Print Email Facebook Twitter Reciprocity and Representation Theorems for Flux- and Field-Normalised Decomposed Wave Fields Title Reciprocity and Representation Theorems for Flux- and Field-Normalised Decomposed Wave Fields Author Wapenaar, C.P.A. (TU Delft ImPhys/Acoustical Wavefield Imaging; TU Delft Applied Geophysics and Petrophysics) Date 2020 Abstract We consider wave propagation problems in which there is a preferred direction of propagation. To account for propagation in preferred directions, the wave equation is decomposed into a set of coupled equations for waves that propagate in opposite directions along the preferred axis. This decomposition is not unique. We discuss flux-normalised and field-normalised decomposition in a systematic way, analyse the symmetry properties of the decomposition operators, and use these symmetry properties to derive reciprocity theorems for the decomposed wave fields, for both types of normalisation. Based on the field-normalised reciprocity theorems, we derive representation theorems for decomposed wave fields. In particular, we derive double- and single-sided Kirchhoff-Helmholtz integrals for forward and backward propagation of decomposed wave fields. The single-sided Kirchhoff-Helmholtz integrals for backward propagation of field-normalised decomposed wave fields find applications in reflection imaging, accounting for multiple scattering. To reference this document use: http://resolver.tudelft.nl/uuid:4faefd4b-d45e-4859-a5d6-b17b3e0e177e DOI https://doi.org/10.1155/2020/9540135 ISSN 1687-9120 Source Advances in Mathematical Physics, 2020, 1-15 Part of collection Institutional Repository Document type journal article Rights © 2020 C.P.A. Wapenaar Files PDF AMP_20.pdf 968.78 KB Close viewer /islandora/object/uuid:4faefd4b-d45e-4859-a5d6-b17b3e0e177e/datastream/OBJ/view