By G. Wahba (auth.), Andreas Vogel, Charles O. Ofoegbu, Rudolf Gorenflo, Bjorn Ursin (eds.)
Read 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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Extra info 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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Lb) where y denotes the nxl observation vector, x the unknown mxl parameter vector, u the unknown nxl error vector, A the nxm coefficient matrix of rank q, 0 2 the unknown scalar variance component, and In the nxn identity matrix (after homogeneization); E means statistical "expectation" and D "dispersion". 2) which are not uniquely solvable due to the rank deficiency d := m - q > O. Of course, the integer d also describes the dimension of the nullspace N(A) thereby indicating the problem to be ill-posed.
Kaufmann. L. W .. 1976, Reort-hogonalizat-ion and st-able alg-orit,hms f'or updat,ing the Gram-Schmidt, QR-1'actorizat,ions. • 1"72-795. ).. Matemat-ikai es Ertesito 12, 457-472. V. •1968, Nonlinear Pl'ogranuning: Sequent-ial Unconst-rained Mnimizat-ion Techniques, John Wiley & Sons. New York. raint Optimization, John YOl'k-Toronto. Met-hods Wiley & of" Sons,. Optimizat-ion Chicest.. er-New Gill.. , Golub.. , Murray, W. orizat-ions.. Mat,hem. of' putation 28, 505-535. E. , 1978.. hem. '. 2. 1974.
University of Bonn, NuBallee 8, 5300 Bonn 1, FRG Abstract Anisotropic behavior of singlephase poly crystalline material is controlled by its constituent crystal grains and their spatial orientation within the specimen. More specifically, a macroscopic physical property in a given direction is the mean value of the corresponding property of the individual crystallites with respect to the statistical distribution of their orientations. Thus, the orientation distribution is a mathematical approach of describing and quantifying anisotropy.