Using the pseudospectral technique on curved grids for 2D acoustic forward modelling1

The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ‘staircase fashion‘causing spurious diffractions. It is the aim of this work to eliminate these non-physical diffractions by using curved grids that generally follow the interfaces. A further advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled. One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so-called multiblock strategy). The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space. The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods.     

Pyroxene-melt equilibria

Using a literature survey of analyses of high-Ca pyroxene and co-existing silicate melt pairs and analyses of low-Ca pyroxene-silicate melt pairs, we have performed a thermodynamic analysis of pyroxene-melt equilibria. Three sets of mixing model pairs have been considered, based on two mixing models for liquid silicate solutions and two for pyroxene solid solutions. A modified version of a model developed by Bottinga and Weill (1972) for the mixing properties of silicate melts, in which the melt is considered to be composed of independent network-forming and network-modifying quasi-lattices, more successfully accounts for variations in melt composition than does a model which considers the melt to be composed of simple oxides which mix ideally. An empirical model for the mixing properties of pyroxenes, in which the M1 and M2 sites are considered to be equivalent and are combined as a hypothetical ‘M’ site, is as successful in accounting for variations in pyroxene composition at high temperatures as an ideal multisite mixing model.Using a variety of pyroxene-melt relations, and combinations of the mixing models outlined above, we have developed several pyroxene-melt and low-Ca pyroxene-high-Ca pyroxene geothermometers which have internally-consistent precisions of approximately ±20°C (1σ). One of the two-pyroxene geothermometers has been used to calculate ‘quench’ temperatures for a number of eucrites. Computed temperatures are subsolidus, and are consistent with independent geothermometers and with petrographic observations. The equations may also be used to calculate the composition of pyroxene crystallizing from a silicate melt of known composition, with or without independent knowledge of temperature. Internally consistent precisions vary, but are approximately ± 3 mol% Fs, ± 5 mol% En, and ±4 mol% Wo (all 1σ). These equations may have application in modeling the evolution of mineral compositions during differentiation of basaltic magmas, particularly terrestrial layered intrusions and the lunar magma ocean.     

Zur Lagerstättengenetischen Deutung der Isotopenverhältnisse am Blei und Schwefel

Zusammenfassung Es werden einige der Voraussetzungen untersucht, unter denen sich aus den Isotopenverhältnissen von Blei, Schwefel und anderen am Aufbau einer Lagerstätte beteiligten Elementen Aussagen über die Bildungsbedingungen und genetischen Zusammenhänge herleiten lassen.Am Blei interessiert in diesem Zusammenhang in erster Linie die Anomalie gegenüber demHolmes-Houtermanschen Bleimodell, während das Absolutalter nur zur Kontrolle bzw. zum Einhängen in das geologische Zeitschema benötigt wird. Auf die Entstehungsursachen der Anomalien wird im Abschnitt B eingegangen.Bei den leichteren Elementen — wie z. B. H, C, O und S — treten im Verlaufe geochemischer Prozesse Isotopen-Trenn-Effekte auf, und man kann daher aus den Isotopenverhältnissen bspw. auf eine voraufgegangene Teilnahme am exogenen Kreislauf schließen. Derartige Messungen sollen möglichst vollständig in die Untersuchungen einbezogen werden und wurden im vorliegenden Programm bereits für den Schwefel des Bleiglanzes (PbS) durchgeführt (Abschnitt C).Im Abschnitt D wird kurz auf die Meßtechnik eingegangen, und Abschnitt E gibt einen Überblick auf die Meßergebnisse an Lagerstätten des Westharzes (Oberharz, St. Andreasberg, Rammelsberg). Die Auswertung der Blei-Messungen (Abschnitt F) und Schwefel-Messungen (Abschnitt G) bringt für das gewählte Modell-Arbeitsgebiet interessante Ergänzungen der bekannten genetischen Zusammenhänge, so daß die Übertragung der Untersuchungstechnik auf andere Lagerstättengebiete nützlich erscheint.Die Messungen wurden größtenteils im Massenspektrometer-Laboratorium der Bundesanstalt für Bodenforschung, Hannover, durchgeführt. Das Probenmaterial stammt aus eigenen Aufsammlungen sowie aus den Sammlungen der Herren Berging. E.Bock, St. Andreasberg, Dr. E.Kraume, Goslar, und Prof. Dr. H.Rose, Hamburg. Außerdem wurden die ersten Teilergebnisse eines gemeinsam mit Herrn Dr.-Ing. H.Hüttenhain, Clausthal, begonnenen Untersuchungsprogramms verwertet.Ich möchte an dieser Stelle allen im Text genannten Herren für die Überlassung von Untersuchungsmaterial und für fruchtbare Anregungen danken, vor allen Dingen aber auch meinem bisherigen Kollegen, Herrn Dipl.-Phys. H.Lenz, sowie den Damen M.Fassbender, U.Rätsch und U.Römer für die Durchführung der zahlreichen Analysen und Auswertungen.     

