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Download Geophysical Data Inversion Methods and Applications: by G. Wahba (auth.), Andreas Vogel, Charles O. Ofoegbu, Rudolf PDF

By G. Wahba (auth.), Andreas Vogel, Charles O. Ofoegbu, Rudolf Gorenflo, Bjorn Ursin (eds.)

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Read Online or Download Geophysical Data Inversion Methods and Applications: Proceedings of the 7th International Mathematical Geophysics Seminar held at the Free University of Berlin, February 8–11, 1989 PDF

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Additional resources for Geophysical Data Inversion Methods and Applications: Proceedings of the 7th International Mathematical Geophysics Seminar held at the Free University of Berlin, February 8–11, 1989

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Thus, the orientation distribution is a mathematical approach of describing and quantifying anisotropy. Unfortunately, the orientation distribution function (odf) can generally not be measured directly. Therefore it is common practice to measure pole distribution functions (pdfs) of several distinct refiexions in X-ray or neutron diffraction experiments with a texture goniometer. Recovering the odf from its corresponding pdfs is then the crucial prerequisite of quantitative texture analysis. This mathematical problem of texture goniometry is essentially a projection problem because the measured pdfs represent integral properties of the specimen along given lines; it may also be addressed as a tomographical problem specified by the crystal and statistical specimen symmetries and the properties of the diffraction experiment.

Due to the specifics of the problem these are unable to recover the part of the odf represented by the odd terms of the (infinite) series expansion. g. 'In inversion procedure. This approach leads to a system of linear equations which is large, sparse, structureless, highly (colurnn)rank deficient, and often inconsistent. Its entropy maximizing solution is proposed here because it yields the least presumptive odf with the smallest information content consistent with the experimental data thus avoiding artificial components, especially "ghosts" caused by the specific properties of the diffraction experiment.

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