Probabilistic model for eruptions and associated flood events in the Katla caldera,Iceland

Eruptions in the subglacial Katla caldera, South Iceland, release catastrophic jokulhlaups (meltwater floods). The ice surface topography divides the caldera into three drainage sectors (Ko, So and En sectors) that drain onto Myrdalssandur, Solheimasandur and Markarfljot plains, respectively. In historical times, floods from the Ko sector have been dominant, with only two recorded So events. Geological records indicate that floods from the En sector occur every 500–800 years. A probabilistic model for an eruption is formulated in general terms by a stochastic parameter that simulates a series giving the time interval in years between two consecutive events. The model also contains a Markovian matrix that controls the location of the event and thereby what watercourse is hit by the flood. A record of Katla eruptions since the 8th and the 9th century a.d., and geological information of volcanogenic floods towards the west over the last 8,000 years is used to calibrate the model. The model is then used to find the probabilities for floods from the three sectors: Ko, So and En. The simulations predict that the most probable eruption interval for the En sector and the So sector is several times smaller than the average time interval, implying infrequent periods of high activity in these sectors. A correlation is found between the magnitude of eruptions and the following time intervals. Using the statistical approach and considering this magnitude–time interval correlation, the probability of an eruption in Katla volcano is considered to be 20% within the next 10 years. This compares to a probability of 93% if only a simple average is considered. These probabilities do not take account of long-term eruption precursors and should therefore be regarded as minimum values.     

Formation and development of normal-fault calderas and the initiation of large explosive eruptions

The ring fractures that form most collapse calderas are steeply inward-dipping shear fractures, i.e., normal faults. At the surface of the volcano within which the caldera fault forms, the tensile and shear stresses that generate the normal-fault caldera must peak at a certain radial distance from the surface point above the center of the source magma chamber of the volcano. Numerical results indicate that normal-fault calderas may initiate as a result of doming of an area containing a shallow sill-like magma chamber, provided that the area of doming is much larger than the cross-sectional area of the chamber and that the internal excess pressure in the chamber is smaller than that responsible for doming. This model is supported by the observation that many caldera collapses are preceded by a long period of doming over an area much larger than that of the subsequently formed caldera. When the caldera fault does not slip, eruptions from calderas are normally small. Nearly all large explosive eruptions, however, are associated with slip on caldera faults. During dip slip on, and doming of, a normal-fault caldera, the vertical stress on part of the underlying chamber suddenly decreases. This may lead to explosive bubble growth in this part of the magma chamber, provided its magma is gas rich. This bubble growth can generate an excess fluid pressure that is sufficiently high to drive a large fraction of the magma out of the chamber during an explosive eruption. Received: 2 January 1997 / Accepted: 22 April 1998     

Logical data modelling for geographical applications

Abstract.

A formal, yet practical, GeoRelational Data Model (GRDM) is presented for the logical database design phase of the development of spatial information systems. Geographic applications are viewed in the context of information systems development. The generic needs of modelling spatial data are analyzed; it is concluded that they are not served satisfactorily by existing data models, so specifications of modelling tools for spatial application design are given. GRDM provides a set of representational constructs (relations and layers for the logical schema; virtual layers, object classes and spatial constraints for the user views) on top of well-established models. It constitutes part of a full, easily automated application design methodology. Extensive examples demonstrate the relevance, and ease-of-use of the platform-independent GRDM.     

Structure of an active foreland fold and thrust belt,Papua New Guinea

Geological structure of the active foreland fold and thrust belt of Papua New Guinea has been interpreted using high-quality seismic-reflection data. Three en échelon anticlines, the Strickland, Cecilia and Wai Asi, are located along the frontal margin of the Papuan Fold Belt. All three are foreland-vergent and cut by hinterland-dipping thrust faults that sole into a common detachment beneath the Oligocene to Miocene Darai Limestone. Two of the anticlines are linked by a right-lateral transfer zone. Folding occurs primarily in the upper 2000 m of strata, which consist of Darai Limestone overlain by Miocene to Quaternary siliciclastic sedimentary rocks. Beneath the Darai Limestone lies the less-competent shaly Ieru Formation, which exhibits disharmonic folding and variable bed thickness. Seismic-reflection data clearly show that the Plio-Pleistocene upper Era Beds are deformed to the same extent as the underlying Darai Limestone, demonstrating that most of the observed deformation has occurred during the Late Pliocene and Pleistocene.     

Evolution of non-linear α 2-dynamos and taylor's constraint

A key non-linear mechanism in a strong-field geodynamo is that a finite amplitude magnetic field drives a flow through the Lorentz force in the momentum equation and this flow feeds back on the field-generation process in the magnetic induction equation, equilibrating the field. We make use of a simpler non-linear?α?²-dynamo to investigate this mechanism in a rapidly rotating fluid spherical shell. Neglecting inertia, we use a pseudo-spectral time-stepping procedure to solve the induction equation and the momentum equation with no-slip velocity boundary conditions for a finitely conducting inner core and an insulating mantle. We present calculations for Ekman numbers (E) in the range 2.5× 10^?3 to 5.0× 10^?5, for?α?=α ₀cos?θ?sin?π?(r?r_i ) (which vanishes on both inner and outer boundaries). Solutions are steady except at lower E and higher values of?α?₀. Then they are periodic with a reversing field and a characteristic rapid increase then equally rapid decrease in magnetic energy. We have investigated the mechanism for this and shown the influence of Taylor's constraint. We comment on the application of our findings to numerical hydrodynamic dynamos.     

Focusing patterns of seismicity with relocation and collapsing

Seismicity is generally concentrated on faults or in fault zones of varying, sometimes complex geometry. An earthquake catalog, compiled over time, contains useful information about this geometry, which can help understanding the tectonics of a region. Interpreting the geometrical distribution of events in a catalog is often complicated by the diffuseness of the earthquake locations. Here, we explore a number of strategies to reduce this diffuseness and hence simplify the seismicity pattern of an earthquake catalog. These strategies utilize information about event locations contained in their overall catalog distribution. They apply this distribution as an a priori constraint on relocations of the events, or as an attractor for each individual event in a collapsing scheme, and thereby focus the locations. The latter strategy is not a relocation strategy in a strict sense, although event foci are moved, because the movements are not driven by data misfit. Both strategies simplify the seismicity pattern of the catalog and may help to interpret it. A synthetic example and a real-data example from an aftershock sequence in south west Iceland are presented to demonstrate application of the strategies. Entropy is used to quantify their effect.     

Ellipticity corrections for seismic phases

The advent of broad-band seismology has meant that use is being made of a wide range of seismic phases, for many of which ellipticity corrections have not been readily available. In particular, when many seismic phases are used in location schemes, it is important that the systematic effects of ellipticity are included for each phase.
An efficient and effective procedure for constructing ellipticity corrections is to make use of the ray-based approach of Dziewonksi & Gilbert (1976), as reformulated by Doornbos (1988), in conjunction with the rapid evaluation of traveltimes and slownesses for a given range using the tauspline procedure of Buland & Chapman (1983).
Ellipticity coefficients have been tabulated for a wide range of seismic phases and are available in electronic form. The ellipticity correction procedures have been extended to include an allowance for diffraction phenomena, for example P _diff, S _diff diffracted along the core-mantle boundary. Corrections for additional phases can be generated by building the ellipticity coefficients from suitable combinations of the coefficients for different phase segments.