Methodology and use of tensor invariants for satellite gravity gradiometry

Although its use is widespread in several other scientific disciplines, the theory of tensor invariants is only marginally adopted in gravity field modeling. We aim to close this gap by developing and applying the invariants approach for geopotential recovery. Gravitational tensor invariants are deduced from products of second-order derivatives of the gravitational potential. The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space. Thus, we refrain from the classical methods for satellite gravity gradiometry analysis, i.e., in terms of individual gravity gradients, in favor of the alternative invariants approach. The invariants approach requires a tailored processing strategy. Firstly, the non-linear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization and iterative solution of the resulting least-squares problem. From the computational point of view, efficient linearization by means of perturbation theory has been adopted. It only requires the computation of reference gravity gradients. Secondly, the deduced pseudo-observations are composed of all the gravitational tensor elements, all of which require a comparable level of accuracy. Additionally, implementation of the invariants method for large data sets is a challenging task. We show the fundamentals of tensor invariants theory adapted to satellite gradiometry. With regard to the GOCE (Gravity field and steady-state Ocean Circulation Explorer) satellite gradiometry mission, we demonstrate that the iterative parameter estimation process converges within only two iterations. Additionally, for the GOCE configuration, we show the invariants approach to be insensitive to the synthesis of unobserved gravity gradients.     

Bayesian estimation of seismic hazard for two sites in Switzerland

Seismic hazard analysis is based on data and models, which both are imprecise and uncertain. Especially the interpretation of historical information into earthquake parameters, e.g. earthquake size and location, yields ambiguous and imprecise data. Models based on probability distributions have been developed in order to quantify and represent these uncertainties. Nevertheless, the majority of the procedures applied in seismic hazard assessment do not take into account these uncertainties, nor do they show the variance of the results. Therefore, a procedure based on Bayesian statistics was developed to estimate return periods for different ground motion intensities (MSK scale).Bayesian techniques provide a mathematical model to estimate the distribution of random variables in presence of uncertainties. The developed method estimates the probability distribution of the number of occurrences in a Poisson process described by the parameter . The input data are the historical occurrences of intensities for a particular site, represented by a discrete probability distribution for each earthquake. The calculation of these historical occurrences requires a careful preparation of all input parameters, i.e. a modelling of their uncertainties. The obtained results show that the variance of the recurrence rate is smaller in regions with higher seismic activity than in less active regions. It can also be demonstrated that long return periods cannot be estimated with confidence, because the time period of observation is too short. This indicates that the long return periods obtained by seismic source methods only reflects the delineated seismic sources and the chosen earthquake size distribution law.     

Probability distribution of eigenspectra and eigendirections of a twodimensional,symmetric rank two random tensor

Let there be given a twodimensional symmetric rank two tensor of random type (examples:strain, stress) which is either directly observed or indirectly estimated from observations by an adjustment procedure. Under the assumption of normalityof tensor components we compute the joint probability density functionas well as the marginal probability density functionsof its eigenspectra (eigenvalues) and eigendirections (orientation parameters). Due to the nonlinearity of the relation between eigenspectra-eigendirections and the random tensor components, via the inverse nonlinear error propagationbiases and aliases of their first and centralized second moments (mean value, variance-covariance) are expressed in terms of Jacobianand Hessianmatrices. The joint probability density function and the first and second moments thus form the fundamental of hypothesis testing and qualify control of eigenspectra (eigenvalues, principal components) and eigendirections (orientation parameters, eigenvectors, principial direction) of a twodimensional, symmetric rank two random tensor.     

Sediment oxygen profiles in a super-oxygenated antarctic lake

Perennially ice-covered lakes are found in the McMurdo Dry Valleys of southern Victoria Land, Antarctica. In contrast to temperate lakes that have diurnal photic periods, antarctic (and arctic) lakes have a yearly photic period. An unusual feature of the antarctic lakes is the occurrence of O2 at supersaturated levels in certain portions of the water column. Here we report the first sediment O2 profiles obtained using a microelectrode from a perennially ice-covered antarctic lake. Sediment cores collected in January and October 1987 from Lake Hoare in Taylor Valley show oxygenation down to 15, and in some cases, 25 cm. The oxygenation of sediments several centimeters below the sediment-water interface is atypical for lake sediments and may be characteristic of perennially ice-covered lakes. There is a significant difference between the observed January and October sediment O2 profiles. Several explanations may account for the difference, including seasonality. A time-dependent model is presented which tests the feasibility of a seasonal cycle resulting from the long photoperiod and benthic primary production in sediments overlain by a highly oxygenated water column.     

