Iterative resolution estimation in least‐squares Kirchhoff migration

We apply iterative resolution estimation to least‐squares Kirchhoff migration. Reviewing the theory of iterative optimization uncovers the common origin of different optimization methods. This allows us to reformulate the pseudo‐inverse, model resolution and data resolution operators in terms of effective iterative estimates. When applied to Kirchhoff migration, plots of the diagonal of the model resolution matrix reveal low illumination areas on seismic images and provide information about image uncertainties. Synthetic and real data examples illustrate the proposed technique and confirm the theoretical expectations.     

Dynamics and role of the Durban cyclonic eddy in the KwaZulu-Natal Bight ecosystem

The semi-permanent Durban Eddy is a mesoscale, lee-trapped, cold-core cyclonic circulation that occurs off the east coast of South Africa between Durban in the north and Sezela, some 70 km to the south. When present, strong north-eastward countercurrents reaching 100 cm s^–1 are found inshore. It is hypothesised that the cyclone is driven by the strong south-westward flowing Agulhas Current offshore of the regressing shelf edge near Durban. Analysis of ADCP data and satellite imagery shows the eddy to be present off Durban approximately 55% of the time, with an average lifespan of 8.6 days, and inter-eddy periods of 4 to 8 days. After spin-up the eddy breaks loose from its lee position and propagates downstream on the inshore boundary of the Agulhas Current. The eddy is highly variable in occurrence, strength and downstream propagation speeds. There is no detectable seasonal cycle in eddy occurrence, with the Natal Pulse causing more variability than any seasonal signal. A thermistor array deployed in the eddy centre, together with ship CTD data, indicates upward doming of the thermal structure in the eddy core associated with cooler water and nutrients being moved higher in the water column, stimulating primary production. Together with the use of satellite imagery, our findings indicate a second mechanism of upwelling, viz. divergent upwelling in the northern limb of the eddy. Satellite-tracked surface drifters released in the eddy demonstrated the potential for nutrient-rich eddy water to be transported northwards along the inshore regions of the KwaZulu-Natal (KZN) Bight, thus contributing to the functioning of the bight ecosystem, as well as southwards along the KZN and Transkei coasts – both by the eddy migrating downstream and by eddy water being recirculated into the inshore boundary of the Agulhas Current itself.     

Sharks caught in the KwaZulu-Natal bather protection programme,South Africa. 14. The smooth hammerhead shark Sphyrna zygaena (Linnaeus)

The current study provides long-term catch-rate, biological and feeding data for smooth hammerhead sharks, Sphyrna zygaena, caught in South Africa’s KwaZulu-Natal bather protection programme. In total, 2 512 S. zygaena were caught in net installations between 1978 and 2014, and 72 S. zygaena were caught on drumlines between 2007 and 2014. There was no significant log-linear year trend in the net catch rate over time (slope = 0.0054, t = 1.808, p = 0.07). However, there was a significant temporal increase in mean size of the captured sharks (slope = 0.0012, t = 3.502, p < 0.001). A quasi-Poisson generalised additive mixed model showed that increasing latitude, winter months, colder sea temperatures and the deployment of drumlines all had a significant positive effect on the catch rate of sharks in nets. The size frequency of the catch was unimodal, with significantly more females caught in the nets and more males on the drumlines. The majority (93.1%) of all sharks caught were immature and measured between 80 and 120 cm precaudal length. Teleosts and cephalopods dominated the sharks’ diet in terms of all dietary indices. The prey species consumed indicate that immature S. zygaena are feeding primarily within the pelagic zone of shallow coastal habitats.     

Seismic wave attenuation in fluid-saturated porous media

Contrary to the traditional view, seismic attenuation in Biot's theory of fluid-saturated porous media is due to viscous damping of local (not global) pore-fluid motion. Since substantial inhomogeneities in fluid permeability of porous geological materials are to be expected, the regions of highest local permeability contribute most to the wave energy dissipation while those of lowest permeability dominate the fluid flow rate if they are uniformly distributed. This dichotomy can explain some of the observed discrepancies between computed and measured attenuation of compressional and shear waves in porous earth. One unfortunate consequence of this result is the fact that measured seismic wave attenuation in fluid-filled geological materials cannot be used directly as a diagnostic of the global fluid-flow permeability.     

