Dolerite intrusion morphology at Majuba Colliery, northeast Karoo Basin, Republic of South Africa

Dolerite sills, at times transgressive, and dykes are common at Majuba Colliery. Their behaviour within the Karoo stratigraphic pile limits and controls the effectiveness of extracting the deep-seated Gus coal seam. Due to the intrusion of dolerites, the coal seam elevation can vary by as much as 70 m. Data from 452 boreholes, 88 of which were drilled to granitic gneiss basement and data from the underground development were used to construct cross-sections through the colliery. Based on texture, geochemistry and mode of emplacement, there exist four different dolerite types (T1 to T4) at Majuba. These are intruded into sedimentary rocks of the Karoo Supergroup although one, the T3 dolerite, has been found intruded into basement gneiss. In the east, an ultramafic intrusion of pre-Karoo Supergroup age created a basement high. By far, the greatest number of dolerite sills intruded within a sandstone unit, and have identical sandstones in the footwall and hangingwall, rather than intruding along lithological boundaries.     

Lisbon earthquake scenarios: A review on uncertainties, from earthquake source to vulnerability modelling

This paper briefly reviews the main topics developed in the last 15 years dealing with advances on predicting earthquake scenarios for the Lisbon Region. These developments, which have been reverted into seismic scenario simulators, include the entire earthquake process, as different modules, from the seismic source to vulnerability modelling. Recent achievements in several modules are presented, describing the level of uncertainties associated with the source, attenuation, soil effect, typology classification and inventory of the building stock, and vulnerability assessment of each typology. One simplified model is shown, and results of other models are compared for two selected occurrence scenarios. The paper ends with a brief appointment on the selection of scenario types, a key point in the application of simulators, and highlights the issues where more research and development should be made to optimize the gains in knowledge and to reduce overall uncertainties.     

Linearized seismic waveform inversion using a multiple re-weighted least-squares method with QR preconditioning

Linearized inversion methods such as Gauss‐Newton and multiple re‐weighted least‐squares are iterative processes in which an update in the current model is computed as a function of data misfit and the gradient of data with respect to model parameters. The main advantage of those methods is their ability to refine the model parameters although they have a high computational cost for seismic inversion. In the Gauss‐Newton method a system of equations, corresponding to the sensitivity matrix, is solved in the least‐squares sense at each iteration, while in the multiple re‐weighted least‐squares method many systems are solved using the same sensitivity matrix. The sensitivity matrix arising from these methods is usually not sparse, thus limiting the use of standard preconditioners in the solution of the linearized systems. For reduction of the computational cost of the linearized inversion methods, we propose the use of preconditioners based on a partial orthogonalization of the columns of the sensitivity matrix. The new approach collapses a band of co‐diagonals of the normal equations matrix into the main diagonal, being equivalent to computing the least‐squares solution starting from a partial solution of the linear system. The preconditioning is driven by a bandwidth L which can be interpreted as the distance for which the correlation between model parameters is relevant. To illustrate the benefit of the proposed approach to the reduction of the computational cost of the inversion we apply the multiple re‐weighted least‐squares method to the 2D acoustic seismic waveform inversion problem. We verify the reduction in the number of iterations in the conjugate'gradient algorithm as the bandwidth of the preconditioners increases. This effect reduces the total computational cost of inversion as well.     

Final stages of N-body star cluster encounters

We performed numerical simulations of star cluster encounters with Hernquist's treecode on a CRAY YMP-2E computer. We used different initial conditions (relative positions and velocities, cluster sizes, masses and concentration degrees) with the total number of particles per simulation ranging from 4608 to 20 480. Long-term interaction stages (up to 1 Gyr) when the pair coalesces into a single cluster are compared with isolated LMC clusters. Evidence is found that, when seen in a favourable plane, these resulting clusters show elliptical shapes as a result of the disruption of one of the companions. These elliptical shapes are essentially time-independent, but they do depend on the initial structural parameters of the pair components. We also analysed the fraction of stars that are ejected to the field by the interaction. We found that this fraction can be almost 50 per cent for the disrupted cluster. These simulations can represent a possible mechanism with which to explain the ellipticity observed in several star clusters in the Magellanic Clouds.