Pitfalls in Nonlinear Inversion

— We discuss and illustrate graphically with simple 2-D problems, four common pitfalls in geophysical nonlinear inversion. The first one establishes that the Lagrange multiplier, used to incorporate a priori information in the geophysical inverse problem, should be the largest value still compatible with a reasonable data fitting. This procedure should be used only when the interpreter is sure about the importance of the a priori information used to stabilize the inverse problem relative to the geophysical observations. Because this is rarely the case, the user should use the smallest Lagrange multiplier still producing stable solutions. The second pitfall is an attempt to automatically estimate the Lagrange multiplier by decreasing it along the iterative process used to solve the nonlinear optimization problem. Consequently, at the last iteration, the Lagrange multiplier may be so small that the problem may become ill-posed and any computed solution in this case is meaningless. The third pitfall is related to the incorporation of a priori information by a technique known as “Jumping.” This formulation, from the viewpoint of the class of Acceptable Gradient Methods, is incomplete and may lead to a premature halt in the iteration, and, consequently, to solutions far from the true one. Finally, the fourth pitfall is an inadequate convergence criterion which stops the iteration when the data misfit drops just below the noise level, irrespective of the fact that the functional to be minimized may not have attained its minimum. This means that the a priori information has not been completely incorporated, so that this stopping criterion partially neutralizes the effect of the stabilizing functional, and opens the possibility of obtaining unstable, meaningless estimates.     

The CP 2 Analytical Plotter

This paper examines the rationale behind the design and development of the CP 2 analytical plotter and shows how the final product, in terms of both hardware and software, has been influenced by the needs of a commercial air survey company.     

Efficient time truncation in two-dimensional bem analysis of transient wave propagation problems

An efficient time truncation algorithm for transient two-dimensional wave propagation analysis by the boundary element method is proposed. First the complete (without any truncation) formulation is reviewed and subsequently time truncation concepts are discussed. Three applications are presented, where the efficiency of complete and truncated algorithms is compared. The most important conclusions inferred from the numerical analyses are: (i) time truncation errors can be controlled and made as small as required and (ii) time truncation algorithms lead to considerable savings in both CPU time and storage area.     

An evaluation of proposed platinum group element contents in the parental magmas of the Bushveld complex

Samples collected by the authors and representing three proposed parental magmas of the Bushveld complex were analyzed for their platinum group element (PGE) contents by three different laboratories. Results differ strongly between laboratories, but imply that the parental magmas may have had flatter chondrite normalized patterns and an overall lower content than previously reported. It seems, however, that the Bushveld magmas were enriched in PGE's relative to average mafic rocks. A clear difference between the three magma types could not be substantiated. At present the PGE content of proposed parental melts of the Bushveld complex must be considered to be insufficiently known to warrant any quantitative models.     

Wie der Gesundheitsingenieur seine Zusammenarbeit mit dem Biologen sieht

Ohne Zusammenfassung     

An improved model of the condensation nucleus counter with stereo-photomicrographic recording

Summary A new model of the condensation nucleus counter with stereo-photomicrographic recording is described which is distinguished by perfect symmetry in its construction, reduced turbulence, two separate microscopes with photographic attachments and a novel dark-field illumination which eliminates completely fogging of the graticule even after prolonged use of the instrument. A view-finder microscope permits observations of the graticule so that the instrument can also be used for counting nuclei by eye. When the graticule is removed the droplets can be photographed in space stereoscopically.The use of the counter and its accessories is described and the dimensions and range of the instrument given.

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Zusammenfassung Es wird ein neues Model des Kondensationskernzählers mit stereo-photomikrographischer Registrierung beschrieben, welches sich durch vollkommene Symmetrie der Konstruktion, reduzierte Turbulenz, zwei gesonderte Mikroskope mit photographischen Zusatzeinrichtungen und einer neuartigen Dunkelfeldbeleuchtung auszeichnet, welche das Beschlagen der Zählplatte, selbst nach langem Gebrauche des Instrumentes, völlig eliminiert. Ein Suchermikroskop gestattet die Beobachtung des Zählglases, so dass das Instrument auch als Kernzähler für Augenbeobachtungen gebraucht werden kann. Wenn die Zählplatte entfernt wird, können die Tröpfchen im Raume stereoskopisch photographiert werden.Der Gebrauch des Kernzählers und seines Zugehörs wird beschrieben, sowie die Dimensionen des Instrumentes und der mit ihm mögliche Umfang der Kernzählungen angegeben.

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The research reported in this article has been sponsored and supported in part by the Geophysics Research Directorate of the Air Force Cambridge Research Center, Air Research and Development Command, United States Air Force, under Contract AF 61(052)-26, through the European Office, ARDC in Brussels.     

The atmospheric electric fog effect at de bilt

Summary In a polluted area, conductivity measurements do not provide significantly better fog forecasts than result from the trend of synoptic reports.