Reciprocity and Representation Theorems for Flux- and Field-Normalised Decomposed Wave Fields

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
59 Downloads (Pure)


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.
Original languageEnglish
Article number9540135
Pages (from-to)1-15
Number of pages15
JournalAdvances in Mathematical Physics
Publication statusPublished - 2020


Dive into the research topics of 'Reciprocity and Representation Theorems for Flux- and Field-Normalised Decomposed Wave Fields'. Together they form a unique fingerprint.

Cite this