest that LPM spatial heterogeneity generated by the upper layer mesoscale hydrodynamics extends into deeper layers. Consequently, the superficial mesoscale dynamics may significantly contribute to the biogeochemical cycling between the upper and meso-pelagic layers.

Particle camera and settling chamber measurements at site PC (GeoB11834-3) and SC (GeoB12914-4) off Cape Blanc/Mauritania

Particles sinking out of the euphotic zone are important vehicles of carbon export from the surface ocean. Most of the particles produce heavier aggregates by coagulating with each other before they sink. We implemented an aggregation model into the biogeochemical model of Regional Oceanic Modelling System (ROMS) to simulate the distribution of particles in the water column and their downward transport in the Northwest African upwelling region. Accompanying settling chamber, sediment trap and particle camera measurements provide data for model validation. In situ aggregate settling velocities measured by the settling chamber were around 55 m d**-1. Aggregate sizes recorded by the particle camera hardly exceeded 1 mm. The model is based on a continuous size spectrum of aggregates, characterised by the prognostic aggregate mass and aggregate number concentration. Phytoplankton and detritus make up the aggregation pool, which has an averaged, prognostic and size dependent sinking. Model experiments were performed with dense and porous approximations of aggregates with varying maximum aggregate size and stickiness as well as with the inclusion of a disaggregation term. Similar surface productivity in all experiments has been generated in order to find the best combination of parameters that produce measured deep water fluxes. Although the experiments failed to represent surface particle number spectra, in the deep water some of them gave very similar slope and spectrum range as the particle camera observations. Particle fluxes at the mesotrophic sediment trap site off Cape Blanc (CB) have been successfully reproduced by the porous experiment with disaggregation term when particle remineralisation rate was 0.2 d**-1. The aggregation-disaggregation model improves the prediction capability of the original biogeochemical model significantly by giving much better estimates of fluxes for both upper and lower trap. The results also point to the need for more studies to enhance our knowledge on particle decay and its variation and to the role that stickiness play in the distribution of vertical fluxes.

Seawater carbonate chemistry and swimming behaviors of the raphidophyte Heterosigma akashiwo in a laboratory experiment

We investigated the effects of pH on movement behaviors of the harmful algal bloom causing raphidophyte Heterosigma akashiwo. Motility parameters from >8000 swimming tracks of individual cells were quantified using 3D digital video analysis over a 6-h period in 3 pH treatments reflecting marine carbonate chemistry during the pre-industrial era, currently, and the year 2100. Movement behaviors were investigated in two different acclimation-to-target-pH conditions: instantaneous exposure and acclimation of cells for at least 11 generations. There was no negative impairment of cell motility when exposed to elevated PCO2 (i.e., low pH) conditions but there were significant behavioral responses. Irrespective of acclimation condition, lower pH significantly increased downward velocity and frequency of downward swimming cells (p < 0.001). Rapid exposure to lower pH resulted in 9% faster downward vertical velocity and up to 19% more cells swimming downwards (p < 0.001). Compared to pH-shock experiments, pre-acclimation of cells to target pH resulted in ~30% faster swimming speed and up to 46% faster downward velocities (all p < 0.001). The effect of year 2100 PCO2 levels on population diffusivity in pre-acclimated cultures was >2-fold greater than in pH-shock treatments (2.2 × 105 µm**2/s vs. 8.4 × 104 µm**2/s). Predictions from an advection-diffusion model, suggest that as PCO2 increased the fraction of the population aggregated at the surface declined, and moved deeper in the water column. Enhanced downward swimming of H. akashiwo at low pH suggests that these behavioral responses to elevated PCO2 could reduce the likelihood of dense surface slick formation of H. akashiwo through reductions in light exposure or growth independent surface aggregations. We hypothesize that the HAB alga's response to higher PCO2 may exploit the signaling function of high PCO2 as indicative of net heterotrophy in the system, thus indicative of high predation rates or depletion of nutrients.

An approach for particle sinking velocity measurements in the 3-400 µm size range and considerations on the effect of temperature on sinking rates

The flux of organic particles below the mixed layer is one major pathway of carbon from the surface into the deep ocean. The magnitude of this export flux depends on two major processes-remineralization rates and sinking velocities. Here, we present an efficient method to measure sinking velocities of particles in the size range from approximately 3-400 µm by means of video microscopy (FlowCAM®). The method allows rapid measurement and automated analysis of mixed samples and was tested with polystyrene beads, different phytoplankton species, and sediment trap material. Sinking velocities of polystyrene beads were close to theoretical values calculated from Stokes' Law. Sinking velocities of the investigated phytoplankton species were in reasonable agreement with published literature values and sinking velocities of material collected in sediment trap increased with particle size. Temperature had a strong effect on sinking velocities due to its influence on seawater viscosity and density. An increase in 9 °C led to a measured increase in sinking velocities of 40 %. According to this temperature effect, an average temperature increase in 2 °C as projected for the sea surface by the end of this century could increase sinking velocities by about 6 % which might have feedbacks on carbon export into the deep ocean.

