A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Risk measures with the CxLS property

In the present contribution, we characterise law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (Math. Finance 16:419–441, 2006), we show that these risk measures can be identified with a class of generalised shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (Math. Finance, 2014, http://onlinelibrary.wiley.com/doi/10.1111/mafi.12080/abstract) and Bellini and Bignozzi (Quant. Finance 15:725–733, 2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterisation of robustness for convex risk measures in terms of a weak notion of mixture continuity.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Comparing Input- and Output-Oriented Measures of Technical Efficiency to Determine Local Returns to Scale in DEA Models

This paper shows how one can infer the nature of local returns to scale at the input- or output-oriented efficient projection of a technically inefficient input-output bundle, when the input- and output-oriented measures of efficiency differ.

Relative abundance and ranges of selected diatoms from Pliocene-Pleistocene sections of ODP Leg 177, Atlantic sector of the Southern Ocean

During Ocean Drilling Program (ODP) Leg 177, seven sites were drilled aligned on a transect across the Antarctic Circumpolar Current in the Atlantic sector of the Southern Ocean. The primary scientific objective of Leg 177 was the study of the Cenozoic paleoceanographic and paleoclimatic history of the southern high latitudes and its relationship with the Antarctic cryosphere development. Of special emphasis was the recovery of Pliocene-Pleistocene sections, allowing paleoceanographic studies at millennial or higher time resolution, and the establishment of refined biostratigraphic zonations tied to the geomagnetic polarity record and stable isotope records. At most sites, multiple holes were drilled to ensure complete recovery of the section. A description of the recovered sections and the construction of a multihole splice for the establishment of a continuous composite is presented in the Leg 177 Initial Reports volume for each of the sites (Gersonde, Hodell, Blum, et al., 1999). Here we present the relative abundance pattern and the stratigraphic ranges of diatom taxa encountered from shore-based light microscope studies completed on the Pliocene-Pleistocene sequences from six of the drilled sites (Sites 1089-1094). No shore-based diatom studies have been conducted on the Pliocene-Pleistocene sediments obtained at Site 1088, located on the northern crest of the Agulhas Ridge, because of the scattered occurrence and poor preservation of diatoms in these sections (Shipboard Scientific Party, 1999b). The data included in our report present the baseline of a diatom biostratigraphic study of Zielinski and Gersonde (2002), which (1) includes a refinement of the southern high-latitude Pliocene-Pleistocene diatom zonation, in particular for the middle and late Pleistocene, and (2) presents a biostratigraphic framework for the establishment of age models of the recovered sediment sections. Zielinski and Gersonde (2002) correlated the diatom ranges with the geomagnetic polarity record established shipboard (Sites 1090 and 1092) (Shipboard Scientific Party, 1999c, 1999d) and on shore (Sites 1089, 1091, 1093, and 1094) by Channell and Stoner (2002). The Pliocene-Pleistocene diatom zonation proposed by Zielinski and Gersonde (2002) relies on a diatom zonation from Gersonde and Bárcena (1998) for the northern belt of the Southern Ocean. Because of latitudinal differentiation of sea-surface temperature, nutrients, and salinity between Antarctic and Subantarctic/subtropical water masses, the Pliocene-Pleistocene stratigraphic marker diatoms are not uniformly distributed in the Southern Ocean (Fenner, 1991; Gersonde and Bárcena, 1998). As a consequence, Zielinski and Gersonde (2002) propose two diatom zonations for application in the Antarctic Zone south of the Polar Front (Southern Zonation, Sites 1094 and 1093) and the area encompassing the Polar Front Zone (PFZ) and the Subantarctic Zone (Northern Zonation, Sites 1089-1092). This accounts especially for the Pleistocene zonation where Hemidiscus karstenii, whose first abundant occurrence datum and last occurrence datum defines the subzonation of the northern Thalassiosira lentiginosa Zone, occurs only sporadically in the cold-water realm south of the PFZ and thus is not applicable in sections from this area. However, newly established marker species assigned to the genus Rouxia (Rouxia leventerae and Rouxia constricta) are more related to cold-water environments and allow a refinement of the Pleistocene stratigraphic zonation for the southern cold areas. A study relying on quantitative counts of both Rouxia species confirms the utility of these stratigraphic markers for the identification of sequences attributed to marine isotope Stages 6 and 8 in the southern Southern Ocean (Zielinski et al., 2002).

