Optimization of Cell Parameterizations for Tomographic Inverse Problems

—?We develop algorithms for the construction of irregular cell (block) models for parameterization of tomographic inverse problems. The forward problem is defined on a regular basic grid of non-overlapping cells. The basic cells are used as building blocks for construction of non-overlapping irregular cells. The construction algorithms are not computationally intensive and not particularly complex, and, in general, allow for grid optimization where cell size is determined from scalar functions, e.g., measures of model sampling or a priori estimates of model resolution. The link between a particular cell j in the regular basic grid and its host cell k in the irregular grid is provided by a pointer array which implicitly defines the irregular cell model. The complex geometrical aspects of irregular cell models are not needed in the forward or in the inverse problem. The matrix system of tomographic equations is computed once on the regular basic cell model. After grid construction, the basic matrix equation is mapped using the pointer array on a new matrix equation in which the model vector relates directly to cells in the irregular model. Next, the mapped system can be solved on the irregular grid. This approach avoids forward computation on the complex geometry of irregular grids. Generally, grid optimization can aim at reducing the number of model parameters in volumes poorly sampled by the data while elsewhere retaining the power to resolve the smallest scales warranted by the data. Unnecessary overparameterization of the model space can be avoided and grid construction can aim at improving the conditioning of the inverse problem. We present simple theory and optimization algorithms in the context of seismic tomography and apply the methods to Rayleigh-wave group velocity inversion and global travel-time tomography.     

Diffraction of plane sh waves in a half-space

Scattering of antiplane shear waves (SH) in two dimensions by surface and near-surface defects in a homogeneous, isotropic elastic semi-infinite medium has been studied. Attention has been focused here in the range of medium to long wavelengths. A combined finite element and analytical technique has been used to study the problems of scattering by semi-circular and triangular canyons. The results for the former case are compared with the known exact solution and those for the latter case are compared with some available approximate solutions. Finally a problem of multiple scattering by a triangular canyon and a nearby circular tunnel is studied. Numerical results are presented showing the effects of multiple scattering and different angles of incidence. These results are of interest in earthquake engineering.     

Joint two-dimensional observations of ground magnetic and ionospheric electric fields associated with auroral zone currents: Current systems associated with local auroral break-ups

On 15 February, 1977, ground magnetic, ionospheric electric and auroral signatures of a multiple onset substorm were observed simultaneously by the Scandinavian Magnetometer Array (SMA), the Scandinavian Twin Auroral Radar Experiment (STARE) and the Finnish all-sky camera chain. Between 21:00 and 21:30 U.T., i.e. around local magnetic midnight, three consecutive local auroral break-ups were observed over Scandinavia. Each of these break-ups was preceded by a clear fading of the aurora and magnetic fields (while the electric fields remained unaffected), and occurred slightly south of the Harang discontinuity in the region of north-westward-directed electric fields. They were associated with a sudden change in direction of the electric field from north-west to south-west and the appearance of a westward equivalent current in the localized active region (about 1200 × 300 km²). These observations matched the features to be expected during the generation of a Cowling channel by a strong increase of the ionospheric conductivities due to precipitating auroral electrons. Numerical model calculations, based on the observations during the initial brightening and peak development of the second, most conspicuous break-up, show that the field-aligned currents at the northern and southern border of the active region are indeed very weak. However, highly localized and intense upward field-aligned currents at the western edge of the active region and more widespread and less intense downward currents in the eastern half preserve current continuity of the westward Cowling current and complete the substorm current wedge.     

An in situ XAS study of copper(I) transport as hydrosulfide complexes in hydrothermal solutions (25-592 °C, 180-600 bar): Speciation and solubility in vapor and liquid phases

Chloride and hydrosulfide are the principal ligands assumed to govern transport of copper in hydrothermal fluids. Existing solubility experiments suggest that Cu(I)-hydrosulfide complexes are dominant compared to chloride complexes at low salinities in alkaline solutions (H₂S_(aq)/HS⁻ pH buffer), and may be important in transporting Cu in low density magmatic vapors, potentially controlling the liquid-vapor partitioning of Cu. This study provides the first in situ evidence of the solubility of copper sulfides and the nature and structure of the predominant Cu species in sulfur-containing fluids at temperatures up to 592 °C and pressures of 180-600 bar. XANES and EXAFS data show that at elevated T (?200 °C), Cu solubility occurs via a linear Cu complex. At 428 °C in alkaline solutions, Cu is coordinated by two sulfur atoms in a distorted linear coordination (angle ∼150-160°). This geometry is consistent with the species predicted by earlier solubility studies. In addition, in situ measurements of the solubility of chalcocite in 2 m NaHS solutions performed in this study are in remarkably good agreement with the solubilities calculated using available thermodynamic data for Cu(I)-hydrosulfide complexes, also supporting the interpretation of speciation in these studies and validating the extrapolation of low-T thermodynamic properties for to high P-T. Data on phase separation for the 2 m NaHS solution show that while significant amounts of copper can be partitioned into the vapor phase, there is no indication for preferential partitioning of Cu into the vapor. This is consistent with recent partitioning experiments conducted in autoclaves by Pokrovski et al. (2008a) and Simon et al. (2006). XANES data suggest that the species present in the low density phase is very similar to that present in the high density liquid, i.e., , although Cu(HS)(H₂S)⁰ cannot be excluded on the basis of XAS data.     

Zur Bemessung unterirdischer Enteisenungsanlagen Teil 1: Chemisch-analytische Methoden der Erkundung und Bemessung

In underground deferrization processes there exists a dynamic cation exchange euquilibrium for Fe-II to the solid phase of the underground when an Fe-II containing ground water is delivered. Methods of investigation for the estimation of the initial oxygen demand and of the Fe-II content of the aquifer are tested and described in detail. At dynamic filtering tests and within the framework of technically simpler batch-tests the oxygen demand was higher than expected according to the stoichiometric Fe-II share. A relatively good agreement was obtained between the results of both procedures. Fe-II bound to solid matter is measured by a developed Fe-III difference method. Fe-II can be extracted and determined also directly with 1,10-phenanthroline. Moreover, the determination method of the distribution coefficient with its influencing factors is described. Finally, the results of regression relations are explained.     

Spectrum of cosmic fireballs

A progress report on cosmic fireballs is presented. The main new results are: (a) the phenomenon should be almost universal, and most explosive -ray sources should show the characteristic fireball spectrum; (b) even if the radiation density is insufficient, pair production in electron-proton or electron-electron scattering might start the fireball; (c) some computed fireball spectra are shown. They all have in common a 1/E low-energy behaviour, a 100 keV flattening, and a 0.5 MeV cut-off.Paper presented at the Symposium on Cosmic Gamma-Ray Bursts, held at Toulouse, France, 26–29 November, 1979.