Cycle anatomy and variability in the storm-dominated type cincinnatian (Upper Ordovician): coming to grips with cycle delineation and genesis

Although parasequence and sequence are scale-independent terms, they are frequently applied only to specific scales of cycles. For example, meter-scale cycles are commonly assumed to be parasequences or PACs. In the Upper Ordovician Kope and Fairview Formations of northern Kentucky, we examined a succession of 50 meter-scale cycles that have been variously interpreted as deepening-upward, shallowing-upward, or showing no relationship with water depth. Our analysis shows that these cycles, characterized by shifts in storm-bed proximality, are highly variable in their thickness and internal construction. Most cycles are best considered high-frequency sequences, because deepening-upward intervals are common, and many cycles contain evidence of abrupt basinward shifts in facies as expected at sequence boundaries. A minority fit the parasequence model of shallowing-upward cycles bounded by flooding surfaces. Larger, 20 m scale cycles are defined by systematic thickening and thinning trends of meter-scale cycles. However, meter-scale cycles do not display any systematic trends in cycle anatomy as a function of position within the 20 m cycles or position within the Kope and Fairview Formations. The high cycle variability and the lack of systematic stratigraphic organization with respect to longer-term cyclicity reflect either the irregularity of relative sea-level changes, the poor recording of sea-level changes in this deep-water setting, or the generation of these cycles by climate-induced cyclicity in storm intensity. These three mechanisms would generate similar patterns at the outcrop scale, so it is not possible at the present to distinguish between them.     

The Ms = 6.2, June 15, 1995 Aigion earthquake (Greece): evidence for low angle normal faulting in the Corinth rift

We present the results of a multidisciplinary study of the M_s = 6.2, 1995, June 15, Aigion earthquake (Gulf of Corinth, Greece). In order to constrain the rupture geometry, we used all available data from seismology (local, regional and teleseismic records of the mainshock and of aftershocks), geodesy (GPS and SAR interferometry), and tectonics. Part of these data were obtained during a postseismic field study consisting of the surveying of 24 GPS points, the temporary installation of 20 digital seismometers, and a detailed field investigation for surface fault break. The Aigion fault was the only fault onland which showed detectable breaks (< 4 cm). We relocated the mainshock hypocenter at 10 km in depth, 38 ° 21.7 N, 22 ° 12.0 E, about 15 km NNE to the damaged city of Aigion. The modeling of teleseismic P and SH waves provides a seismic moment M_o = 3.4 10¹⁸ N.m, a well constrained focal mechanism (strike 277 °, dip 33 °, rake – 77°), at a centroidal depth of 7.2 km, consistent with the NEIC and the revised Harvard determinations. It thus involved almost pure normal faulting in agreement with the tectonics of the Gulf. The horizontal GPS displacements corrected for the opening of the gulf (1.5 cm/year) show a well-resolved 7 cm northward motion above the hypocenter, which eliminates the possibility of a steep, south-dipping fault plane. Fitting the S-wave polarization at SERG, 10 km from the epicenter, with a 33° northward dipping plane implies a hypocentral depth greater than 10 km. The north dipping fault plane provides a poor fit to the GPS data at the southern points when a homogeneous elastic half-space is considered: the best fit geodetic model is obtained for a fault shallower by 2 km, assuming the same dip. We show with a two-dimensional model that this depth difference is probably due to the distorting effect of the shallow, low-rigidity sediments of the gulf and of its edges. The best-fit fault model, with dimensions 9 km E–W and 15 km along dip, and a 0.87 m uniform slip, fits InSAR data covering the time of the earthquake. The fault is located about 10 km east-northeast to the Aigion fault, whose surface breaks thus appears as secondary features. The rupture lasted 4 to 5 s, propagating southward and upward on a fault probably outcropping offshore, near the southern edge of the gulf. In the shallowest 4 km, the slip – if any – has not exceeded about 30 cm. This geometry implies a large directivity effect in Aigion, in agreement with the accelerogram aig which shows a short duration (2 s) and a large amplitude (0.5 g) of the direct S acceleration. This unusual low-angle normal faulting may have been favoured by a low-friction, high pore pressure fault zone, or by a rotation of the stress directions due to the possible dip towards the south of the brittle-ductile transition zone. This fault cannot be responsible for the long term topography of the rift, which is controlled by larger normal faults with larger dip angles, implying either a seldom, or a more recently started activity of such low angle faults in the central part of the rift.     

