Publications

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The geometry of ray paths through realistic Earth models can be extremely complex due to the vertical and lateral heterogeneity of the velocity distribution within the models. Calculation of high fidelity ray paths and travel times through these models generally involves sophisticated algorithms that require significant assumptions and approximations. To test such algorithms it is desirable to have available analytic solutions for the geometry and travel time of rays through simpler velocity distributions against which the more complex algorithms can be compared. Also, in situations where computational performance requirements prohibit implementation of full 3D algorithms, it may be necessary to accept the accuracy limitations of analytic solutions in order to compute solutions that satisfy those requirements. Analytic solutions are described for the geometry and travel time of infinite frequency rays through radially symmetric 1D Earth models characterized by an inner sphere where the velocity distribution is given by the function V (r) = A-Br{sup 2}, optionally surrounded by some number of spherical shells of constant velocity. The mathematical basis of the calculations is described, sample calculations are presented, and results are compared to the Taup Toolkit of Crotwell et al. (1999). These solutions are useful for evaluating the fidelity of sophisticated 3D travel time calculators and in situations where performance requirements preclude the use of more computationally intensive calculators. It should be noted that most of the solutions presented are only quasi-analytic. Exact, closed form equations are derived but computation of solutions to specific problems generally require application of numerical integration or root finding techniques, which, while approximations, can be calculated to very high accuracy. Tolerances are set in the numerical algorithms such that computed travel time accuracies are better than 1 microsecond.

Mode-stirred chamber and anechoic chamber measurements were made on two sets of canonical test objects (cylindrical and rectangular) with varying numbers of thin slot apertures. The shielding effectiveness was compared to determine the level of correction needed to compensate the mode-stirred data to levels commensurate with anechoic data from the same test object.

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Er(D,T){sub 2-x} {sup 3}He{sub x}, erbium di-tritide, films of thicknesses 500 nm, 400 nm, 300 nm, 200 nm, and 100 nm were grown and analyzed by Transmission Electron Microscopy, X-Ray Diffraction, and Ion Beam Analysis to determine variations in film microstructure as a function of film thickness and age, due to the time-dependent build-up of {sup 3}He in the film from the radioactive decay of tritium. Several interesting features were observed: One, the amount of helium released as a function of film thickness is relatively constant. This suggests that the helium is being released only from the near surface region and that the helium is not diffusing to the surface from the bulk of the film. Two, lenticular helium bubbles are observed as a result of the radioactive decay of tritium into {sup 3}He. These bubbles grow along the [111] crystallographic direction. Three, a helium bubble free zone, or 'denuded zone' is observed near the surface. The size of this region is independent of film thickness. Four, an analysis of secondary diffraction spots in the Transmission Electron Microscopy study indicate that small erbium oxide precipitates, 5-10 nm in size, exist throughout the film. Further, all of the films had large erbium oxide inclusions, in many cases these inclusions span the depth of the film.