The Bingham distribution of quaternions and its spherical radon transform in texture analysis

被引：43

作者：

Kunze, K ^{[1
]}

Schaeben, H

机构：

[1] ETH, Dept Earth Sci, CH-8092 Zurich, Switzerland

[2] Univ Min & Technol, D-09596 Freiburg, Germany

来源：

MATHEMATICAL GEOLOGY | 2004年 / 36卷 / 08期

关键词：

rotations; crystallographic preferred orientations; texture components; fiber textures; pole figures; spherical statistics;

D O I：

10.1023/B:MATG.0000048799.56445.59

中图分类号：

P [天文学、地球科学];

学科分类号：

07 ;

摘要：

Spherical geometry of quaternions is employed to characterize the Bingham distribution on the 3-dimensional sphere S(3)subset of R-4 as being uniquely composed of a bipolar, a circular and a spherical component. A new parametrization of its dispersion parameters provides a classification of patterns of crystallographic preferred orientations (CPO, or textures). It is shown that the Bingham distribution can represent most types of ideal CPO patterns; in particular single component, fiber and surface textures are represented by rotationally invariant bipolar, circular and spherical distributions, respectively. Pole figures of given crystal directions are derived by the spherical Radon transform of the Bingham probability density function of rotations, which are displayed for general and special cases.

引用

页码：917 / 943

页数：27

共 27 条

[11]

Kuipers J.B., 1999, Quaternions and Rotation Sequences

[12]

KUNZE K, 1991, VEROFF ZENTRALINSTIT, V117

[13] STANDARD FUNCTIONS IN THE TEXTURE ANALYSIS [J].

MATTHIES, S .

PHYSICA STATUS SOLIDI B-BASIC RESEARCH, 1980, 101 (02) :K111-K115

[14] STANDARD DISTRIBUTIONS FOR THE CASE OF FIBER TEXTURES [J].

MATTHIES, S ;

HELMING, K ;

STEINKOPFF, T ;

KUNZE, K .

PHYSICA STATUS SOLIDI B-BASIC RESEARCH, 1988, 150 (01) :K1-K5

[15]

Matthies S., 1987, STANDARD DISTRIBUTIO

[16]

MEISTER L, 2004, IN PRESS MATH METHOD

[17] APPLICATION OF THE BINGHAM DISTRIBUTION FUNCTION IN PALEOMAGNETIC STUDIES [J].

ONSTOTT, TC .

JOURNAL OF GEOPHYSICAL RESEARCH, 1980, 85 (NB3) :1500-1510

[18]

PRENTICE MJ, 1980, J R STAT SOC B, V48, P214

[19] Texture approximation or texture modelling with components represented by the von Mises-Fisher matrix distribution on SO(3) and the Bingham distribution on S-+(4) [J].

Schaeben, H .

JOURNAL OF APPLIED CRYSTALLOGRAPHY, 1996, 29 (pt 5) :516-525

[20]

SCHAEBEN H, 1981, THESIS RWTH AACHEN

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