Early miocene post-collisional calc-alkaline magmatism along the easternmost segment of the periadriatic fault system (Slovenia and Croatia)

Summary Early Miocene calc-alkaline igneous rocks from the easternmost segment of the Periadriatic fault system can be subdivided into two series of different alkalinity: (1) Volcanics which occur in the vicinity of the Velenje-Rogatec Line range from high-alumina basalt via low-K and medium-K andesites to medium-K dacites. (2) In the Pohorje Mountains mafic rocks are lacking. A high-K tonalitic pluton crystallized at pressures of about 0.7 GPa as indicated by Al-in-hornblende barometry and accessory magmatic epidote. Rapid exhumation of the tonalite during dextral transtension along the Periadriatic fault system is indicated by tonalitic pebbles in Helvetian (?) clastic sediments. High-K andesitic to dacitic volcanics are interlayered with, and dikes cut, the clastic sediments.Compositional variations shown by the volcanics from the Velenje-Rogatec Line are consistent with fractionation of the observed phenocryst assemblages (olivine, plagioclase, clinopyroxene, orthopyroxene, titanomagnetite). Substantial fractionation of plagioclase is indicated by decreasing Sr/Nd and Sr/Y values and increasing negative Eu anomalies with increasing SiO₂. All samples have chondrite-normalized HREE > 9.6 and low (Tb/Yb)_n ratios (1.29–1.08). With increasing SiO₂, the abundances of HREE and Y (18 to 39 ppm) increase and those of Sc (32.5 to 20.9 ppm) decrease slightly. These features, together with low Hf/Lu and Zr/Y values (10.1–5.7 and 5.7–3.6, respectively), rule out garnet as a major fractionating phase. Since (La/Yb)_n values (3.24–6.59) do not increase with SiO₂ and chondrite-normalized REE patterns do not show concave-upward shapes, fractionation of amphibole was probably insignificant. Although Rb/Cs values ( 18) are generally low, a significant contribution by continental crustal materials to the magmas by an AFC process is suggested by negative correlations of Nb/U(7.16 to 3.14) and Nb/Th(2.14 to 0.87) values with SiO₂, as well as by low Hf/Ta(7.8–3.4), and in part also by K/Rb (340-71) and Zr/Rb (5.0–1.7) values.Rocks from the Pohorje Mountains have high abundances of U. Values of Nb/U and Nb/Th are low (3.55 to 1.85 and 1.27 to 0.64, respectively) and are negatively correlated with SiO₂. These features, in combination with high values of Ba/Nb (56 to 93), Ba/La (23–30), and Rb/Cs (19–56), as well as with previously published ¹⁸O values ( 9) for the tonalite indicate a substantial contribution of the continental crust to these magmas. High Sr abundances (455 to 984 ppm) and moderate negative Eu anomalies suggest that fractionation of plagioclase was of minor importance. Although the rocks have relatively low Sc (9.3 to 3.8 ppm) and Y (21 to 14 ppm) contents, low (Tb/Yb)_n values (1.67–1.14) indicate that garnet was not a major fractionating phase. Instead, fractionation of amphibole is a viable mechanism to explain the combination of high (La/Yb)_n (21.8–13.1) and low (Tb/Yb)_n.

