On closest isotropic tensors and their norms

Noseworthy, Andrea D. (2018) On closest isotropic tensors and their norms. Masters thesis, Memorial University of Newfoundland.

[img] [English] PDF - Accepted Version
Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

Download (449kB)


Theoretical seismology, which is the subject of the thesis, could be viewed as a subject of continuum mechanics, whose mathematical structure relies on tensors. For instance, Hooke’s Law, which underlies the theory of elasticity—a branch of continuum mechanics—is a tensorial equation. A generally anisotropic tensor, obtained from physical measurements, can be approximated by another tensor belonging to a particular material-symmetry class. This tensor is referred to as the effective tensor; among all tensors in a particular symmetry class, it is the closest to the given anisotropic tensor. This ‘closeness’ that we refer to, draws upon the notion of a norm. In this thesis, we compare the effective tensors belonging to the isotropic symmetry class obtained using three different norms—the Frobenius-36, the Frobenius-21, and the operator norms. Furthermore, we utilize another method—a ‘L₂ slowness-curve fit’ method—and compare the results herein. Finally, we explore the associated errors and analyze the relationship between the mathematical and physical models.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/13207
Item ID: 13207
Additional Information: Includes bibliographical references (pages 49-51).
Keywords: Isotropic, Tensor, Norm
Department(s): Science, Faculty of > Earth Sciences
Date: March 2018
Date Type: Submission
Library of Congress Subject Heading: Seismology; Continuum mechanics; Calculus of tensors

Actions (login required)

View Item View Item


Downloads per month over the past year

View more statistics