Applying essentially non‐oscillatory interpolation to controlled‐source electromagnetic modelling*

Modelling and inversion of controlled‐source electromagnetic (CSEM) fields requires accurate interpolation of modelled results near strong resistivity contrasts. There, simple linear interpolation may produce large errors, whereas higher‐order interpolation may lead to oscillatory behaviour in the interpolated result. We propose to use the essentially non‐oscillatory, piecewise polynomial interpolation scheme designed for piecewise smooth functions that contains discontinuities in the function itself or in its first or higher derivatives. The scheme uses a non‐linear adaptive algorithm to select a set of interpolation points that represent the smoothest part of the function among the sets of neighbouring points. We present numerical examples to demonstrate the usefulness of the scheme. The first example shows that the essentially non‐oscillatory interpolation (ENO) scheme better captures an isolated discontinuity. In the second example, we consider the case of sampling the electric field computed by a finite‐volume CSEM code at a receiver location. In this example, the ENO interpolation performs quite well. However, the overall error is dominated by the discretization error. The other examples consider the comparison between sampling with essentially non‐oscillatory interpolation and existing interpolation schemes. In these examples, essentially non‐oscillatory interpolation provides more accurate results than standard interpolation, especially near discontinuities.     

On the marine geochemistry of nickel

Nickel has been measured on four Geosecs profiles from the Atlantic and Pacific. The resulting distribution is oceanographically consistent: the concentration levels are over a factor of five lower than any previously reported. Values range from as low as 3 nmoles/kg in surface waters to 12 nmoles/kg in the deep North Pacific. The form of the Pacific profiles indicates that nickel is involved in the biogeochemical cycle and is regenerated both at shallow depths, like phosphate and in the deep waters like silicate. The oceanic residence time is ca. 10,000 years. While ferromanganese phases may be the ultimate sink for nickel they do not control its distribution in the water column.     

Chemical features of the Luna 16 regolith sample

The Luna 16 regolith sample differs from Apollo 11, 12 and 14 regolith and basalt samples by having smaller negative Eu and Sr anomalies and nearly chondritic Eu/Sm and Eu/Sr ratios although the overall REE, Ba, Sr and U concentrations are 25 to 45 times chondrites. Major element data, in particular FeO vs. Al₂O₃, show that the Luna 16 regolith sample is composed of materials that follow a quantitatively different Fe/Al variation than do Apollo 11, 12, 14 and 15 samples. The small Eu and Sr anomalies and the displaced Fe/Al variation are two chemical features unique to the Luna 16 regolith sample. The Luna 16 regolith sample can contain little if any of the rock types abundant at Apollo sites, thus indicating that the unique chemical features are typical of local or nearby materials and indicate a separate petrogenetic province for major component rock types of the Luna 16 regolith.     

Development of continental margins of the Atlantic Ocean and successive breakup of the Pangaea-3 supercontinent

Comparative tectonic analysis of passive margins of the Atlantic Ocean has been performed. Tectonotypes of both volcanic and nonvolcanic margins are described, and their comparison with other passive Atlantic margins is given. The structural features of margins, peculiarities of magmatism, its sources and reasons for geochemical enrichment of melts are discussed. The important role of melting of the continental lithosphere in the development of magmatism is demonstrated. Enriched EM I and EM II sources are determined for the lower parts of the volcanic section, and a depleted or poorly enriched source is determined for the upper parts of the volcanic section based on isotope data. The conclusions of the paper relate to tectonic settings of the initial occurrence of magmatism and rifting and breakup during the period of opening of the Mesozoic Ocean. It was found out that breakup and magmatism at proximal margins led only to insignificant structural transformations and reduction of the thickness of the ancient continental crust, while very important magmatic events happened later in the distal zone. New growth of magmatic crust at the stage of continental breakup is determined as a typical feature of distal zones of the margins under study. The relationship of development of margins with the impact of deep plumes as the source of magmatic material or a heat source only is discussed. Progradation of the zone of extension and breakup into the areas of cold lithosphere of the Atlantic and the formation of a single tectonomagmatic system of the ocean are under consideration.     

