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A novel optimization‐based pole‐figure inversion method: comparison with WIMV and maximum entropy methods
Author(s) -
Bernier Joel V.,
Miller Matthew P.,
Boyce Donald E.
Publication year - 2006
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188980602468x
Subject(s) - algorithm , principle of maximum entropy , minification , inversion (geology) , mathematics , computer science , mathematical optimization , artificial intelligence , paleontology , structural basin , biology
An optimization‐based method for pole‐figure (PF) inversion that utilizes the orientation distribution function (ODF) gradient for conditional control of the solution is presented. The novel PF inversion method, coined the hybrid ‐seminorm minimization (HHSM), is empirically shown to be versatile, general and robust in the presence of simulated experimental errors. Finite elements (FE) and Rodrigues space are used for the representation and parameterization of the orientation space throughout. The versatility of the FE representation is significantly enhanced from previous implementations by introducing a method for obtaining discrete approximations to spherical harmonic modes from the local FE basis functions. A comparative study with similar implementations of the basic WIMV algorithm and the maximum entropy method is undertaken using several model ODFs of varying sharpness and symmetry. Randomly distributed noise is added to the synthetic PFs to simulate experimental errors and assess the stability of each method. Solution consistency is assessed by inverting two sets of measured PFs, one complete, one incomplete, using several meshes on the orientation space with an increasing number of degrees of freedom. The HHSM method is shown to compare favorably in tests with both the WIMV method and the maximum entropy method.