Numerical method for calculating the surface wave field in the presence of caustics

Due to the lateral heterogeneity of the upper layers of the Earth, paths of surface waves deviate from arcs of great circles. Because of the sphericity of the Earth, the paths intersect on a hemisphere opposite to the epicenter and form caustics consisting of two branches, with their tangent point being a cusp. For this reason, the field of surface waves cannot be analyzed in terms of the ray theory at distances larger than 90°. The asymptotic approach to the analysis of the field in the vicinity of such caustics is very ill-suited for numerical implementation. The difficulties of such an approach to the field calculation are aggravated by the fact that such caustics are superimposed in some regions. Therefore, it is suggested to use the theorem of representation, according to which the field within a certain contour is expressed as an integral whose integrand contains values of the function itself, its derivative along the normal to the contour, and Green’s function. The field on the contour (the circle bounding a hemisphere centered at the epicenter) is calculated by the ray method because rays do not intersect on this hemisphere. These data are used for the construction of the field on the opposite hemisphere assumed to be homogeneous, which enables the construction of Green’s function for this hemisphere. This limitation is not very stringent because the configuration of rays and caustics on this hemisphere is mainly determined by the field on the circle. The integral in the representation theorem is calculated numerically. Numerical examples are presented for models in which one caustic or two superimposed caustics form. These calculations yield constraints on variations in the amplitude and phase of the wave. Rayleigh wave fields are also calculated for a model of the real Earth. It is shown that, at some points, the Rayleigh wave spectrum can be strongly distorted because caustics corresponding to different periods differ in shape.     

A reassessment of the role of tidal dispersion in estuaries and bays

The role of tidal dispersion is reassessed, based on a consideration of the relevant physical mechanisms, particularly those elucidated by numerical simulations of tide-induced dispersion. It appears that the principal influence of tidal currents on dispersion occurs at length scales of the tidal excursion and smaller; thus the effectiveness of tidal dispersion depends on the relative scale of the tidal excursion to the spacing between major bathymetric and shoreline features. In estuaries where the typical spacing of topographic features is less than the tidal excursion, tidal dispersion may contribute significantly to the overall flushing. In estuaries and embayments in which the typical spacing between major features is larger than the tidal excursion, the influence of tidal dispersion will be localized, and it will not markedly contribute to overall flushing. Tidal dispersion is most pronounced in regions of abrupt topographic changes such as headlands and inlets, where flow separation occurs. The strong strain rate in the region of flow separation tends to stretch patches of fluid into long filaments, which are subsequently rolled up and distorted by the transient eddy field. The dispersion process accomplished by the tides varies strongly as a function of position and tidal phase and thus does not lend itself to parameterization by an eddy diffusion coefficient.     

Die mesozoische Magnafazies-Abfolge in den nördlichen Anden (Peru,Ekuador, Kolumbien)

Zusammenfassung Die weit über 100 sedimentären Formationen und Gruppen im mesozoischen epikontinentalen bis kontinentalen Oriente Andino der nördlichen Anden (Peru, Ekuador und Kolumbien) werden 6 zeitlich aufeinanderfolgenden Magnafazies-Einheiten zugeordnet. Dabei zeichnet sich deutlich eine einheitliche paläogeographisch-sedimentäre Entwicklung in den genannten Räumen ab, obwohl sich der geologische Bau der andinen West- bzw. Küstenkordilleren im Norden (Kolumbien, Ekuador) grundsätzlich vom Süden (Peru, Chile) unterscheidet.

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Over 100 sedimentary formations and groups are known from the epicontinental to continental Mesozoic (Oriente Andino sensu H.Bürgl) in the Andean region of Peru, Ecuador and Colombia. These lithostratigraphic (or facial) complexes are attached to 6 magnafacies-units which follow each other chronologically, thereby clearly evidencing a uniform paleogeographic-sedimentary development in the mentioned areas, although the geological structure of the Western respectively Coastal Cordilleras of the North (Colombia, Ecuador) is fundamentally different from that of the Southern ones (Peru, Chile).

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Resumen Más de 100 grupos y formaciones sedimentarios des »Oriente Andino« (sensu H.Bürgl) en los Andes septentrionales (PerÚ, Ecuador, Colombia) están asociados a 6 unidades magnafaciales que se suceden cronológicamente. Este »Oriente Andino« abarca las cuencas sedimentarias de tipo epicontiental a continental de la época mesozoica. Se bosqueja así claramente, en las áreas mencionadas, una evolución paleogeográfica-sedimentológica bastante uniforme, aunque las estructuras geológicas de las Cordilleras Occidentales (o Costeras, respectivamente) de la parte septentrional (Colombia, Ecuador) se diferencian fundamentalmente de las del Sur (PerÚ, Chile).

