The Transition from Three-Dimensional Embedding to Two-Dimensional Euler-Lagrange Deformation Tensor of the Second Kind: Variation of Curvature Measures

Based on the Stein formulation of changes of curvature parameters, we describe the changes of Riemann two-dimensional manifolds of surface geometries. The three-dimensional left and right Euclidean manifolds with the curvature parameters “geodetic curvature, normal curvature, geodetic torsion” characterize the embedding “Riemann to Euclid” or 2d into 3d. The variation in time of the Euler-Lagrange deformation tensor of the second kind, in short “curvature variation” is studied.     

Multivariate statistical analysis of deformation tensors: independent vs. correlated tensor observations

In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), stochastic behaviors of principal components of deformation tensors (strain tensor and tensor of change of curvature (TCC)), based on the intrinsic assumption of geometrical modeling of surface deformation analysis, are discussed. We divided the contents into two parts: In the first, we considered independent random vectors of repeated tensor measurements. In the second step, we considered correlations among repeated measurements. Then, covariance components between tensor elements by Helmert estimator, based on prior information of variance components, are estimated. As a case study, both assumptions are applied to the estimation of principal components of deformation rate tensor observations in Zagros region (Western Iran). The results of numerical analysis showed that greatest shortening is accommodated in oblique orientation (NS) with respect to the Main Recent Fault (MRF), northwest part of North Zagros, Central Iran block and MRF, respectively. Most of the extensions occurred in the east part of the belt. The pattern of eigenspace components of TCC shows highest positive values across the NW region, nearly in orthogonal direction to the MRF and Main Zagros Fault (MZF). The pattern has insignificant values in the Central Zagros. It takes the significant negative values across the SW part, especially along the SPF and Persian Gulf shore. The effect of non-independent observations on the estimation of eigenspace components of deformation tensors (strain tensor and TCC) shows that the estimation of covariance components has influence on the confidence intervals of eigenspace components, especially in seismically active regions of the belt (along the Persian Gulf shore, NW of the belt and region between the Central Iran block and MRF). The results demonstrate the importance of considering the correlation structure among the observations on statistical behavior of principal components of deformation tensors in seismically active regions.     

Modelling ocean wave climate with a Bayesian hierarchical space–time model and a log-transform of the data

Long-term trends in the ocean wave climate because of global warming are of major concern to many stakeholders within the maritime industries, and there is a need to take severe sea state conditions into account in design of marine structures and in marine operations. Various stochastic models of significant wave height are reported in the literature, but most are based on point measurements without exploiting the flexible framework of Bayesian hierarchical space–time models. This framework allows modelling of complex dependence structures in space and time and incorporation of physical features and prior knowledge, yet remains intuitive and easily interpreted. This paper presents a Bayesian hierarchical space–time model with a log-transform for significant wave height data for an area in the North Atlantic ocean. The different components of the model will be outlined, and the results from applying the model to data of different temporal resolutions will be discussed. Different model alternatives have been tried and long-term trends in the data have been identified for all model alternatives. Overall, these trends are in reasonable agreement and also agree fairly well with previous studies. The log-transform was included in order to account for observed heteroscedasticity in the data, and results are compared to previous results where a similar model was employed without a log-transform. Furthermore, a discussion of possible extensions to the model, e.g. incorporating regression terms with relevant meteorological data, will be presented.     

Upstream and downstream controls of recent avulsions on the Taquari megafan,Pantanal, south‐western Brazil

Avulsion, the natural relocation of a river, is a key process in the evolution of subaerial fans, river floodplains and deltas. The causes of avulsion are poorly understood, which is partly due to the scarcity of field studies of present avulsions. At present, two avulsions are occurring on the middle and lower Taquari megafan, Pantanal basin, south‐western Brazil. Here we present an analysis of the causes of these avulsions based on field and remote sensing data and show that avulsions on megafans can be controlled by both upstream and downstream processes. The middle fan avulsion (started in 1997–1998) is a result of upstream control: overbank aggradation was caused by the (variable) input of sandy sediment into the system, which caused channel‐belt superelevation and also created an easily erodible subsurface favouring bank retreat, crevassing, and scour of deep floodplain channels. The sandy subsurface in this area is inferred to have been a major factor in the causation of this avulsion under conditions of little gradient advantage. The lower fan avulsion (started c. 1990) results from interplay of upstream and downstream controls, the latter being related to the local base level (the Paraguay River floodplain) at the toe of the fan. Channel and overbank aggradation on the lower fan was influenced by fan sub‐lobe progradation and channel backfilling. Fan sub‐lobe progradation caused a significant gradient advantage of the avulsion channel over the parent channel. Avulsions are commonly supposed to be preferentially triggered by high‐magnitude floods, when there is considerable channel‐belt superelevation. However, both avulsions studied by us were triggered by small to average floods, with modest channel‐belt superelevation. We conclude that flood magnitude and channel‐belt superelevation have been overrated as causes of avulsion, and demonstrate additional causes that influence the growth of crevasses into avulsions. Copyright © 2012 John Wiley & Sons, Ltd.     