Diet and gill morphology of the East Coast redeye round herring Etrumeus wongratanai off KwaZulu-Natal,South Africa

Stomach content analyses and measurements of gillraker morphology were used to assess the diet and feeding ecology of the East Coast redeye round herring Etrumeus wongratanai and provide data for comparisons with other small pelagic fishes off South Africa. Samples were collected by jigging from a kayak off Scottburgh, KwaZulu-Natal (KZN), over the period July 2013–May 2014. In total, 66 stomachs (containing 4 407 prey items) and 66 gill arches were examined. Stomach content analyses indicated that East Coast redeye round herring, at the time of sampling, fed on large (1 500–2 500?µm) particles, with ～2 500?µm particles making the greatest contribution to dietary carbon. The species feeds on larger particles than do anchovy Engraulis encrasicolus and sardine Sardinops sagax, but on particles of a similar size to those consumed by West Coast redeye round herring Etrumeus whiteheadi. There were significant differences in mean gillraker gaps between East Coast redeye round herring and both sardine and anchovy, but not between East Coast and West Coast redeye round herring. The differences in gillraker gaps between East Coast redeye round herring, sardine and anchovy are indicative of resource partitioning through differential feeding, based on zooplankton size. The data suggest that there is no resource partitioning between East and West coast redeye round herring, indicating that competition is likely to occur between them. However, such competition is minimised by limited spatial overlap between these two species.     

Analysis of Thomsen parameters for finely layered VTI media

Since the work of Postma and Backus, much has been learned about elastic constants in vertical transversely isotropic (VTI) media when the anisotropy is due to fine layering of isotropic elastic materials. Nevertheless, there has continued to be some uncertainty about the possible range of Thomsen's anisotropy parameters ε and δ for such media. We use both Monte Carlo studies and detailed analysis of Backus' equations for both two- and three-component layered media to establish the results presented. We show that ε lies in the range ?3/8 ε ½[〈v²_p〉〈v^?2_p〉?1], for finely layered media; smaller positive and all negative values of ε occur for media with large fluctuations in the Lamé parameter λ in the component layers. We show that δ can also be either positive or negative, and that for constant density media, sign (δ) = sign (〈v^?2_p〉 ? 〈v^?2_s〉〈v²_s/v²_p〉). Monte Carlo simulations show that among all theoretically possible random media, positive and negative δ are equally likely in finely layered media. (Of course, the δs associated with real earth materials may span some smaller subset of those that are theoretically possible, but answering this important question is beyond our present scope.) Layered media having large fluctuations in λ are those most likely to have positive δ. This is somewhat surprising since ε is often negative or a small positive number for such media, and we have the general constraint that ε ? δ > 0 for layered VTI media. Since Gassmann's results for fluid-saturated porous media show that the mechanical effects of fluids influence only the Lamé parameter λ, not the shear modulus μ, these results suggest that small positive δ occurring together with small positive ε (but somewhat larger than δ) may be indicative of changing fluid content in a layered earth.     

Influence of the <Emphasis Type="Italic">X</Emphasis>-site composition on tourmaline’s crystal structure: investigation of synthetic K-dravite,dravite, oxy-uvite,and magnesio-foitite using SREF and Raman spectroscopy