Seawater carbonate chemistry and its effects on properties and sinking velocity of aggregates of the coccolithophore Emiliania huxleyi, 2010

Coccolithophores play an important role in organic matter export due to their production of the mineral calcite that can act as ballast. Recent studies indicated that calcification in coccolithophores may be affected by changes in seawater carbonate chemistry. We investigated the influence of CO2 on the aggregation and sinking behaviour of the coccolithophore Emiliania huxleyi (PML B92/11) during a laboratory experiment. The coccolithophores were grown under low (~180 µatm), medium (~380 µatm), and high (~750 µatm) CO2 conditions. Aggregation of the cells was promoted using roller tables. Size and settling velocity of aggregates were determined during the incubation using video image analysis. Our results indicate that aggregate properties are sensitive to changes in the degree of ballasting, as evoked by ocean acidification. Average sinking velocity was highest for low CO2 aggregates (~1292 m d-1) that also had the highest particulate inorganic to particulate organic carbon (PIC/POC) ratio. Lowest PIC/POC ratios and lowest sinking velocity (~366 m d-1) at comparable sizes were observed for aggregates of the high CO2 treatment. Aggregates of the high CO2 treatment showed a 4-fold lower excess density (~4.2*10**-4 g cm**-3) when compared to aggregates from the medium and low CO2 treatments (~1.7 g*10**-3 cm**-3). We also observed that more aggregates formed in the high CO2 treatment, and that those aggregates contained more bacteria than aggregates in the medium and low CO2 treatment. If applicable to the future ocean, our findings suggest that a CO2 induced reduction of the calcite content of aggregates could weaken the deep export of organic matter in the ocean, particularly in areas dominated by coccolithophores.

Experiment: Response of Nodularia spumigena to pCO2

The filamentous and diazotrophic cyanobacterium Nodularia spumigena plays a major role in the productivity of the Baltic Sea as it forms extensive blooms regularly. Under phosphorus limiting conditions Nodularia spumigena has a high enzyme affinity for dissolved organic phosphorus (DOP) by production and release of alkaline phosphatase. Additionally, it is able to degrade proteinaceous compounds by expressing the extracellular enzyme leucine aminopeptidase. As atmospheric CO2 concentrations are increasing, we expect marine phytoplankton to experience changes in several environmental parameters including pH, temperature, and nutrient availability. The aim of this study was to investigate the combined effect of CO2-induced changes in seawater carbonate chemistry and of phosphate deficiency on the exudation of organic matter, and its subsequent recycling by extracellular enzymes in a Nodularia spumigena culture. Batch cultures of Nodularia spumigena were grown for 15 days aerated with three different pCO2 levels corresponding to values from glacial periods to future values projected for the year 2100. Extracellular enzyme activities as well as changes in organic and inorganic compound concentrations were monitored. CO2 treatment-related effects were identified for cyanobacterial growth, which in turn was influencing exudation and recycling of organic matter by extracellular enzymes. Biomass production was increased by 56.5% and 90.7% in the medium and high pCO2 treatment, respectively, compared to the low pCO2 treatment and simultaneously increasing exudation. During the growth phase significantly more mucinous substances accumulated in the high pCO2 treatment reaching 363 µg Gum Xanthan eq /l compared to 269 µg Gum Xanthan eq /l in the low pCO2 treatment. However, cell-specific rates did not change. After phosphate depletion, the acquisition of P from DOP by alkaline phosphatase was significantly enhanced. Alkaline phosphatase activities were increased by factor 1.64 and 2.25, respectively, in the medium and high compared to the low pCO2 treatment. In conclusion, our results suggest that Nodularia spumigena can grow faster under elevated pCO2 by enhancing the recycling of organic matter to acquire nutrients.

Stretch effects extracted from propagating spherical premixed flames with detailed chemistry

This paper is concerned with extracting stretch effects from outward propagating spherical flames with full chemistry. It is a continuation of a recently published study from this laboratory where it is shown that single-step chemistry is insufficient to explain the experimental results on methane, propane and hydrogen-air systems. Comparisons of the present full chemistry calculations with the experimental results for several fuel/air systems are good/excellent, with the exception of rich propane-air for which it is argued that soot chemistry with attendant radiation loss need to be invoked. The reversal in trends of stretch effects due to change in pressure, initial temperature and N-2 dilution (observed in experiments) can be predicted well by full chemistry but not with simple single-step chemistry. Analysis of the results shows the important role played by many intermediate species and explains why full chemistry is needed to predict stretch effects.

Characteristics of a CW HF chemical-laser calculated from a simplified two-dimensional model

A two-dimensional simplified model of an HF chemical laser is introduced. Using an implicit finite difference scheme, the solution of two adjacent parallel streams with diffusion mixing and chemical reaction is generated. A contour of mixing and reaction boundary is obtained without presupposition. The distribution of the HF(v) concentrations, gas temperature and the optical small signal gain (alpha sub V, J) on the flowing plane (X, Y) are presented. Compared with the solution solved directly from a set of Navier-Stokes equations, the results of these two methods agree with each other qualitatively. The influences of the different velocity, temperature (T sub 0) and composition of the two streams on the small signal gain after the nozzle exit are investigated. It is interesting that for larger J with a fixed v, the peaks of alpha sub v-T sub 0 profiles move towards higher T sub 0. The computing method is simple and only a short computing time is needed.

Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere.

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.