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.

Focused fluid transfer through the mantle above subduction zones

Volcanic arcs above subduction zones are enriched in volatiles and fluid-mobile elements with respect to mid-oceanic ridge basalts. There is general consensus that this particular subduction zone signature is generated by fluid-induced extraction of these elements from subducted oceanic crust and its sedimentary cover. However, how these fluids are transferred through the mantle wedge to the locus of partial melting and what modification the fluids will experience is unresolved. Here we investigate the interaction of slab fluids with the mantle wedge through a series of high-pressure experiments. We explore two end-member processes of focused and porous reactive flow of hydrous slab melts through the mantle. Transfer by porous flow leads to the formation of hydrous minerals that sequester fluid-mobile elements and residual fluids characterized by trace element patterns inconsistent with typical arc lavas. In contrast, no hydrous minerals are formed in the reaction zone of experiments mimicking focused flow, and the typical trace element signature acquired during fluid extraction from the slab is preserved, indicating that this is an efficient process for element transfer through the mantle wedge.

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.

Accumulation rates of volcanic glass and ice-rafted debris in sediments of the North Pacific Ocean

Mass accumulation rates (MAR) of different components of North Pacific deep-sea sediment provide detailed information about the timing of the onset of major Northern Hemisphere glaciation that occurred at 2.65 Ma. An increase in explosive volcanism in the Kamchatka-Kurile and Aleutian arcs occured at this same time, suggesting a link between volcanism and glaciation. Sediments recovered by piston-coring techniques during ODP Leg 145 provide a unique opportunity to undertake a detailed test of this possibility. Here we use volcanic glass as a proxy for explosive volcanism and ice-rafted debris (IRD) as a proxy for glaciation. The MAR of both glass and IRD increase markedly at 2.65 Ma. Further, the flux of the volcanic glass increased just prior the flix of ice-radted material, suggesting that the cooling resulting from explosive volcanic eruptions may have been the ultimate trigger for the mid-Pliocene glacial intensification.

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).

(Table 2) Chemical composition of gases in basalts from DSDP Leg 65 Holes

Basalts from different structural provinces in the ocean basins, such as mid-ocean ridges, island arcs, and oceanic plateaus, show marked differences in major and minor element composition stemming from differences in magma source. In addition, there are variations even within individual provinces, based on such processes as crystal fractionation, secondary alteration, and hydrothermal alteration. It is also known that hydrothermal processes can cause changes in the gas composition of submarine basalts. For example, Zolotarev et al. (1978) have established that hydrothermal alteration frequently causes an increase in the CO2 content of basalts. If the homogeneity in composition and concentration of organic gases in oceanic basalts is associated with degassing during epimagmatic alteration, it would be interesting to investigate the relative abundance of gas phases in young basalts from midoceanic ridges. This chapter deals with the distribution of organic gases and CO2 in young basalts recovered on Leg 65 from the Gulf of California. Our aim was to establish the relationship between gas composition and degree of alteration.

