SAMPLING AND MINIMUM PHASE FROM BOTH A CONTINUOUS AND DISCRETE POINT OF VIEW*

Examples show that the sampling operation–i.e., the change from the continuous time domain to the discrete time domain–does not necessarily preserve the minimum-phase property. Further examples can be constructed to show that the resampling operation on the discrete time domain does not necessarily preserve the minimum-phase property. Finally it can be shown that the minimum-phase property can be either created or destroyed by sampling or resampling.     

MIGRATION IN THE PRESENCE OF NOISE*

It is shown that the so-called Kirchhoff-summation operator is of a very wide-band nature and even contains an evanescent part. As a consequence, discretization may cause serious aliasing errors, particularly for small extrapolation steps. It is proposed to use in all practical cases band-limited versions of the summation operator, the spatial cut-off frequency being determined by the spatial Fourier spectrum of the coherent noise.     

Methods of Analyzing Qninones in Water and Their Application in Studying the Effects of Hydrophytes on Phenols. Part 1: Quinone Determination with Benzene Sulfinic Acid

By the example of some phenols and qninones, in aqueous solutions possibilities for the quantitative determination are tested separately and in the mixture. Methods for thin-layer chromatography and spectrophotometry were developed. There can be chromatographically deteeted between 5 and 80 μg of substance. Phenol and quinone concentrations of 1.5 · 10^?3 … 0.5 · 10^?4 M were spectrophotometrically investigated.     

Correspondence analysis applied to volcanic aerosols

A statistical analysis of volcanic aerosol based on 1,083 variables including concentration, grain-size and site variabilities establishes correlations between sites and among chemical elements.Variation curves of element concentration show parallel behaviour. High coefficients of correlation between anions and cations confirm associations between elements.     

Crystallization history of Kilauea Iki lava lake as seen in drill core recovered in 1967–1979

Kilauea Iki lava lake formed during the 1959 summit eruption, one of the most picritic eruptions of Kilauea Volcano in the twentieth century. Since 1959 the 110 to 122 m thick lake has cooled slowly, developing steadily thickening upper and lower crusts, with a lens of more molten lava in between. Recent coring dates, with maximum depths reached in the center of the lake, are: 1967 (26.5 m). 1975 (44.2 m), 1976 (46.0 m) and 1979 (52.7 m). These depths define the base of the upper crust at the time of drilling. The bulk of the core consists of a gray, olivine-phyric basalt matrix, which locally contains coarser-grained diabasic segregation veins. The most important megascopic variation in the matrix rock is its variation in olivine content. The upper 15 m of crust is very olivine-rich. Abundance and average size of olivine decrease irregularly downward to 23 m; between 23 and 40 m the rock contains 5–10% of small olivine phenocrysts. Below 40 m. olivine content and average grainsize rise sharply. Olivine contents remain high (20–45%, by volume) throughout the lower crust, except for a narrow (< 6 m) olivine depleted zone near the basalt contact. Petrographically the olivine phenocrysts in Kilauea Iki can be divided into two types. Type 1 phenocrysts are large (1–12 mm long), with irregular blocky outlines, and often contain kink bands. Type 2 crystals are relatively small (0.5–2 mm in length), euhedral and undeformed. The variations in olivine content of the matrix rock are almost entirely variations in the amount of type 1 olivines. Sharp mineral layering of any sort is rare in Kilauea Iki. However, the depth range 41–52 m is marked by the frequent occurrence of steeply dipping (70°–90°) bands or bodies of slightly vuggy olivine-rich rock locally capped with a small cupola of segregation-vein material. In thin section there is clear evidence for relative movement of melt and crystals within these structures. The segregation veins occur only in the upper crust. The most widely distributed (occurring from 4.5–59.4 m) are thin veins (most < 5 cm thick), which cut the core at moderate angles and appear to have been derived from the immediately adjacent wall-rock by filter pressing. There is also a series of thicker (0.1–1.5 m) segregation veins, which recur every 2–3 m, between 20 and 52 m. These have subhorizontal contacts and appear, from similarities in thickness and spacing, to correlate between drill holes as much as 100 m apart. These large veins are not derived from the adjacent wallrock: their mechanism of formation is still problematical. The total thickness of segregation veins in Kilauea Iki is 3–6 m in the central part of the lake, corresponding to 6–11% of the upper crust. Whole-rock compositions for Kilauea Iki fall into two groups: the matrix rock ranges from 20-7.5% MgO, while the segregation veins all contain between 6.0 and 4.5% MgO. There are no whole-rock compositions of intermediate MgO content. Samples from < 12 m show eruption-controlled chemistry. Below that depth, matrix rock compositions have higher Al₂O₃, TiO₂ and alkalies, and lower CaO and FeO, at a given MgO content than do the eruption pumices. The probable causes of this are assimilation of low-melting components from foundered crust, plus removal of olivine, plus removal of minor augite, for rocks with MgO contents of < 8.0%. Given the observed rate of growth of the upper crust, one can infer that significant removal of the type 1 olivine phenocrysts from the upper part of the lake began in 1963 and ceased sometime prior to 1972. The process. probably gravitative settling, appears to have been inhibited earlier by gas streaming from the lower part of the lens of melt. The olivine cumulate zone, which extends into the upper crust, contains relatively few (25–40%) olivine crystals, few of which actually touch each other. The diffuseness of the cumulate zone raises the possibility that the crystals were coated with a relatively visous boundary layer of melt which moved with them. Calculations of the Stokes’ law settling rates of the largest olivine crystals found at the base of the crust in 1975–76 suggest that the «melt» had a viscosity of > 10⁶ poises, and probably had the properties of a Bingham body, rather than a Newtonian fluid, by that date, which was several years after olivine removal ceased.     

Silicic differentiates of abyssal oceanic magmas: Evidence for late-magmatic vapor transport of potassium

Massive, nearly holocrystalline dolerites from DSDP Hole 417D contain from 0.5 to 1.5% of granophyric patches composed mainly of Na-plagioclase and quartz. These patches are compositionally similar to other crystalline silicic rocks from oceanic spreading centers and differ from rarer abyssal silicic glasses. Crystalline varieties withSiO₂60wt.% generally haveNa/K>10, whereas silicic glasses have Na/K in the range 3–6. While crystal fractionation readily accounts for the Na₂O and K₂O contents of abyssal silicic glasses, both the 417D granophyres and other crystalline abyssal silicic rocks have much lower K₂O than that predicted by any reasonable crystal-liquid fractionation model. We propose that high-temperature vapor phase transport is responsible for removal of potassium during late-stage crystallization of these rocks. This allows for the formation of cogenetic silicic glassy and crystalline rocks with greatly different Na/K ratios. These observations and interpretations lead to a more confident assignment of high Na/K silicic rocks of oceanic and ophiolitic environments to a cogenetic origin with basaltic oceanic crust.