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

[1]

Altmann S.A., 1986, Rotations, Quaternions and Double Groups

[2] ANTIPODALLY SYMMETRIC DISTRIBUTION ON SPHERE [J].

BINGHAM, C .

ANNALS OF STATISTICS, 1974, 2 (06) :1201-1225

[3]

Bingham C., 1964, THESIS YALE U

[4]

BUNGE HJ, 1982, TEXTURE ANAL MAT SCI, P193

[5] The spherical X-ray transform [J].

Cerejeiras, P ;

Schaeben, H ;

Sommen, F .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2002, 25 (16-18) :1493-1507

[6]

ESCHNER T, 1994, TEXTURES GEOLOGICAL, P15

[7] UBER DIE IDEALEN ORIENTIERUNGEN EINER WALZTEXTUR [J].

GREWEN, J ;

WASSERMANN, G .

ACTA METALLURGICA, 1955, 3 (04) :354-360

[8]

Gurlebeck K., 1997, Quaternionic and Clifford Calculus for Physicists Engineers

[9] DIFFERENTIAL OPERATORS ON HOMOGENEOUS SPACES [J].

HELGASON, S .

ACTA MATHEMATICA, 1959, 102 (3-4) :239-299

[10]

HELGASON S, 1999, RADON TRANSFORM

← 1 2 3 →