Schwefelisotope im marinen Kreislauf und das δ34 S der früheren Meere

Zusammenfassung Durch Isotopenfraktionierung bei der bakteriellen Reduktion marinen Sulfats enthalten die Sedimente im Mittel einen Überschuß an³²S (³⁴S s – 5), während³²S im marinen Sulfat angereichert ist. Der ³⁴S-Wert im heutigen Meerwasser beträgt etwa + 20 . Evaporit-³⁴S-Messungen zeigen, daß dieser Wert im Cambrium, Silur und Devon höher war, bis zum Perm dann auf etwa + 11 abnahm und anschließend wieder zum heutigen Wert anstieg.Der hohe ⁴³S-Wert in der geologischen Frühzeit wird mit extremer Anreicherung biogener Sulfide in den Schwarzschiefern erklärt, der Abfall zum Perm mit Rückführung großer Mengen von Sediment-Schwefel im Laufe der caledonischen und varistischen Orogenesen und der Wiederanstieg im Erdmittelalter mit erneuter Anhäufung toniger Sedimente.Aufgrund modellmäßiger Abschätzungen und der Gesamtheit aller verfügbaren Meßwerte (etwa 800) wird versucht, die Entwicklungslinie des Meerwasser-³⁴S-Wertes zeichnerisch darzustellen.Hinweis auf praktische Bedeutung: Informationen über Stoffbilanz geologischer Vorgänge, Interpretation von ³⁴S-Meßwerten an normalen Gesteinen und Erzen, Zuordnung von Proben unbekannten Alters.

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Summary Due to an isotope fractionation involved in the bacterial reduction of marine sulfate the sediments as a whole contain an excess of³²S (³⁴S – 5), while marine sulfate is enriched in³⁴S. Recent seawater has ³⁴S + 20. Evaporite measurements indicate a still higher value in Cambrian, Silurian and Devonian time. Then the ³⁴S decreased to about + 11 in the Upper Permian and later on increased once more to the modern value.The accumulation of abnormally large quantities of biogenic sulfides in the slates of that era accounts for the high ³⁴S value in the early Palaeozoic. A considerable fraction of light sulfur has been brought back to the oceans by weathering solutions of the Caledonian and Variscan orogenies, and in Mesozoic times another accumulation of slates has taken place.From a synopsis of the data available (some 800) and from model estimations an attempt has been made to construct the marine sulfur gd³⁴S evolution curve. Some practical consequences are lined out: informations on material balance of geological processes, interpretation of ³⁴S-data of normal rocks and ores, sample dating in the case of doubtful age.

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Résumé Un fractionnement isotopique pendant la réduction bactérienne du sulfate marin a pour conséquence un excédent de³²S dans la masse totale des sédiments (³⁴S – 5) et un enrichissement de³⁴S dans le sulfate marin. Dans les océans actuels le ³⁴S est + 20 ; nous pouvons conclure des ³⁴S des échantillons de sulfates d'évaporites, qu'aux temps cambrien, silurien et dévonien cette valeur fut plus élevée. Puis elle a diminué jusqu'à + 11 au Permien supérieur pour remonter ensuite à la valeur actuelle.La valeur élevée de ³⁴S au Paléozoïque inférieur doit être expliquée par une accumulation extraordinaire de sulfures biogènes dans les ardoises noires de cette époque. La décomposition d'une fraction considérable de ces roches pendant les orogenèses calédonienne et varisque entraînait à l'océan du soufre léger. Au Mésozoïque une autre accumulation d'ardoises commençait. Par l'examen de toutes valeurs disponibles (environ 800) et par certaines estimations on a tenté de tracer la courbe de l'évolution de la valeur du ³⁴S marin.Quelques conséquences pratiques sont indiquées: informations sur le bilan matériel des procès sus-géologiques, interprétation des ³⁴S de roches et minerais normaux, datation d'échantillons d'âge problématique.

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. S³⁴ , , ( 2%); 1,1%. .

