Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.     

Controls on modern alluvial fan processes in the central Alps,northern Italy

Alluvial fan development in Alpine areas is often affected by catastrophic sedimentary processes associated with extreme ?oods events, causing serious risks for people living on the fans. Hazard assessment in these areas depends on proper identi?cation of the dominant sedimentary processes on the fans. Data from a set of 209 alluvial fans from the central Alps of Italy are presented in this paper and analysed with the help of various statistical techniques (linear regression, principal components analysis, cluster analysis, discriminant analysis and logistic regression). First, we used modern sedimentary facies and historical records (?ood events since 15th century), to distinguish between the two dominant sedimentary processes on alluvial fans: debris ?ows and stream?ows. Then, in order to analyse the main controls on past and present fan processes, 36 morphological, geological and land‐use variables were analysed. As with observations for arid‐environment fans, catchment morphology is the most in?uential factor in the study area, whereas geology and land use are minor controls. The role of climatic change and landsliding within the catchments also seems to be very important and is discussed. Statistical techniques also help in differentiating groups of alluvial fans by sets of controlling factors, including stage and type of evolution. Finally, by using discriminant analysis and logistic regression, we classi?ed alluvial fans according to the dominant sedimentary process, with a success rate ranging between 75 and 92 per cent. Copyright © 2004 John Wiley & Sons, Ltd.     

Large boulder accumulations by extreme waves along the Adriatic coast of southern Apulia (Italy)

The Adriatic coast of southern Apulia (Italy) is marked by the presence of large boulder accumulations. Boulders are up to 8 t in weight and arranged either in small groups or rows composed of a few imbricated elements. The lower surface of some of the boulders is covered by biogenic encrustation which suggests that they were possibly carved from the mid or sublittoral zone and that they capsized during their transport. Other boulders, detached from the supratidal zone, have their surface affected by tilted rock pools. New horizontal solution pans are continually forming.A detailed survey of a large boulder accumulation was carried out at Torre Santa Sabina. Direct observations were also made concerning the carving out and transportation of one single boulder during the severe storms in that area on January 4th, 2002 and on January 12th, 2003. Collated data from both the survey and the direct observations including some radiocarbon age determinations and hydrodynamic calculations suggest that the studied accumulation was due to the superimposed effects of one or two tsunami as well as of storm waves. Tsunami would be responsible for the detachment and transportation of the largest boulders, while storm waves may have been responsible for the carving out and transportation of the newer, smaller blocks and for moving once again the largest boulders. It was in this way that a typical boulder accumulation was produced.The collated data suggest that two tsunami may have recently struck the Adriatic coast of southern Apulia. The first possibly took place on the Dalmatian coast as a result of the earthquake on April 6, 1667 which destroyed Ragusa (modern day Dubrovnik). The second tsunami would have accompanied the strong earthquake which took place in southern Apulia on February 20, 1743.     

6: Classification of VMS deposits: Lessons from the South Uralides

VMS deposits of the South Urals developed within the evolving Urals palaeo-ocean between Silurian and Late Devonian times. Arc-continent collision between Baltica and the Magnitogorsk Zone (arc) in the south-western Urals effectively terminated submarine volcanism in the Magnitogorsk Zone with which the bulk of the VMS deposits are associated. The majority of the Urals VMS deposits formed within volcanic-dominated sequences in deep seawater settings. Preservation of macro and micro vent fauna in the sulphide bodies is both testament to the seafloor setting for much of the sulphides but also the exceptional degree of preservation and lack of metamorphic overprint of the deposits and host rocks. The deposits in the Urals have previously been classified in terms of tectonic setting, host rock associations and metal ratios in line with recent tectono-stratigraphic classifications. In addition to these broad classes, it is clear that in a number of the Urals settings, an evolution of the host volcanic stratigraphy is accompanied by an associated change in the metal ratios of the VMS deposits, a situation previously discussed, for example, in the Noranda district of Canada.Two key structural settings are implicated in the South Urals. The first is seen in a preserved marginal allochthon west of the Main Urals Fault where early arc tholeiites host Cu–Zn mineralization in deposits including Yaman Kasy, which is host to the oldest macro vent fauna assembly known to science. The second tectonic setting for the South Urals VMS is the Magnitogorsk arc where study has highlighted the presence of a preserved early forearc assemblage, arc tholeiite to calc-alkaline sequences and rifted arc bimodal tholeiite sequences. The boninitc rocks of the forearc host Cu–(Zn) and Cu–Co VMS deposits, the latter hosted in fragments within the Main Urals Fault Zone (MUFZ) which marks the line of arc-continent collision in Late Devonian times. The arc tholeiites host Cu–Zn deposits with an evolution to more calc-alkaline felsic volcanic sequences matched with a change to Zn–Pb–Cu polymetallic deposits, often gold-rich. Large rifts in the arc sequence are filled by thick bimodal tholeiite sequences, themselves often showing an evolution to a more calc-alkaline nature. These thick bimodal sequences are host to the largest of the Cu–Zn VMS deposits.The exceptional degree of preservation in the Urals has permitted the identification of early seafloor clastic and hydrolytic modification (here termed halmyrolysis sensu lato) to the sulphide assemblages prior to diagenesis and this results in large-scale modification to the primary VMS body, resulting in distinctive morphological and mineralogical sub-types of sulphide body superimposed upon the tectonic association classification.It is proposed that a better classification of seafloor VMS systems is thus achievable using a three stage classification based on (a) tectonic (hence bulk volcanic chemistry) association, (b) local volcanic chemical evolution within a single edifice and (c) seafloor reworking and halmyrolysis.     

Tetrahedral Plots of the Phase Relations for Basalts

The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.