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Untermiozäner, kalkalkaliner Post-Kollisions-Magmatismus entlang des östlichsten Segmentes des periadriatischen Störungssystems (Slowenien und Kroatien)

Zusammenfassung Untermiozäne Kalkalkali-Magmatite aus dem östlichen Bereich des Periadriatischen Lineaments gliedern sich in zwei Serien unterschiedlicher Alkalinität: (1) Entlang der Velenje-Rogatec-Linie treten High-Al-Basalte, Low-K- und Medium-K-Andesite und Medium-K-Dazite auf. (2) Im Pohorje-Gebirge, wo basische Magmatite fehlen, kristallisierte ein High-K-Tonalit bei Drücken von ca. 0.7 GPa (Al-in-Hornblende-Barometer, magmatischer Epidot). Gerölle dieses Tonalits in einer untermiozänen (Helvet?) klastischeu Abfolge belegen eine schnelle Heraushebung des Tonalits durch dextrale Transtension im östlichsten Bereich des periadriatischen Lineaments. Eingeschaltet in die klastischen Sedimente sind andesitische bis dazitische Pyroklastika und Laven sowie diskordante dazitische Gänge, die alle der High-K-Serie angehören.Die chemische Variation innerhalb der Vulkanitserie von der Velenje-Rogatec-Linie läßt sich durch Fraktionierung der Einsprenglingsminerale Olivin, Plagioklas, Klinopyroxen, Orthopyroxen und Titanomagnetit erklären. Abnehmende Sr/Nd- und Sr/Y-Werte und zunehmende negative Eu-Anomalien mit steigendem SiO₂ weisen auf eine bedeutende Plagioklas-Fraktionierung hin. Alle Vulkanite besitzen hohe Gehalte an schweren Seltenen Erden (chondritnormiert > 9.6) und geringe (Tb/Yb)_n-Werte (1.29–1.08). Mit zunehmendem SiO₂ nehmen die Gehalte an Yb(2.02 bis 4.30 ppm) und Y(18 bis 39 ppm) zu, während die Sc-Gehalte (32.5 bis 20.9 ppm) nur geringfügig abnehmen. Diese Charakteristika, zusammen mit geringen Hf/Lu- und Zr/Y-Werten (10.1–5.87 bzw. 5.7–3.6), schließen Granat als wesentliche, fraktionierende Phase aus. Da die (La/Yb)_n-Verhältnisse (3.24–6.59) nicht mit SiO₂ korrelieren und die chondritnormierten SeltenenErden-Muster keine nach oben konkaven Formen aufweisen, spielte die Fraktionierung von Amphibol keine wesentliche Rolle. Trotz geringer Rb/Cs-Werte ( 18) wird eine beträchtliche krustale Kontamination der Magmen angenommen. Für einen AFC-Prozeß sprechen negative Korrelationen von Nb/U(7.16–3.14) und Nb/Th(2.14–0.87) mit SiO₂ (bei steigenden Nb-, U- und Th-Gehalten), geringe Hf/Ta-Werte (7.8–4.3) und teilweise auch geringe K/Rb- (340-71) und Zr/Rb-Verhältnisse (5.0–1.7).Die Magmatite des Pohorje-Gebirges weisen hohe U-Gehalte sowie geringe Nb/U-und Nb/Th-Verhältnisse auf (3.55–1.85 bzw. 1.27–0.64), die eine schwache negative Korrelation mit SiO₂ zeigen. Zusammen mit hohen Ba/Nb-(56–93), Ba/La-(23-30) und Rb/Cs-Verhältnissen (19–56) sowie bereits publizierten ⁸O-Werten ( 9) weisen diese Eigenschaften auf einen beträchtlichen Anteil assimilierten Krustenmaterials in den Magmen hin. Hohe Sr-Gehalte (455–984 ppm) und relativ geringe negative Eu-Anomalien machen es unwahrscheinlich, daß während des AFC-Prozesses in der Unterkruste wesentliche Mengen an Plagioklas fraktioniert wurden. Obwohl die Gehalte an Sc (9.3–3.8 ppm) und Y (21–14 ppm) relativ gering sind, scheidet Granat aufgrund der geringen (Tb/Yb)_n- Verhältnisse (1.67–1.14) als dominierende Fraktionierungsphase aus. Die Kombination von hohen (La/Yb)_n- Verhältnissen (21.8–13.1) und geringen (Tb/Yb)_n-Verhältnissen deutet eher auf Amphibol als wichtige, fraktionierende Phase hin.

