Print Email Facebook Twitter Reciprocity Theorems for One-Way Wave Fields in Curvilinear Coordinate Systems Title Reciprocity Theorems for One-Way Wave Fields in Curvilinear Coordinate Systems Author Frijlink, M. Wapenaar, C.P.A. Faculty Civil Engineering and Geosciences Department Geotechnology Date 2010-08-19 Abstract One-way wave equations conveniently describe wave propagation in media with discontinuous and/or rapid variations in one direction, but with smooth and slow variations in the complementary transverse directions. In the past, reciprocity theorems have been developed in terms of one-way wave fields. The boundaries of the integration volumes and the variations of the medium parameters must adhere to strict conditions. The variations must have the smoothness required by pseudodifferential operators, while the boundaries have to be flat. To extend the applicability to nonflat boundaries, this paper formulates one-way wave equations and corresponding reciprocity theorems in terms of curvilinear coordinates of the semiorthogonal (SO) type. In SO coordinate systems, one of the covariant basis vectors is orthogonal to the others, which can be nonorthogonal among each other. The same applies to the contravariant basis vectors. Furthermore, the orthogonal directions coincide; that is, the orthogonal co- and contravariant basis vectors coincide. SO coordinates are characterized by a local property of the basis vectors. An extra specification is necessary to make them conform in any way to nonflat boundaries. This can be done in terms of so-called lateral Cartesian (LC) coordinates. Cartesian coordinates are mapped to LC coordinates by applying an invertible transformation to one coordinate while keeping the others the same. LC coordinates are a straightforward means to describe or conform to nonflat boundaries. Applications of the extended reciprocity theorems include removal of multiple reflections, removal of complex propagation effects, wave field extrapolation, and synthesis of unrecorded data. Subject reciprocity theoremscurvilinear coordinatesone-way wave fields To reference this document use: http://resolver.tudelft.nl/uuid:82033a15-8402-4b47-b7ae-733b3a1f03ac DOI https://doi.org/10.1137/080739185 Publisher Society for Industrial and Applied Mathematics ISSN 1936-4954 Source SIAM Journal on Imaging Sciences, 3 (3), 2010 Part of collection Institutional Repository Document type journal article Rights (c) 2010 The Author(s)Society for Industrial and Applied Mathematics Files PDF Frijlink.pdf 307.02 KB Close viewer /islandora/object/uuid:82033a15-8402-4b47-b7ae-733b3a1f03ac/datastream/OBJ/view