The crystal structures of synthetic K-dravite [^XK^YMg ₃ ^Z Al ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W (OH)], dravite [^XNa^YMg ₃ ^Z Al ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W (OH)], oxy-uvite [^XCa^YMg ₃ ^Z Al ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W O], and magnesio-foitite [^X?^Y(Mg₂Al)^ZAl ₆ ^T Si₆O₁₈(BO₃) ₃ ^V (OH) ₃ ^W (OH)] are investigated by polarized Raman spectroscopy, single-crystal structure refinement (SREF), and powder X-ray diffraction. The use of compositionally simple tourmalines characterized by electron microprobe analysis facilitates the determination of site occupancy in the SREF and band assignment in the Raman spectra. The synthesized K-dravite, oxy-uvite, and magnesio-foitite have significant Mg–Al disorder between their octahedral sites indicated by their respective average 〈Y–O〉 and 〈Z–O〉 bond lengths. The Y- and Z-site compositions of oxy-uvite (^YMg_1.52Al_1.48(10) and ^ZAl_4.90Mg_1.10(15)) and magnesio-foitite (^YAl_1.62Mg_1.38(18) and ^ZAl_4.92Mg_1.08(24)) are refined from the electron densities at each site. The Mg–Al ratio of the Y and Z sites is also determined from the relative integrated peak intensities of the Raman bands in the O–H stretching vibrational range (3250–3850 cm^?1), producing values in good agreement with the SREF data. The unit cell volume of tourmaline increases from magnesio-foitite (1558.4(3) ų) to dravite (1569.5(4)–1571.7(3) ų) to oxy-uvite (1572.4(2) ų) to K-dravite (1588.1(2) ų), mainly due to lengthening of the crystallographic c-axis. The increase in the size of the X-site coordination polyhedron from dravite (Na) to K-dravite (K) is accommodated locally in the crystal structure, resulting in the shortening of the neighboring O1–H1 bond. In oxy-uvite, Ca²⁺ is locally associated with a deprotonated W (O1) site, whereas vacant X sites are neighbored by protonated W (O1) sites. Increasing the size of the X-site-occupying ion does not detectably affect bonding between the other sites; however, the higher charge of Ca and the deprotonated W (O1) site in oxy-uvite are correlated to changes in the lattice vibration Raman spectrum (100–1200 cm^?1), particularly for bands assigned to the T ₆O₁₈ ring. The Raman spectrum of magnesio-foitite shows significant deviations from those of K-dravite, dravite, and oxy-uvite in both the lattice and O–H stretching vibrational ranges (100–1200 and 3250–3850 cm^?1, respectively). The vacant X site is correlated with long- and short-range changes in the crystal structure, i.e., deformation of the T ₆O₁₈ ring and lengthening of the O1–H1 and O3–H3 bonds. However, X-site vacancies in K-dravite, dravite, and oxy-uvite result only in the lengthening of the neighboring O1–H1 bond and do not result in identifiable changes in the lattice-bonding environment.     

Water quality in New Zealand rivers: current state and trends

River water quality, particularly in lowland catchments, is a matter of concern to the New Zealand public. We assessed river water quality and biological state and trends using data from more than 900 monitoring sites. Parallel state and trend analyses were carried out using all sites and a subset of lowland river sites. Median water-quality state in urban and pastoral land-cover classes was poorer than in exotic forest and natural land-cover classes, and lowland sites in the urban and pastoral classes had the poorest water quality. Nutrient and Escherichia coli concentrations increased and visual clarity and Macroinvertebrate Community Index scores decreased as proportions of catchments in high-intensity agricultural and urban land cover increased. Ten-year trends (2004–2013) indicated recent improvements in ammoniacal nitrogen, dissolved reactive phosphorus and total phosphorus in the pastoral and urban classes, possibly reflecting improved land management. In contrast, trends in nitrate-nitrogen in the exotic forest and cool-dry/pastoral classes indicated worsening conditions.     

Summer and winter differences in zooplankton biomass,distribution and size composition in the KwaZulu-Natal Bight,South Africa

Zooplankton biomass and distribution in the KwaZulu-Natal Bight were investigated in relation to environmental parameters during summer (January–February 2010) and winter (July–August 2010). Mean zooplankton biomass was significantly higher in winter (17.1 mg dry weight [DW] m^–3) than in summer (9.5 mg DW m^?3). In summer, total biomass was evenly distributed within the central bight, low off the Thukela River mouth and peaked near Durban. In winter, highest biomass was found offshore between Richards Bay and Cape St Lucia. Zooplankton biomass in each size class was significantly, negatively related to sea surface temperature and integrated nitrate, but positively related to surface chlorophyll a and dissolved oxygen. Zooplankton biomass was significantly related to bottom depth, with greatest total biomass located inshore (<50 m). Distribution across the shelf varied with zooplankton size. Seasonal differences in copepod size composition suggest that a smaller, younger community occupied the cool, chlorophyll-rich waters offshore from the St Lucia upwelling cell in winter, and a larger, older community occurred within the relatively warm and chlorophyll-poor central bight in summer. Nutrient enrichment from quasi-permanent upwelling off Durban and Richards Bay appears to have a greater influence on zooplankton biomass and distribution in the bight than the strongly seasonal nutrient input from the Thukela River.