Heat flow measurements in the Weddell Sea

From January to March 1987, heat flow measurements were tried at four sites (Sites 689, 690, 695, and 696) during ODP Leg 113, in the Weddell Sea, Antarctica. At Site 690 (Maud Rise), a convex upward shaped temperature vs. depth profile was observed. This profile cannot be explained by steady-state conduction through solid materials only. We conclude that the minimum heat flow value at Site 690 is 45 mW/m2. A prominent bottom simulating reflector (BSR) was observed at 600 mbsf at Site 695. However, the observed temperature is too high to explain the BSR as a gas hydrate. The origin of the BSR remains unknown, although it is probably of biogenic origin as observed in the Bering Sea during DSDP Leg 19. After correcting for the effects of sedimentation, heat flow values at Sites 695 and 696 are 69 and 63 mW/m2, respectively. Furthermore, we compiled heat flow data south of 50°S. In the Weddell Sea region, the eastern part shows relatively low heat flow in comparison with the western part, with the boundary between them at about 15°W longitude.

Mineral composition and major element oxides of gabbros from ODP Hole 179-1105A, southwest Indian Ridge

Hole 1105A penetrated 158 m of gabbros at a site offset 1.3 km east-northeast from Hole 735B on the Atlantis Bank near the Atlantis II Fracture Zone. A total of 118 m of dominantly medium- to coarse-grained intercalated Fe-Ti oxide gabbro and olivine gabbro was recovered from Hole 1105A that shows many petrographic features similar to those recovered from the upper part of Hole 735B. The main rock types are distinguished based on the constituent cumulus phases, with the most primitive gabbros consisting of olivine, plagioclase, and clinopyroxene. The inferred crystallization order is subsequently Fe-Ti oxides (ilmenite and titanomagnetite), followed by orthopyroxene, then apatite, and finally biotite. Orthopyroxene appears to replace olivine in a narrow middle interval. The magmatic evolution is likewise reflected in the mineral compositions. Plagioclase varies from An66 to An28. Olivine varies from Fo78 to Fo35. The gap in olivine crystallization occurs between Fo46 and Fo40 and coincides approximately with the appearance of orthopyroxene (~En50). The clinopyroxenes show large compositional variation in Mg/(Mg + Fe total) from 0.84 to 0.51. The nonquadrilateral cations of clinopyroxene similarly show large variations with Ti increasing for the olivine gabbros and decreasing for the Fe-Ti oxide gabbros with the decrease in Mg/(Mg + Fe total). The apatites are mainly flourapatites. The compositional variation in the gabbros is interpreted as a comagmatic suite resulting from fractional crystallization. Pyroxene geothermometry suggests equilibration temperatures from 1100°C and below. The coexisting Fe-Ti oxide minerals indicate subsolidus equilibration temperatures from 900°C for olivine gabbros to 700°C for the most evolved apatite-bearing gabbros. The cryptic variation in the olivine gabbros defines two or three lenses, 40 to 60 m thick, each characterized by a distinct convex zoning with a lower segment indicating upward reverse fractionation, a central maximum, and an upper segment showing normal fractionation. The Fe-Ti oxide gabbros show cryptic variations independent of the host olivine gabbros and reveal a systematic upward normal fractionation trend transgressing host olivine gabbro boundaries. Forward fractional crystallization modeling, using a likely parental magma composition from the Atlantis II Fracture Zone (MgO = 7.2 wt%; Mg/[Mg + Fe2+] = 0.62), closely matches the compositions of coexisting olivine, plagioclase, and clinopyroxene. This modeling suggests cosaturation of olivine, plagioclase, and clinopyroxene from 1155°C and the addition of Fe-Ti oxides from 1100°C. The liquid line of descent initially shows increasing FeO with moderately increasing SiO2. After saturation of Fe-Ti oxides, the liquid strongly decreases in FeO and TiO2 and increases in SiO2, reaching dacitic compositions at ~10% liquid remaining. The calculations indicate that formation of olivine gabbros can be accounted for by <65% fractionation and that only the residual 35% liquid was saturated in Fe-Ti oxides. The modeling of the solid fractionation products shows that both the olivine gabbro and the Fe-Ti oxide gabbros contain very small amounts of trapped liquid (<5%). The implications are that the gabbros represent crystal mush that originated in a recharging and tapping subaxial chamber. Compaction and upward melt migration in the crystal mush appear to have been terminated with relatively large amounts of interstitial liquid remaining in the upper parts of the cumulate mush. This termination may have been caused by tectonic disturbances, uplift, and associated withdrawal of magma into the subaxial dike and sill system. Prolonged compaction and cooling of the trapped melt in the mush formed small differentiated bodies and lenses by pressure release migration and crystallization along syntectonic channels. This resulted in differentiation products along lateral and vertical channelways in the host gabbro that vary from olivine gabbro, to Fe-Ti oxide gabbro, gabbronorite, and apatite gabbros and show large compositional variations independent of the host olivine gabbros.