Volcanic evolution of Volcán Aucanquilcha: a long-lived dacite volcano in the Central Andes of northern Chile

Volcán Aucanquilcha, northern Chile, has produced ∼37 km³ of dacite (63–66 wt% silica), mainly as lavas with ubiquitous magmatic inclusions (59–62 wt% silica) over the last ∼1 million years. A pyroclastic flow deposit related to dome collapse occurs on the western side of the edifice and a debris avalanche deposit occurs on the eastern side. The >6,000-m high edifice defines a 9-km E–W ridge and lies at the center of a cluster of more than 15 volcanoes, the Aucanquilcha Volcanic Cluster, that has been active for at least the past 11 million years. The E–W alignment of vents is nearly orthogonal to the arc axis. A majority of Volcán Aucanquilcha was constructed during the first 200,000 years of eruption, whereas the last 800,000 years have added little additional volume. The peak eruptive rate during the edifice-building phases was ∼0.16 km³/ka and the later eruptive rate was ∼0.02 km³/ka. Comparable dacite volcanoes elsewhere show a similar pattern of high volcanic productivity during the early stages and punctuated rather than continuous activity. Volcán Aucanquilcha lavas are dominated by phenocrysts of plagioclase, accompanied by two populations of amphibole, biotite, clinopyroxene, Fe–Ti oxides and (or) orthopyroxene. Accessory phases include zircon, apatite and rare quartz and sanidine. One amphibole population is pargasite and the other is hornblende. The homogeneity of dacite lava from Volcán Aucanquilcha contrasts with the heterogeneity (52–66 wt% silica) at nearby Volcán Ollagüe, which has been active over roughly the same period of time. We attribute this homogeneity at Aucanquilcha to the thermal development of the crust underneath the volcano resulting from protracted magmatism there, whereas Volcán Ollagüe lacks this magmatic legacy.     

Proglacial sediment trapping in recently formed Silt Lake,upper Lillooet Valley,Coast Mountains,British Columbia

The sedimentology of proglacial Silt Lake was assessed by lake sediment coring and monitoring of lacustrine processes during a late‐summer period of high glacier melt to characterize sediment delivery from the heavily glacierized catchment and investigate the sediment trapping dynamics of this upland lake. A complete varve chronology was established for a distal basin of the lake which was exposed by Lillooet Glacier retreat between 1947 and 1962. The varve record showed decreasing sedimentation rates in the basin while the glacier retreated, and as the lake became free of ice contact in the early 1970s. Although recession has continued over recent decades, and glacier proximity to the lake has, therefore, continued decreasing, lacustrine sedimentation rates are now accelerating due to changing basin morphometry caused by delta progradation. Over shorter time scales, lake sedimentation patterns respond to changing runoff conditions, including late‐summer glacier melt intensity, intra‐annual flooding events, diumal runoff fluctuations, and within‐lake turbidity currents. Turbidity currents included quasi‐regular flows during high diurnal discharges and an episodic flushing of temporarily stored sediment from the sandur or delta at a time of low stage. Suspended sediment yield to Silt Lake is estimated to exceed 10³ Mg km^?2 a^?1, a magnitude that surpasses previous local and regional yield estimates for the glacierized headwaters of the Lillooet River valley. Since Silt Lake currently traps a significant prooportion of that upland sediment supply, and the trapping efficiency of the basin has been variable at decadal time scales, the formation and continued development of Lilt Lake has likely had a significant influence on downstream sediment delivery. Lacustrine sediment‐based proxies of long‐term hydroclimatic variability being developed in glacially distal settings should include provisions for dynamic sediment trapping effects in upstream water bodies that often form in the active proglacial environment. Copyright © 2008 John Wiley & Sons, Ltd.     

Multiple volcano deformation sources in a post-rifting period: 1989–2005 behaviour of Krafla,Iceland constrained by levelling,tilt and GPS observations

The Krafla rifting episode, which occurred in North Iceland in 1975–1984, was followed by inflation of a shallow magma chamber until 1989. At that time, gradual subsidence began above the magma chamber and has continued to the present at a declining rate. Pressure decrease in a shallow magma chamber is not the only source of deformation at Krafla, as other deformation processes are driven by exploitation of two geothermal fields, together with plate spreading. In addition, deep-seated magma accumulation appears to take place, with its centre ∼ 10 km north of the Krafla caldera. The relative strength of these sources has varied with time. New results from a levelling survey and GPS measurements in 2005 allow an updated view on the deformation field. Deformation rates spanning 2000–2005 are the lowest recorded in the 30-year history of geodetic studies at the volcano. The inferred rate of 2000–2005 subsidence related to processes in the shallow magma chamber is less than 0.3 cm/yr whereas it was ∼ 5 cm/yr in 1989–1992. Currently, the highest rate of subsidence takes place in the Leirbotnar area, within the Krafla caldera, and appears to be a result of geothermal exploitation.     

New Olivine Reference Material for In Situ Microanalysis

A new olivine reference material – MongOL Sh11‐2 – for in situ analysis has been prepared from the central portion of a large (20 × 20 × 10 cm) mantle peridotite xenolith from a ~ 0.5 My old basaltic breccia at Shavaryn‐Tsaram, Tariat region, central Mongolia. The xenolith is a fertile mantle lherzolite with minimal signs of alteration. Approximately 10 g of 0.5–2 mm gem quality olivine fragments were separated under binocular microscope and analysed by EPMA, LA‐ICP‐MS, SIMS and bulk analytical methods (ID‐ICP‐MS for Mg and Fe, XRF, ICP‐MS) for major, minor and trace elements at six institutions world‐wide. The results show that the olivine fragments are sufficiently homogeneous with respect to major (Mg, Fe, Si), minor and trace elements. Significant inhomogeneity was revealed only for phosphorus (homogeneity index of 12.4), whereas Li, Na, Al, Sc, Ti and Cr show minor inhomogeneity (homogeneity index of 1–2). The presence of some mineral and fluid‐melt micro‐inclusions may be responsible for the inconsistency in mass fractions obtained by in situ and bulk analytical methods for Al, Cu, Sr, Zr, Ga, Dy and Ho. Here we report reference and information values for twenty‐seven major, minor and trace elements.