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100 Oriente Andine (, ) 6 . , ( , ) (, ).

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Der Verf. dankt der Deutschen Forschungsgemeinschaft (Bonn-Bad Godesberg) für Reisebeihilfen während der Jahre 1966 bis 1977.     

Chemical evolution of saline waters in the Jordan-Dead Sea transform and in adjoining areas

The Ca–Mg relationship in groundwaters strongly points to the overall dolomitization and local albitization. The Mg/Ca ratios reveal two trends by which saline waters develop: increase of Mg/Ca ratio by evaporation and decreasing Mg/Ca ratios due to dolomitization and albitization. Br/Cl vs. Na/Cl ratios demonstrate that albitization does not play a major role which leaves dolomitization to be the main source for decreasing Mg/Ca ratios in saline waters. In the eastern and southern Region of Lake Kinneret, salinization occurs by mixing with a Ca/Mg molar ratio <1 brine (Ha’On type). Along the western shoreline of the Lake, a Ca/Mg > 1 dominates, which developed by the albitization of plagioclase in abundant mafic volcanics and the dolomitization of limestones. The most saline groundwater of the Tabgha-, Fuliya-, and Tiberias clusters could be regional derivatives of at least two mother brines: in diluted form one is represented by Ha’On water, the other is a Na-rich brine of the Zemah type. Additionally, a deep-seated Ca-dominant brine may ascend along the fractures on the western side of Lake Kinneret, which is absent on the eastern side. Groundwaters of the Lower Jordan Valley are chemically different on both sides of the Jordan River, indicating that the exchange of water is insignificant. All saline waters from the Dead Sea and its surroundings represent a complex mixture of brines, and precipitation and local dissolution of halite and gypsum. Many wells of the Arava/Araba Valley pump groundwater from the Upper Cretaceous limestone aquifer, the origin of the water is actually from the Lower Cretaceous Kurnub Group sandstones. Groundwater drawn from the Quaternary alluvial fill either originates from Kurnub Group sandstones (Eilat 108, Yaalon 117) or from altered limestones of the Judea Group. The origin of these waters is from floods flowing through wadis incised into calcareous formations of the Judea Group. On the other hand, as a result of step-faulting, hydraulic contact is locally established between the Kurnub- and the Judea Groups aquifers facilitating the inter-aquifer flow of the confined Kurnub paleowater into the karstic formations of the Judea Group. Two periods of Neogene brine formation are considered: the post-Messinan inland lagoon resulting in drying up of the Sdom Sea and the evaporation of the Pleistocene Samra Lake, which went further through the stage of Lake Lisan to the present Dead Sea. For the first period, major element hydrochemistry suggests that the saline waters and brines in the Jordan-Dead Sea–Arava Valley transform evolved from the gradual evaporation of an accumulating mixture of sea-, ground-, and surface water. Due to the precipitation of carbonates, gypsum, and halite, such an evaporating primary water body was strongly enriched in Mg, Br, and B and shows high molar ratios of Br/Cl, B/Cl, and Mg/Ca but low Na/Cl ratios. The development of the Br/Cl ratio is chemically modelled, showing that indeed brine development is explicable that way. Along with the evaporation brine, evaporites formed which are leached by infiltrating fresh water yielding secondary brines with Na/Cl ratios of 1. When primary brines infiltrated the sub-surface, they were subjected to Mg–Ca exchange in limestones (dolomitization) and to chloritization and albitization in basic igneous rocks turning them into Ca-Cl brines. These tertiary brines are omnipresent in the Rift. The brines of the late Lisan and Dead Sea were generated by evaporating drainage waters, which leached halite, gypsum, and carbonates from the soil and from the sub-surface. All these brines are still being flushed out by meteoric water, resulting in saline groundwaters. This flushing is regionally enhanced by intensive groundwater exploitation. In variable proportions, the Neogene and late Lisan Lake and Recent Dead Sea brines have to be considered as the most serious sources of salinization of groundwaters in the Rift. Deep-seated pre-Sdom brines cannot strictly be excluded, but if active they play a negligible role only. An erratum to this article can be found at     

Discharge estimation of submarine springs in the Dead Sea based on velocity or density measurements in proximity to the water surface