Major element and mineral composition of gabbroic xenoliths and megacrysts from Jeju Island, South Korea

Gabbroic xenoliths and diverse megacrysts (e.g., clinopyroxenes, amphiboles and plagioclases), which correspond to the lithology ranging from gabbro-norite to gabbro, occur in the Pleisto-Holocene alkali basalts from Jeju Island, South Korea. The gabbroic xenoliths consist primarily of moderate-K2O plagioclase, Ti-Al-rich clinopyroxene and CaO-rich orthopyroxene; additionally, TiO2-rich amphibole (kaersutite) and Ti-Fe oxides might or might not be present. The plagioclase is the most dominant phase (approx. 60-70 vol.%). The xenoliths and megacrysts provide evidence for the modal metasomatism of the lower continental crust by the mafic magmas during the Pleistocene. The coarse grain size (up to 5 mm), moderate Mg# [=100xMg/(Mg+Fe(total)) atomic ratio] of pyroxenes (70-77) and textural features (e.g., poikilitic) indicate that the gabbroic xenoliths are consistent with a cumulus origin. The clinopyroxenes from these xenoliths are enriched in REE with smooth convex-upward MREE patterns, which are expected for cumulus minerals formed from a melt enriched in incompatible trace elements. The strikingly similar major and trace element variations and the patterns of constituent minerals clearly indicate a genetic link between the gabbroic xenoliths (plus megacrysts) and the host basalt, indicating that the xenoliths belong to the Jeju Pleisto-Holocene magma system. On the basis of the textural features, the mineral equilibria and the major and trace element variations, the xenoliths appear to have crystallized from basaltic melts at the reservoir-roof environment within the lower crust (4-7 kbars) above the present Moho estimates beneath Jeju Island, where the xenoliths represent wall rocks. Following the consolidation of the xenolith lithologies, volatile- and incompatible element-enriched melt/fluid, as metasomatic agents, infiltrated through the grain boundaries and/or cracks and reacted with the preexisting anhydrous phases, which produced the metasomatic amphiboles. This volatile-enriched melt/fluid could have evolved from the initially anhydrous compositions to the volatile-saturated compositions by the active fractional crystallization in the Jeju Pleisto-Holocene magma system. This process was significant in that it was a relatively young event and played an important role in the formation of the hydrous minerals and the metasomatization of the lower continental crust, which is a plume-impacted area along the Asian continental margin. The major and trace element analyses of the mineral phases from the xenoliths were performed to define the principal geochemical characteristics of the crustal lithosphere segment represented by the studied xenoliths.

Preliminary ichthyolith biostratigraphy and age profiles at DSDP Sites 91-595 and 91-596

Seventy meters of Cenozoic and Mesozoic pelagic clay cored at DSDP Sites 595 and 596 provide the basis for a preliminary analysis of ichthyolith biostratigraphy in the southwest Pacific. A most likely order of the more reliable ichthyolith events is compared with a synthesis of ichthyolith biostratigraphy in the North Pacific and with dated composite ranges. The resultant preliminary ichthyolith stratigraphy suggests that the Cenozoic is represented by the upper 20 m at Site 596 and 16 to 22 m at Site 595. Mixing of taxa precludes a clear recognition of the Cretaceous/Tertiary boundary at Site 595. The occurrence of 13 newly described subtypes is recorded in Mesozoic sediments at Sites 595 and 596. These new subtypes and previously described Mesozoic forms may be useful for recognizing Mesozoic subdivisions when their occurrences in sequences dated by other microfossils are investigated.

