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.     

Correlation of seismic activity and fumarole temperature at the Mt. Merapi volcano (Indonesia) in 2000

In this paper we present densely sampled fumarole temperature data, recorded continuously at a high-temperature fumarole of Mt. Merapi volcano (Indonesia). These temperature time series are correlated with continuous records of rainfall and seismic waveform data collected at the Indonesian–German multi-parameter monitoring network. The correlation analysis of fumarole temperature and precipitation data shows a clear influence of tropical rain events on fumarole temperature. In addition, there is some evidence that rainfall may influence seismicity rates, indicating interaction of meteoric water with the volcanic system. Knowledge about such interactions is important, as lava dome instabilities caused by heavy-precipitation events may result in pyroclastic flows. Apart from the strong external influences on fumarole temperature and seismicity rate, which may conceal smaller signals caused by volcanic degassing processes, the analysis of fumarole temperature and seismic data indicates a statistically significant correlation between a certain type of seismic activity and an increase in fumarole temperature. This certain type of seismic activity consists of a seismic cluster of several high-frequency transients and an ultra-long-period signal (<0.002 Hz), which are best observed using a broadband seismometer deployed at a distance of 600 m from the active lava dome. The corresponding change in fumarole temperature starts a few minutes after the ultra-long-period signal and simultaneously with the high-frequency seismic cluster. The change in fumarole temperature, an increase of 5 °C on average, resembles a smoothed step. Fifty-four occurrences of simultaneous high-frequency seismic cluster, ultra-long period signal and increase of fumarole temperature have been identified in the data set from August 2000 to January 2001. The observed signals appear to correspond to degassing processes in the summit region of Mt. Merapi.     

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.     

Effects of spatially structured vegetation patterns on hillslope erosion in a semiarid Mediterranean environment: a simulation study

A general trend of decreasing soil loss rates with increasing vegetation cover fraction is widely accepted. Field observations and experimental work, however, show that the form of the cover‐erosion function can vary considerably, in particular for low cover conditions that prevail on arid and semiarid hillslopes. In this paper the structured spatial distribution of the vegetation cover and associated soil attributes is proposed as one of the possible causes of variation in cover–erosion relationships, in particular in dryland environments where patchy vegetation covers are common. A simulation approach was used to test the hypothesis that hillslope discharge and soil loss could be affected by variation in the spatial correlation structure of coupled vegetation cover and soil patterns alone. The Limburg Soil Erosion Model (LISEM) was parameterized and verified for a small catchment with discontinuous vegetation cover at Rambla Honda, SE Spain. Using the same parameter sets LISEM was subsequently used to simulate water and sediment fluxes on 1 ha hypothetical hillslopes with simulated spatial distributions of vegetation and soil parameters. Storms of constant rainfall intensity in the range of 30–70 mm h^?1 and 10–30 min duration were applied. To quantify the effect of the spatial correlation structure of the vegetation and soil patterns, predicted discharge and soil loss rates from hillslopes with spatially structured distributions of vegetation and soil parameters were compared with those from hillslopes with spatially uniform distributions. The results showed that the spatial organization of bare and vegetated surfaces alone can have a substantial impact on predicted storm discharge and erosion. In general, water and sediment yields from hillslopes with spatially structured distributions of vegetation and soil parameters were greater than from identical hillslopes with spatially uniform distributions. Within a storm the effect of spatially structured vegetation and soil patterns was observed to be highly dynamic, and to depend on rainfall intensity and slope gradient. Copyright © 2005 John Wiley & Sons, Ltd.     

A size classification for debris flows

A 10-fold classification for debris flow size is proposed based on total volume, peak discharge and area inundated by debris. Size classes can be used for regional overview studies where detailed site investigations are either unnecessary, too costly or where the highest hazard and risk creeks need to be identified for further study. They are also useful to compare the regional impact between affected areas and the effects of rainstorms, and they allow lay-people to obtain an understanding of debris flow magnitude and consequences. Finally, different size classes allow the estimation of travel times to points of interest based on empirically derived equations. It is proposed that agencies concerned with debris flows should establish a documentation of debris flow size according to this classification, which serves as a data base for hazard and risk planning.     

Eocene-Pliocene time scale and stratigraphy of the Upper Rhine Graben (URG) and the Swiss Molasse Basin (SMB)

We present a general stratigraphic synthesis for the Upper Rhine Graben (URG) and the Swiss Molasse Basin (SMB) from Eocene to Pliocene times. The stratigraphic data were compiled both from literature and from research carried out by the authors during the past 6 years ; an index of the stratigraphically most important localitites is provided. We distinguish 14 geographical areas from the Helvetic domain in the South to the Hanau Basin in the North. For each geographical area, we give a synthesis of the biostratigraphy, lithofacies, and chronostratigraphic ranges. The relationships between this stratigraphic record and the global sea-level changes are generally disturbed by the geodynamic (e.g., subsidence) evolution of the basins. However, global sea-level changes probably affected the dynamic of transgression–regression in the URG (e.g., Middle Pechelbronn Beds and Serie Grise corresponding with sea-level rise between Ru1/Ru2 and Ru2/Ru3 sequences, respectively) as well as in the Molasse basin (regression of the UMM corresponding with the sea-level drop at the Ch1 sequence). The URGENT-project (Upper Rhine Graben evolution and neotectonics) provided an unique opportunity to carry out and present this synthesis. Discussions with scientists addressing sedimentology, tectonics, geophysics and geochemistry permitted the comparison of the sedimentary history and stratigraphy of the basin with processes controlling its geodynamic evolution. Data presented here back up the palaeogeographic reconstructions presented in a companion paper by the same authors (see Berger et al. in Int J Earth Sci 2005).     

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.