Let แ be the Lie algebra of vector fields on an affine smooth curve โบ. Our goal is to establish an orbit method for แ. Since แ is infinite-dimensional, we face some technical problems. Without having groups acting on แ, we try nevertheless to define the notion of ''orbits.'' So, we focus our attenti
Backus and gilbert method for vector fields
โ Scribed by Rolando Grave de Peralta Menendez; Sara L. Gonzalez Andino
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 46 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1065-9471
No coin nor oath required. For personal study only.
โฆ Synopsis
This report describes the theory of Backus and Gilbert with special emphasis for the case of vector fields as required for the solution of the electromagnetic inverse problem. A description of the method is presented with the detailed mathematical derivation of the coefficients that determine the solution for the retrieval of vector fields. Such derivation, to our knowledge, has never been reported in the literature. We also identify some crucial points that can (and had) lead to misuse of this solution and describe some disadvantages of this theory for the case of vector fields suggesting some alternatives to deal with them.
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