Uppermost Jurassic to lower Cretaceous benthic foraminifera from ODP Hole 123-765C

Benthic foraminifers were studied in 99 samples collected from the lower 200 m of Hole 765C. The studied section ranges from the Tithonian to Aptian, and benthic foraminifers can be subdivided into five assemblages on the basis of faunal diversity and stratigraphic ranges of distinctive species. Compared with deep-water assemblages from Atlantic DSDP sites and Poland, assemblages from the Argo Abyssal Plain display a higher diversity of agglutinated forms, which comprise the autochthonous assemblages. Assemblages at the base of Hole 765C are wholly composed of agglutinated forms, reflecting deposition beneath the carbonate compensation depth (CCD). Most calcareous benthic species are found in turbidite layers, and the presence of an upper Valanginian Praedorothia praehauteriviana Assemblage may indicate deposition at or just below the CCD. The P. praehauteriviana Assemblage from Hole 765C is the temporal equivalent of similar assemblages from DSDP Holes 534A, 416A, 370, 105, and 101 in the Atlantic Ocean and Hole 306 in the Pacific Ocean. Stratigraphic ranges of cosmopolitan agglutinated species at Site 765 generally overlap with their reported ranges in the Atlantic and in the bathyal flysch sequences of the Carpathians; however, several species from Hole 765C have not been previously reported from Uppermost Jurassic to Lower Cretaceous abyssal sediments.

Glacier mass balances of Stubacher Sonnblickkees, Hohe Tauern Range, Eastern Alps, Austria, 1958/1959 to 2012/2013