Model of Formation and Development of Spring Thermal Bar

A mathematical model simulating the thermo- and hydrodynamic processes near the thermal bar in the period of lake warming in spring is considered. A closed system of Reynolds type equations is constructed based on the Navier–Stokes nonlinear system of equations using the Boussinesq approximation and a special technique for isolating large-scale structures in turbulent medium. The turbulent viscosity coefficient is evaluated in the course of problem solution. The results of calculations are shown to agree well with field observation data.     

Magnetic properties of basalts and geodynamics of the rift zone in the southern Red Sea

Magnetic properties of young rift basalts in the southern Red Sea are studied in detail. It is found that basalt samples dredged in the rift zone are characterized by a large spread in magnetic parameters. The magnetic properties of the basalts are shown to indicate a complex evolution of the Red Sea rift zone. Titanomagnetite grains of the basalts are mostly affected by single-phase oxidation processes and have preserved paleomagnetic information. However, basalts discovered near the rift axis yield evidence of multiphase oxidation of titanomagnetite grains, which is untypical of young oceanic basalts. These basalts have high Curie points and large values of the natural remanent magnetization and Koenigsberger parameter. The corresponding samples were taken in nontransform zones where rocks have experienced the action of significant tectonic forces and, moreover, anomalous geomagnetic field patterns correlate with the position of these zones. Using the magnetic properties of the basalts, the northern segment of the rift axis is relocated.     

Book reviews

Mineralium Deposita -     

The altitude dependence of the O2(A3Σu+) vibrational distribution in the terrestrial nightglow

A simple vibrational relaxation model which reproduces the observed altitude integrated vibrational distribution of the Herzberg I bands in the nightglow is used to derive the altitude profiles of the individual vibrational levels at 1 km intervals in the 85–115 km height range. The possible errors associated with using rocket-borne photometer measurements of a limited number of bands in the O₂(A³Σ_u⁺?X³Σ_g^?) system to infer the total Herzberg I emission profile are assessed.     

Mineralogy,petrology and chemistry of lithic fragments from Luna 20 fines: origin of the cumulate ANT suite and its relationship to high-alumina and mare basalts

Bulk analyses of 157 lithic fragments of igneous origin and analyses of their constituent minerals (plagioclase, pyroxene, olivine, Mg-Al spinel, chromite, ilmenite, armalcolite, baddeleyite, zirkelite, K-feldspar, interstitial glass high in SiO₂ and K₂O) have been used to characterize the lunar highland rock suites at the Luna 20 site. The predominant suite is composed of ANT (anorthositic-noritic-troctolitic) rocks, as found at previous Apollo and Luna sites. This suite consists of an early cumulate member, spinel troctolite, and later cumulate rocks which are gradational from anorthosite to noritic and troctolitic anorthosite to anorthositic norite and troctolite; anorthositic norite is the most abundant rock type and its composition is close to the average composition for the highland rocks at this site. Spinel troctolite is a distinctive member of this suite and is characterized by the presence of Mg-Al spinel, magnesian olivine (average, Fo₈₃), and plagioclase. High-alumina basalt with low alkali content is another important rock type and melt of this composition may be parental to the cumulate ANT suite. Alkalic high-alumina basalt (KREEP) was not found in our sample, but may be genetically related to the ANT suite in that it may have formed by partial melting of rocks similar to those of the ANT suite. Fractional crystallization of low alkali, high-alumina basalt probably cannot produce alkalic high-alumina basalt because the enrichment in KREEP component is many times greater than the simultaneous change in major element components. Formation of alkalic high-alumina basalt by mechanical mixing of ANT rocks with very KREEP-rich components is not likely because the high-alumina basalt suite falls on a cotectic in the anorthiteolivine-silica system. Mare basalts may also be genetically related in that they may have been derived by remelting of rocks formed from residual liquids of fractional crystallization of parental low-alkali, high-alumina basalt, plus mafic cumulate crystals; the resultant melt would have a negative Eu anomaly and high $\text{Fe}\text{Mg}$ and $\text{pyroxene}\text{plagioclase}$ ratios.