The Dead Sea is a closed lake, the water level of which is lowering at an alarming rate of about 1 m/year. Factors difficult to determine in its water balance are evaporation and groundwater inflow, some of which emanate as submarine groundwater discharge. A vertical buoyant jet generated by the difference in densities between the groundwater and the Dead Sea brine forms at submarine spring outlets. To characterize this flow field and to determine its volumetric discharge, a system was developed to measure the velocity and density of the ascending submarine groundwater across the center of the stream along several horizontal sections and equidistant depths while divers sampled the spring. This was also undertaken on an artificial submarine spring with a known discharge to determine the quality of the measurements and the accuracy of the method. The underwater widening of the flow is linear and independent of the volumetric spring discharge. The temperature of the Dead Sea brine at lower layers primarily determines the temperature of the surface of the upwelling, produced above the jet flow, as the origin of the main mass of water in the submarine jet flow is Dead Sea brine. Based on the measurements, a model is presented to evaluate the distribution of velocity and solute density in the flow field of an emanating buoyant jet. This model allows the calculation of the volumetric submarine discharge, merely requiring either the maximum flow velocity or the minimal density at a given depth.     

Sediment transport and trapping in the Hudson River estuary

The Hudson River estuary has a pronounced turbidity maximum zone, in which rapid, short-term deposition of sediment occurs during and following the spring freshet. Water-column measurements of currents and suspended sediment were performed during the spring of 1999 to determine the rate and mechanisms of sediment transport and trapping in the estuary. The net convergence of sediment in the lower estuary was approximately 300,000 tons, consistent with an estimate based on sediment cores. The major input of sediment from the watershed occurred during the spring freshet, as expected. Unexpected, however, was that an even larger quantity of sediment was transported landward into the estuary during the 3-mo observation period. The landward movement was largely accomplished by tidal pumping (i.e., the correlation between concentration and velocity at tidal frequencies) during spring tides, when the concentrations were 5 to 10 times higher than during neap tides. The landward flux is not consistent with the long-term sediment budget, which requires a seaward flux at the mouth to account for the excess input from the watershed relative to net accumulation. The anomalous, landward transport in 1999 occurred in part because the freshet was relatively weak, and the freshet occurred during neapetides when sediment resuspension was minimal. An extreme freshet occurred during 1998, which may have provided a repository of sediment just seaward of the mouth that re-entered the estuary in 1999. The amplitude of the spring freshet and its timing with respect to the spring-neap cycle cause large interannual variations in estuarine sediment flux. These variations can result in the remobilization of previously deposited sediment, the mass of which may exceed the annual inputs from the watershed.     

A long-term volcanic hazard event tree for Teide-Pico Viejo stratovolcanoes (Tenerife,Canary Islands)

We propose a long-term volcanic hazards event tree for Teide-Pico Viejo stratovolcanoes, two complex alkaline composite volcanoes that have erupted 1.8–3 km³ of mafic and felsic magmas from different vent sites during the last 35 ka. This is the maximum period that can be investigated from surface geology and also represents an upper time limit for the appearance of the first phonolites on that volcano. The whole process of the event tree construction was divided into three stages. The first stage included the determination of the spatial probability of vent opening for basaltic and phonolitic eruptions, based on the available geological and geophysical data. The second, involved the analysis of the different eruption types that have characterised the volcanic activity from Teide during this period. The third stage focussed on the generation of the event tree from the information obtained in the two previous steps and from the application of a probabilistic analysis on the occurrence of each possible eruption type. As for other volcanoes, the structure of the Teide-Pico Viejo Event Tree was subdivided into several steps of eruptive progression from general to more specific events. The precursory phase was assumed as an unrest episode of any geologic origin (magmatic, hydrothermal or tectonic), which could be responsible for a clear increase of volcanic activity revealed by geophysical and geochemical monitoring. According to the present characteristics of Teide-Pico Viejo and their past history, we started by considering whether the unrest episode would lead to a sector collapse or not. If the sector collapse does not occur but an eruption is expected, this could be either from the central vents or from any of the volcanoes' flanks. In any of these cases, there are several possibilities according to what has been observed in the period considered in our study. In the case that a sector collapse occurs and is followed by an eruption we considered it as a flank eruption. We conducted an experts elicitation judgement to assign probabilities to the different possibilities indicated in the event tree. We assumed long term estimations based on existing geological and historical data for the last 35 Ka, which gave us a minimum estimate as the geological record for such a long period is incomplete. However, to estimate probabilities for a short term forecast, for example during an unrest episode, we would need to include in the event tree additional information from the monitoring networks, as any possible precursors that may be identified could tell us in which direction the system will evolve. Therefore, we propose to develop future versions of the event tree to include also the precursors that might be expected on each path during the initial stages of a new eruptive event.