Stubacher Sonnblickkees (SSK) is located in the Hohe Tauern Range (Eastern Alps) in the south of Salzburg Province (Austria) in the region of Oberpinzgau in the upper Stubach Valley. The glacier is situated at the main Alpine crest and faces east, starting at elevations close to 3050 m and in the 1980s terminated at 2500 m a.s.l. It had an area of 1.7 km² at that time, compared with 1 km² in 2013. The glacier type can be classified as a slope glacier, i.e. the relief is covered by a relatively thin ice sheet and there is no regular glacier tongue. The rough subglacial topography makes for a complex shape in the surface topography, with various concave and convex patterns. The main reason for selecting this glacier for mass balance observations (as early as 1963) was to verify on a complex glacier how the mass balance methods and the conclusions - derived during the more or less pioneer phase of glaciological investigations in the 1950s and 1960s - could be applied to the SSK glacier. The decision was influenced by the fact that close to the SSK there was the Rudolfshütte, a hostel of the Austrian Alpine Club (OeAV), newly constructed in the 1950s to replace the old hut dating from 1874. The new Alpenhotel Rudolfshütte, which was run by the Slupetzky family from 1958 to 1970, was the base station for the long-term observation; the cable car to Rudolfshütte, operated by the Austrian Federal Railways (ÖBB), was a logistic advantage. Another factor for choosing SSK as a glaciological research site was the availability of discharge records of the catchment area from the Austrian Federal Railways who had turned the nearby lake Weißsee ('White Lake') - a former natural lake - into a reservoir for their hydroelectric power plants. In terms of regional climatic differences between the Central Alps in Tyrol and those of the Hohe Tauern, the latter experienced significantly higher precipitation , so one could expect new insights in the different response of the two glaciers SSK and Hintereisferner (Ötztal Alps) - where a mass balance series went back to 1952. In 1966 another mass balance series with an additional focus on runoff recordings was initiated at Vernagtfener, near Hintereisferner, by the Commission of the Bavarian Academy of Sciences in Munich. The usual and necessary link to climate and climate change was given by a newly founded weather station (by Heinz and Werner Slupetzky) at the Rudolfshütte in 1961, which ran until 1967. Along with an extension and enlargement to the so-called Alpine Center Rudolfshütte of the OeAV, a climate observatory (suggested by Heinz Slupetzky) has been operating without interruption since 1980 under the responsibility of ZAMG and the Hydrological Service of Salzburg, providing long-term met observations. The weather station is supported by the Berghotel Rudolfshütte (in 2004 the OeAV sold the hotel to a private owner) with accommodation and facilities. Direct yearly mass balance measurements were started in 1963, first for 3 years as part of a thesis project. In 1965 the project was incorporated into the Austrian glacier measurement sites within the International Hydrological Decade (IHD) 1965 - 1974 and was afterwards extended via the International Hydrological Program (IHP) 1975 - 1981. During both periods the main financial support came from the Hydrological Survey of Austria. After 1981 funds were provided by the Hydrological Service of the Federal Government of Salzburg. The research was conducted from 1965 onwards by Heinz Slupetzky from the (former) Department of Geography of the University of Salzburg. These activities received better recognition when the High Alpine Research Station of the University of Salzburg was founded in 1982 and brought in additional funding from the University. With recent changes concerning Rudolfshütte, however, it became unfeasible to keep the research station going. Fortunately, at least the weather station at Rudolfshütte is still operating. In the pioneer years of the mass balance recordings at SSK, the main goal was to understand the influence of the complicated topography on the ablation and accumulation processes. With frequent strong southerly winds (foehn) on the one hand, and precipitation coming in with storms from the north to northwest, the snow drift is an important factor on the undulating glacier surface. This results in less snow cover in convex zones and in more or a maximum accumulation in concave or flat areas. As a consequence of the accentuated topography, certain characteristic ablation and accumulation patterns can be observed during the summer season every year, which have been regularly observed for many decades . The process of snow depletion (Ausaperung) runs through a series of stages (described by the AAR) every year. The sequence of stages until the end of the ablation season depends on the weather conditions in a balance year. One needs a strong negative mass balance year at the beginning of glacier measurements to find out the regularities; 1965, the second year of observation resulted in a very positive mass balance with very little ablation but heavy accumulation. To date it is the year with the absolute maximum positive balance in the entire mass balance series since 1959, probably since 1950. The highly complex ablation patterns required a high number of ablation stakes at the beginning of the research and it took several years to develop a clearer idea of the necessary density of measurement points to ensure high accuracy. A great number of snow pits and probing profiles (and additional measurements at crevasses) were necessary to map the accumulation area/patterns. Mapping the snow depletion, especially at the end of the ablation season, which coincides with the equilibrium line, is one of the main basic data for drawing contour lines of mass balance and to calculate the total mass balance (on a regular-shaped valley glacier there might be an equilibrium line following a contour line of elevation separating the accumulation area and the ablation area, but not at SSK). - An example: in 1969/70, 54 ablation stakes and 22 snow pits were used on the 1.77 km² glacier surface. In the course of the study the consistency of the accumulation and ablation patterns could be used to reduce the number of measurement points. - At the SSK the stratigraphic system, i.e. the natural balance year, is used instead the usual hydrological year. From 1964 to 1981, the yearly mass balance was calculated by direct measurements. Based on these records of 17 years, a regression analysis between the specific net mass balance and the ratio of ablation area to total area (AAR) has been used since then. The basic requirement was mapping the maximum snow depletion at the end of each balance year. There was the advantage of Heinz Slupetzky's detailed local and long-term experience, which ensured homogeneity of the series on individual influences of the mass balance calculations. Verifications took place as often as possible by means of independent geodetic methods, i.e. monoplotting , aerial and terrestrial photogrammetry, more recently also the application of PHOTOMODELLER and laser scans. The semi-direct mass balance determinations used at SSK were tentatively compared with data from periods of mass/volume change, resulting in promising first results on the reliability of the method. In recent years re-analyses of the mass balance series have been conducted by the World Glacier Monitoring Service and will be done at SSK too. - The methods developed at SSK also add to another objective, much discussed in the 1960s within the community, namely to achieve time- and labour-saving methods to ensure continuation of long-term mass balance series. The regression relations were used to extrapolate the mass balance series back to 1959, the maximum depletion could be reconstructed by means of photographs for those years. R. Günther (1982) calculated the mass balance series of SSK back to 1950 by analysing the correlation between meteorological data and the mass balance; he found a high statistical relation between measured and determined mass balance figures for SSK. In spite of the complex glacier topography, interesting empirical experiences were gained from the mass balance data sets, giving a better understanding of the characteristics of the glacier type, mass balance and mass exchange. It turned out that there are distinct relations between the specific net balance, net accumulation (defined as Bc/S) and net ablation (Ba/S) to the AAR, resulting in characteristic so-called 'turnover curves'. The diagram of SSK represents the type of a glacier without a glacier tongue. Between 1964 and 1966, a basic method was developed, starting from the idea that instead of measuring years to cover the range between extreme positive and extreme negative yearly balances one could record the AAR/snow depletion/Ausaperung during one or two summers. The new method was applied on Cathedral Massif Glacier, a cirque glacier with the same area as the Stubacher Sonnblickkees, in British Columbia, Canada. during the summers of 1977 and 1978. It returned exactly the expected relations, e.g. mass turnover curves, as found on SSK. The SSK was mapped several times on a scale of 1:5000 to 1:10000. Length variations have been measured since 1960 within the OeAV glacier length measurement programme. Between 1965 and 1981, there was a mass gain of 10 million cubic metres. With a time lag of 10 years, this resulted in an advance until the mid-1980s. Since 1982 there has been a distinct mass loss of 35 million cubic metres by 2013. In recent years, the glacier has disintegrated faster, forced by the formation of a periglacial lake at the glacier terminus and also by the outcrops of rocks (typical for the slope glacier type), which have accelerated the meltdown. The formation of this lake is well documented. The glacier has retreated by some 600 m since 1981. - Since August 2002, a runoff gauge installed by the Hydrographical Service of Salzburg has recorded the discharge of the main part of SSK at the outlet of the new Unterer Eisboden See. The annual reports - submitted from 1982 on as a contractual obligation to the Hydrological Service of Salzburg - document the ongoing processes on the one hand, and emphasize the mass balance of SSK and outline the climatological reasons, mainly based on the met-data of the observatory Rudolfshütte, on the other. There is an additional focus on estimating the annual water balance in the catchment area of the lake. There are certain preconditions for the water balance equation in the area. Runoff is recorded by the ÖBB power stations, the mass balance of the now approx. 20% glaciated area (mainly the Sonnblickkees) is measured andthe change of the snow and firn patches/the water content is estimated as well as possible. (Nowadays laserscanning and ground radar are available to measure the snow pack). There is a net of three precipitation gauges plus the recordings at Rudolfshütte. The evaporation is of minor importance. The long-term annual mean runoff depth in the catchment area is around 3.000 mm/year. The precipitation gauges have measured deficits between 10% and 35%, on average probably 25% to 30%. That means that the real precipitation in the catchment area Weißsee (at elevations between 2,250 and 3,000 m) is in an order of 3,200 to 3,400 mm a year. The mass balance record of SSK was the first one established in the Hohe Tauern region (and now since the Hohe Tauern National Park was founded in 1983 in Salzburg) and is one of the longest measurement series worldwide. Great efforts are under way to continue the series, to safeguard against interruption and to guarantee a long-term monitoring of the mass balance and volume change of SSK (until the glacier is completely gone, which seems to be realistic in the near future as a result of the ongoing global warming). Heinz Slupetzky, March 2014