     

The Triassic Santa Juana Formation at the lower Biobío River, south central Chile

A sequence of Triassic rocks is exposed near the town of Concepción, Chile. These clastic strata are interpreted as the deposits of rivers, lakes, playas, and alluvial fans. The deposits comprise conglomerates, arkosic sandstones, and sand-, silt- and mudstones. Four facies associations comprising eight sedimentary facies can be distinguished. Plant fossils from the sedimentary sequence of the Santa Juana Formation indicate a Carnian age. The flora includes ferns (Gleichenites, Cladophlebis, Dictyophyllum, Thaumatopteris, Asterotheca, Saportaea) and seed ferns (Kurtziana, Antevsia, Dicroidium), ginkgophytes (Sphenobaiera), cycads (Pseudoctenis), conifers (Heidiphyllum, Telemachus, Rissikia), and gymnosperms of uncertain affinities (Linguifolium, Gontriglossa). Two new species are presented: Pseudoctenis santajuanensis and Gontriglossa reinerae.     

Thallium isotope composition of the upper continental crust and rivers—An investigation of the continental sources of dissolved marine thallium

The thallium (Tl) concentrations and isotope compositions of various river and estuarine waters, suspended riverine particulates and loess have been determined. These data are used to evaluate whether weathering reactions are associated with significant Tl isotope fractionation and to estimate the average Tl isotope composition of the upper continental crust as well as the mean Tl concentration and isotope composition of river water. Such parameters provide key constraints on the dissolved Tl fluxes to the oceans from rivers and mineral aerosols.The Tl isotope data for loess and suspended riverine detritus are relatively uniform with a mean of ε²⁰⁵Tl = −2.0 ± 0.3 (ε²⁰⁵Tl represents the deviation of the ²⁰⁵Tl/²⁰³Tl isotope ratio of a sample from NIST SRM 997 Tl in parts per 10⁴). For waters from four major and eight smaller rivers, the majority were found to have Tl concentrations between 1 and 7 ng/kg. Most have Tl isotope compositions very similar (within ±1.5 ε²⁰⁵Tl) to that deduced for the upper continental crust, which indicates that no significant Tl isotope fractionation occurs during weathering. Based on these results, it is estimated that rivers have a mean natural Tl concentration and isotope composition of 6 ± 4 ng/kg and ε²⁰⁵Tl = −2.5 ± 1.0, respectively.In the Amazon estuary, both additions and losses of Tl were observed, and these correlate with variations in Fe and Mn contents. The changes in Tl concentrations have much lower amplitudes, however, and are not associated with significant Tl isotope effects. In the Kalix estuary, the Tl concentrations and isotope compositions can be explained by two-component mixing between river water and a high-salinity end member that is enriched in Tl relative to seawater. These results indicate that Tl can display variable behavior in estuarine systems but large additions and losses of Tl were not observed in the present study.     

Performance of the In Situ Microcosm Technique for Measuring the Degradation of Organic Chemicals in Aquifers

An in situ microcosm (ISM) consists of a stainless steel cylinder isolating about 2 L of the aquifer and is equipped with valves allowing for loading and sampling from the ground surface. During the last five years, this technique has been used frequently to study the degradation of organic chemicals in polluted and pristine aquifers representing different redox environments. The ISM technique has great potential for providing field-relevant degradation potentials and rate constants, but care must be taken in using the equipment and interpreting the results. This paper provides details concerning the installation and operation of an ISM and presents experiences concerning data interpretation and monitoring of redox conditions.     

Response of ionospheric electric fields to variations in the interplanetary magnetic field

The STARE system (Scandinavian Twin Auroral Radar Experiment) provides estimates of electron drift velocities, and hence also of the electric field in the high-latitude E-region ionosphere between 65 and 70 degrees latitude. The occurrence of drift velocities larger than about 400 m/s (equivalent to an electric field of 20 mV/m) have been correlated with the magnitude of the Interplanetary Magnetic Field (IMF) components B_z and B_y at all local times. Observation days have been considered during which both southward (B_z<0) and northward (B_z>0) IMF occurred. The occurrence of electric fields larger than 20 mV/m increases with increases in B_z magnitudes when B_z<0. It is found that the effects of southward IMF continue for some time following the northward turnings of the IMF. In order to eliminate such residual effects for B_z<0, we have, in the second part of the study, considered those days which were characterized by a pure northward IMF. The occurrence is considerably lower during times when B_z>0, than during those when B_z is negative. These results are related to the expansion and contraction of the auroral oval. The different percentage occurrences of large electric field for B_y>0 and B_y<0 components of the IMF during times when B_z>0, clearly display a dawn-dusk asymmetry of plasma flow in the ionosphere. The effects of the time-varying solar-wind speed, density, IMF fluctuations, and magnetospheric substorms on the occurrence of auroral-backscatter observations are also discussed.