## Statistical Analysis of Spherical DataThis is the first comprehensive, yet clearly presented, account of statistical methods for analysing spherical data. The analysis of data, in the form of directions in space or of positions of points on a spherical surface, is required in many contexts in the earth sciences, astrophysics and other fields, yet the methodology required is disseminated throughout the literature. Statistical Analysis of Spherical Data aims to present a unified and up-to-date account of these methods for practical use. The emphasis is on applications rather than theory, with the statistical methods being illustrated throughout the book by data examples. |

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### Contents

Terminology and spherical coordinate systems | 17 |

Descriptive and ancillary methods and sampling problems | 29 |

Analysis of a single sample of unit vectors | 101 |

Analysis of a single sample of undirected lines | 152 |

Analysis of two or more samples of vectorial or axial data | 194 |

Correlation regression and temporalspatial analysis | 230 |

ii A test for serial association in a time series of unit axes | 243 |

Appendix A Tables and charts | 249 |

Appendix B Data sets | 278 |

312 | |

321 | |

### Common terms and phrases

approximate axes axial data calculate Chapter colatitude plot common mean direction computed concentration parameter confidence interval confidence region contour plot coordinate system Coordinates Source Analysis correlation corresponding Critical values data are listed Data Coordinates Source data in Figure data set defined described direction cosines discordant eigenvalues eigenvectors elliptical confidence cone Equal-area projection error exponential F-distribution Fisher distribution formal test given goodness-of-fit graphical Kent distribution linear magnetic remanence Mardia median methods modes normal distribution observations obtain orientation matrix outliers palaeomagnetic percentage points permutation test Plunge azimuth polar axis principal axis probability plot problems procedure Q-Q plot random variable References and footnotes rotational symmetry rotationally symmetric sample mean direction sample of data shown in Figure significance probability small circle specified value sphere spherical data Table test statistic tion turbidites uniform distribution unimodal distribution unit vectors vectorial data von Mises distribution Watson bipolar distribution