Cretaceous-Tertiary ichthyoliths of brown clay intervals

The pattern of ichthyolith distribution established in sequences with stratigraphies based on calcareous or siliceous microfossils is used to provide age correlations for three deep-sea pelagic clay intervals that lack the better known microfossils. At Site 637, approximately 25 m of brown clay in Cores 103-637A-21R through 103-637A-23R underlies upper Miocene sediments and is of Paleocene to early Eocene age. At Site 639, 1.7 m of brown clay in Core 103-639C-2R is Eocene to Oligocene. At Site 640, 3.5 m of clay in Cores 103-640A-1R and 103-640A-2R contains a Cretaceous to Paleocene sequence, with the Cretaceous/Tertiary boundary between 84 and 103 cm in Section 103-640A-2R-1.

Model experiment on optimal size of a fish stock with environmental uncertainties

We analyze the effect of environmental uncertainties on optimal fishery management in a bio-economic fishery model. Unlike most of the literature on resource economics, but in line with ecological models, we allow the different biological processes of survival and recruitment to be affected differently by environmental uncertainties. We show that the overall effect of uncertainty on the optimal size of a fish stock is ambiguous, depending on the prudence of the value function. For the case of a risk-neutral fishery manager, the overall effect depends on the relative magnitude of two opposing effects, the 'convex-cost effect' and the 'gambling effect'. We apply the analysis to the Baltic cod and the North Sea herring fisheries, concluding that for risk neutral agents the net effect of environmental uncertainties on the optimal size of these fish stocks is negative, albeit small in absolute value. Under risk aversion, the effect on optimal stock size is positive for sufficiently high coefficients of constant relative risk aversion.

