1887
Volume 33, Issue 4
  • ISSN: 0263-5046
  • E-ISSN: 1365-2397

Abstract

The representation of potential vector and tensor fields by 3 × 1 and 3 × 3 matrices of Cartesian components is ambiguous unless the coordinate directions are also specified, and in particular, whether the system is left- or right handed. In this paper we highlight the nature of the ambiguity, and suggest a unified approach to encompass any mixture of coordinate conventions. Failure to observe the correct conventions can lead to incorrect interpretation of the potential data, and the suggested protocols are a step towards data integrity. Tensors of rank one and of rank two, commonly referred to as vectors and tensors in geophysical contexts, are often recorded as data sets of 3 × 1 and 3 × 3 matrices of numerical Cartesian components. Surveys from different sources may, however, use different coordinate conventions, or the client may be unaware of the coordinate conventions assumed by the provider. In essence, vector and tensor array data are incomplete without also being accompanied by information stating the directions and ordering of the axes of the employed coordinate system. A commonly used system makes the use of North (N), East (E) and Down (D) coordinate directions. But is the ordering of the vector components END or NED? The first is for a lefthanded and the second for a right-handed co-ordinate system. The choice will affect the meaning of the vector and tensor component data. Moreover, standard vector operation software (in particular, cross product routines) assume right-handed reference systems, and can yield incorrect results for left-handed systems unless explicitly adjusted.

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/content/journals/0.3997/1365-2397.33.4.79749
2015-04-01
2021-10-17
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  • Article Type: Research Article
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