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With 9 Figures     

The first record of dinosaurs in the Dalmatian part (Croatia) of the Adriatic-Dinaric carbonate platform (ADCP)

The first discovery of dinosaur footprints on the Dalmatian part of the Adriatic-Dinaric carbonate platform (ADCP) is reported. They constitute the geologically youngest record of footprints on the ADCP. The trackbearing layer was formed in the intertidal environment and represents the final stage of a shallowing-upward cycle. Just below it, a heavy dinoturbated limestone layer can be observed. Microfacies analysis, incorporating evidence from benthic foraminifera and algae, indicates a Late Turonian–Early Coniacian age. The overall morphology and size of the footprints points to sauropod dinosaurs; they represent the largest forms recorded so far on the ADCP. This hints at a prolonged sauropod presence on the platform and to its Late Cretaceous connection to the continent rather than isolation.     

Results from a Multi-disciplinary Sedimentary Pilot Study of Tectonic Lake Iznik (NW Turkey) – Geochemistry and Paleolimnology of the Recent Past

A limnogeological reconnaissance study was carried out on Lake Iznik, located in the southeast of the Marmara region of Turkey, involving a seismic survey and collection of short sediment cores. This lake is located on the middle branch of the North Anatolian Fault Zone (NAFZ), a transform plate boundary between the Eurasian and Anatolian Plates. It is, therefore, tectonically active and offers an opportunity to investigate the interplay of sedimentary and seismo-tectonic processes, as well as climate change and human impact in the region. Short cores of the three sub-basins, maximum length of 35.5 cm, recovered non-laminated, blackish clays and silts with varying amounts of biogenic and minerogenic (allochthonous, autochthonous) material, which documented almost the last 80 years of deposition and environmental history. High sedimentation rates in the deeper core sections are accompanied by changes in land use (conversion of woodland to farmland) in the northern areas of Lake Iznik, which caused the deposition of more weathered material (high K/Na ratios) and higher contents of Mn in the lake. A tendency towards eutrophic conditions within the last 20 years is indicated by high nutrient content (N, TOC, P), decreasing C/N-ratios, and characteristic diatom and cladoceran associations. Also increased pollution is revealed by higher Pb, Cu, and Zn contents and increased supply of human and animal faeces (high coprostanol content) during the last two decades. But simultaneous lower sedimentation rates towards the core tops complicate the reconstruction of recent and past eutrophication and pollution states of Lake Iznik. This requires an extension of the pilot study and deeper sediment cores, to recover non-anthropogenic influenced sediment levels.     

Laboratory Studies Of Wind Stress Over Surface Waves

Simultaneous laboratory observations of wind speed, wind stress, and surfacewind-wave spectra are made under a variety of wind forcing patterns using cleanwater as well as water containing an artificial surfactant. Under typical experimentalconditions, more than half of the total stress is supported by the wave-induced stressrather than by the surface viscous stress. When the surfactant reduces the shortwind-wave spectra, the wind stress also decreases by as much as 20–30% at agiven wind speed. When the wind forcing is modulated in time, the wind stresstends to be higher under decreasing wind than under increasing wind at a givenwind speed, mainly because the response of short wind-wave spectra to varyingwind forcing is delayed in time. These examples clearly demonstrate that therelationship between the wind speed and the wind stress can be significantlymodified if the surface wave field is not in equilibrium with the wind forcing.Next, we examine whether the wind stress is estimated accurately if the wave-inducedstress by all surface wave components is explicitly evaluated by linear superpositionand is added to the surface viscous stress. It is assumed that the surface viscous stressis uniquely related to the wind speed, and that the wind input rate is determined by thelocal, reduced turbulent stress rather than the total stress. Our wind stress estimatesincluding the wave contributions agree well with observed wind stress values, evenif the surface wave field is away from its equilibrium with the wind in the presenceof surface films and/or under time-transient wind forcing. These observations stronglysuggest that the wind stress is accurately evaluated as a sum of the wave-induced stressand the surface viscous stress. At very high winds, our stress estimates tend to be lowerthan the observations. We suspect that this is because of the enhancement of wind stressover very steep (or breaking) short wind-waves.