Analyses of ferromanganese micronodules from the central Arctic Ocean

In order to determine geochemical compositions of Late Cenozoic Arctic seawater, oxide fractions were chemically separated from 15 samples of hand-picked ferromanganese micronodules (50-300 mu m). The success of the chemical separation is indicated by the fact that >97% of the Sr in the oxide fraction is seawater-derived. Rare-earth element (REE) abundances of the Arctic micronodule oxide fractions are much lower than those of bulk Fe-Mn nodules from other ocean basins of the world (e.g., 33 vs. 145 ppm Nd), but the Arctic oxides are enriched in Ce relative to Nd (Ce-N/Nd-N=2.2+/-0.5) and have convex-upward, shale-normalized REE patterns (Nd-N/Gd-N=0.61+/-0.06, Gd-N/Yb-N = 1.5+/-0.2, Nd-N/Yb-N = 0.9+/-0.2), typical of other hydrogenous and diagenetic marine Fe-Mn-oxides. Bulk sediment samples from the central Arctic Ocean have REE abundances and patterns that are characteristic of those of post-Archean shale. Non-detrital fractions (calcite + oxide coatings) of Recent Arctic foraminifera have REE abundances and patterns similar to those of Recent foraminifera from the Atlantic Ocean. Electron microprobe analyses (n=178) of transition elements in 29 Arctic Fe-Mn micronodules from five different stratigraphic intervals of Late Cenozoic sediment indicate that oxide accretion occurred as a result of hydrogenetic and diagenetic processes close to the sediment-seawater interface. Transition element ratios suggest that no oxide accretion occurred during transitions from oxic to suboxic diagenetic conditions. Only K is correlated with Si and Al, and ratios of these elements suggest that they are associated with illite or phillipsite. Ca and Mg are correlated with Mn, which indicates variable substitution of these elements from seawater into the manganate phase. The geochemical characteristics of Arctic Fe-Mn micronodules indicate that the REEs of the oxide fractions were ultimately derived from seawater. However, because of minute contributions of Sr from siliciclastic detritus during diagenesis or during the chemical leaching procedure, Sr isotope compositions of the oxide fractions cannot be used to trace temporal changes in the Sr-87/Sr-86 ratio of Arctic seawater or to improve the chronostratigraphy.

Middle Miocene to Quaternary diatoms in the Nankai Trough and Japan Trench

During Leg 87 of the Deep Sea Drilling Project, eleven holes were drilled at Sites 582 and 583 in the Nankai Trough, off Shikoku, southwestern Honshu, and three holes at Site 584 in the Japan Trench, off northeastern Honshu, Japan. In the former area, a low-latitude diatom zone called the Pseudoeunotia doliolus Zone is recognized in thick upper Quaternary sediments, which yield rare but characteristic admixtures of marine planktonic, marine tychopelagic-tobenthic, and nonmarine diatoms. In the latter area, all the sediments recovered contain abundant to common diatoms, allowing recognition of 12 continuous diatom zones from upper Quaternary through lower middle Miocene. Three hiatuses occur in this area around the Pleistocene/Pliocene boundary and in the upper and middle Miocene. In addition, 19 modified diatom zones for a lower Miocene through upper Quaternary interval are proposed. These middle-to-highlatitude zones are numerically coded (NPD1-NPD12) and represent the entire North Pacific. The establishment of these zones is based primarily on Leg 87 data and other DSDP materials and partially on several Japanese subaerial sequences. Correlation of the new zonal framework with previously established frameworks is attempted by the evaluation of operational usefulness of previously used datums. Resting spores of Chaetoceros and its related forms are recorded with specific intent for the first time, and possible ramifications of its frequency variation are presented. Nine new species are proposed: Delphineis sheshukovae Akiba n. sp., Denticulopsis praelauta Akiba and Koizumi n. sp., Kisseleviella ezoensis Akiba n. sp., Nitzschia umaoiensis Akiba n. sp., Thalassiosira jouseae Akiba n. sp., T. praenidulus Akiba n. sp., T. sancettae Akiba n. sp., T. umaoiensis Akiba n. sp., and T. urahoroensis Akiba n. sp. Transfers of systematic positions of the following four taxa are also proposed: Delphineis simonsenii (Mertz) Akiba n. comb., Ikebea tenuis (Brun) Akiba n. comb., Thalassiosira delicata (Barron) Akiba n. stat., and Thalassiothrixrobusta (Schrader) Akiba n. comb.