Geochemistry of mafic clasts of ODP Holes 125-778A and 125-779A

Clasts of metamorphosed mafic igneous rock of diverse composition were recovered in two drill sites on a serpentine mud volcano in the outer Mariana forearc during Ocean Drilling Program Leg 125. These clasts are xenolithic fragments that have been entrained in the rising serpentine mud, and make up less that 9% of the total rock recovered at Sites 778 and 779. Most samples are metabasalt or metadiabase, although one clast of possible boninite and one cumulate gabbro were recovered. On the basis of trace element signatures, samples are interpreted to represent both arc-derived and mid-ocean ridge-derived compositions. Rocks with extremely low TiO2 (<0.3 wt%) and Zr (<30 ppm) are similar to boninite series rocks. Samples with low TiO2 (<0.9 wt%) and Zr (<50 ppm) and extreme potassium enrichment (K2O/Na2O >3.9) may represent island arc rocks similar to shoshonites. However, the K2O/Na2O ratios are much higher than those reported for shoshonites from modem or ancient arcs and may be the result of metamorphism. Samples with moderate TiO2 (1.4 to 1.5 wt%) and Zr (72 to 85 ppm) are similar to rocks from mid-ocean ridges. A few samples have TiO2 and Zr intermediate between island arc and mid-ocean ridge basalt-like rocks. Two samples have high iron (Fe2O3* = >12.8 to 18.5 wt%) (Fe2O3* = total iron calculated as Fe2O3) and TiO2 (>2.3 wt%) and resemble FeTi basalt recovered from mid-ocean ridges. Metamorphism in most samples ranges from low-temperature zeolite, typical of ocean floor weathering, to prehnite-pumpellyite facies and perhaps lower greenschist. Blue amphibole and lawsonite minerals are present in several samples. One diabase clast (Sample 9) exhibits Ca enrichment, similar to rodingite metamorphism, typical of mafic blocks in serpentinized masses. The presence of both low-grade (clays and zeolites) and higher grade (lawsonite) metamorphism indicates retrograde processes in these clasts. These clasts are fragments of the forearc crust and possibly of the subducting plate that have been entrained in the rising serpentine and may represent the deepest mafic rocks ever recovered from the Mariana forearc. The variable compositions and degree of metamorphism of these clasts requires at least two tectonic origins. The recovery of clasts with mid-ocean ridge and arc chemical affinities in a single drill hole requires these clasts to have been "mixed" on a small scale either (1) in the forearc crustal sequence, or (2) after inclusion in the rising serpentine mud. The source of the MORB-like samples and an explanation for the presence of both MORB-like and arc-like rocks in close proximity is critical to any model of the evolution of the Mariana forearc. The source of the MORB-like samples likely will be one (or more) of the following: (1) accretion of Pacific plate lithosphere, (2) remnants of original forearc crust (trapped plate), (3) volcanism in the supra-subduction zone (arc or forearc) environment, or (4) derivation from the subducting slab by faulting along the dÈcollement.

Element abundances and Nd isotopic composition in boninite and tholeiite from DSDP Hole 60-458

Boninites are unusual high MgO-high SiO2 volcanic rocks found in several western Pacific island arcs. Their high Mg/(Mg + total Fe) (0.55-0.83) and compatible element contents (Ni = 70-450 ppm, Cr = 200-1800 ppm) indicate equilibration with mantle peridotite, but their low TiO2 contents (0.1-0.5%) indicate severe depletion of this source. K, Rb, Sr and Ba abundances in boninites are typical of primitive arc basalts, but ratios such as Ti/Zr and La/Yb are variable (Ti/Zr = 23-67, (La/Yb)e.f. = 0.6-4.7). Evidence for both enrichment and depletion of incompatible elements suggests that boninites are derived from refractory peridotite which has been metasomatically enriched in LREE, Zr, Sr, Ba and alkalis. Wide variations in 143Nd/144Nd (0.51262-0.51296) are correlated with La/Sm, Sm/Nd and Ti/Zr, which enables identification of components in the boninite source. Possible LREE depleted components have relative REE and Ti abundances like those in depleted peridotites and high 143Nd/144Nd ratios which reach MORB-like values. Possible LREE enriched components have relative REE abundances similar to those in metasomatized mantle peridotite nodules, and low 143Nd/144Nd ratios which indicate either sedimentary sources or mantle sources with recent to ancient LREE enrichment. Relative abundances of Ba and Sr in boninites decrease with increasing LREE enrichment and suggest a non-sedimentary source for the LREE enriched material. Enrichment in Ba, Sr and alkalis may result from a third component derived from subducted oceanic crust. Two models can account for the successive generation of boninites and arc tholeiites within a single area: 1) boninites can be derived from the peridotite residue of earlier arc tholeiite generation which is metasomatically enriched in LREE before boninite volcanism, or 2) arc tholeiites and boninites can be derived from a variably depleted peridotite source which has been pervasively enriched in LREE. Areas of fertile peridotite would yield tholeiites while refractory areas would yield boninites.

Mineralogy of serpentine muds of ODP Leg 125 holes (Table 1)

Large serpentinite seamounts are common in the forearc regions between the trench axis and the active volcanic fronts of the Mariana and Izu-Bonin intraoceanic arcs. The seamounts apparently form both as mud volcanoes, composed of unconsolidated serpentine mud flows that have entrained metamorphosed ultramafic and mafic rocks, and as horst blocks, possibly diapirically emplaced, of serpentinized ultramafics partially draped with unconsolidated serpentine slump deposits and mud flows. The clayand silt-sized serpentine recovered from three sites on Conical Seamount on the Mariana forearc region and from two sites on Torishima Forearc Seamount on the Izu-Bonin forearc region is composed predominantly of chrysotile, brucite, chlorite, and clays. A variety of accessory minerals attest to the presence of unusual pore fluids in some of the samples. Aragonite, unstable at the depths at which the serpentine deposits were drilled, is present in many of the surficial cores from Conical Seamount. Sjogrenite minerals, commonly found as weathering products of serpentine resulting from interaction with groundwater, are found in most of the samples. The presence of aragonite and carbonate-hydroxide hydrate minerals argues for interaction of the serpentine deposits with fluids other than seawater. There are numerous examples of sedimentary serpentinite deposits exposed on land that are very similar to the deposits recovered from the serpentine seamounts drilled on ODP Leg 125. We suggest that Conical Seamount may be a type locality for the study of in situ formation of many of these sedimentary serpentinite bodies. Further, we suggest that both the deposits drilled on Conical Seamount and on Torishima Forearc Seamount demonstrate that serpentinization can continue in situ within the seamounts through interaction of the serpentine deposits with both seawater and subduction-related fluids.

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.

Mineralogy at DSDP Legs 58-60

Sediments recovered by drilling during Legs 58, 59, and 60 in the North and South Philippine Sea have been analyzed by X-ray diffractometry. The CaCO3 content was measured separately. The sites encompass several volcanic ridges and intervening inter-arc basin troughs as well as sites on the Mariana arc fore-arc sediment prism and the Mariana Trench. The sediments at all sites received major volcanogenic input from the various arcs; they tend to be rich in volcanic glass, with associated quartz, feldspar, pyroxenes and amphibole. Carbonate is a major component only at Site 445 at the southern end of the Daito Ridge, and at Site 448 on the Palau-Kyushu Ridge. All other sites were either deep relative to the carbonate compensation depth or had very high non-carbonate sedimentation rates. Clay minerals are mainly smectite and illite with lesser variable proportions of chlorite and kaolinite. Smectite predominates over illite except at sites in the Shikoku Basin and the Daito Ridge, and at one site in the Mariana Trench. At several sites, smectite increases and illite decreases with depth. Principal zeolites are phillipsite and clinoptilolite. Analcime occurs in some samples.

Petrology and geochemistry at DSDP Site 59-448

This chemical and petrologic study of rocks from Site 448 on the Palau-Kyushu Ridge is designed to answer some fundamental questions concerning the volcanic origin of remnant island arcs. According to the reconstruction of the Western Pacific prior to about 45 m.y. ago (Hilde et al., 1977), the site of the Palau-Kyushu Ridge was a major transform fault. From a synthesis of existing geological and geophysical data (R. Scott et al., this volume), it appears that the ridge originated by subduction of the Pacific plate under the West Philippine Basin. Thus the Palau-Kyushu Ridge should be a prime example of both initial volcanism of an incipient arc formed by interaction of oceanic lithospheric plates and remnant-arc volcanic evolution. The Palau-Kyushu Ridge was an active island arc from about 42 to 30 m.y. ago, after which initiation of back-arc spreading formed the Parece Vela Basin (R. Scott et al., this volume; Karig, 1975a). This spreading left the western portion of the ridge as a remnant arc that separates the West Philippine Basin from the Parece Vela Basin. In spite of numerous oceanographic expeditions to the Philippine Sea, including the two previous DSDP Legs 6 and 31 (Fischer, Heezen et al., 1971; Karig, Ingle et al., 1975), and even though the origins of inter-arc basins have been linked by various hypotheses to that of remnant island arcs (Karig, 1971, 1972, 1975a, and 1975b; Gill, 1976; Uyeda and Ben-Avraham, 1972; Hilde et al., 1977), very little hard data are available on inactive remnant arcs.