In its most elementary form the acoustic reciprocity principle states that an acoustic response remains the same when the source and receiver are interchanged. However, this is just a special case of a more general reciprocity theorem, already formulated in 1873 by Lord Rayleigh.

Click on the picture above for a brief overview. For a unified reciprocity formulation for diffusion, flow and waves in fluids, solids and fluid-saturated porous solids (including acousto-electric coupling), read Reciprocity theorems for diffusion, flow and waves.

Journal papers on reciprocity

Copyright: The authors and the publishers: Acoustical Society of America (Journal of the Acoustical Society of America), American Geophysical Union (Journal of Geophysical Research, Radio Science), American Society of Mechanical Engineers (Journal of Applied Mechanics), Elsevier (Wave Motion), Geophysical Press (Journal of Seismic Exploration), Hindawi Publishing Corporation (Advances in Mathematical Physics), IOP Publishing (EPL (Europhysics Letters)), MDPI (Applied Sciences, Symmetry), Plenum Publishing Corporation (Subsurface Sensing Technologies and Applications), Royal Astronomical Society (Geophysical Journal International), Royal Society (Proceedings of the Royal Society A), Society of Exploration Geophysicists (Geophysics, The Leading Edge), Society for Industrial and Applied Mathematics (SIAM Journal on Imaging Sciences). These articles may be downloaded for personal use only. Any other use requires prior permission of the authors and the publishers.

(23) Wapenaar, K., 2025, Reciprocity and representation theorems for rotational seismology: under review.

(22) Wapenaar, K., 2025, Green's functions, propagation invariants, reciprocity theorems, wave-field representations and propagator matrices in two-dimensional time-dependent materials: Proc. R. Soc. A, Vol. 481, 20240479.

(21) Wapenaar, K., Aichele, J., and van Manen, D.J., 2024 Waves in space-dependent and time-dependent materials: A systematic comparison: Wave Motion, Vol. 130, 103374.

(20) Wapenaar, K., and Slob, E., 2022, Reciprocity and representations for wave fields in 3D inhomogeneous parity-time symmetric materials: Symmetry, Vol. 14 (11), 2236.

(19) Wapenaar, K., 2022, Wave-field representations with Green's functions, propagator matrices, and Marchenko-type focusing functions: J. Acoust. Soc. Am., Vol. 151 (1), 587-608. Copyright (2022) Author. This article is distributed under a Creative Commons Attribution (CC BY) License. The article appeared in JASA and may be found at doi.org/10.1121/10.0009236.

(18) Wapenaar, K., 2020, Reciprocity and representation theorems for flux- and field-normalised decomposed wave fields: Advances in Mathematical Physics, Vol. 2020, 9540135.

(17) Wapenaar, K., and Reinicke, C., 2019, Unified wave field retrieval and imaging method for inhomogeneous non-reciprocal media: J. Acoust. Soc. Am., Vol. 146 (1), 810-825. Copyright (2019) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The article appeared in JASA and may be found at doi.org/10.1121/1.5114912.

(16) Wapenaar, K., and Reinicke, C., 2019, An acoustic imaging method for layered non-reciprocal media: EPL (Europhysics Letters), Vol. 125, 34003.

(15) Wapenaar, K., 2019, Unified matrix-vector wave equation, reciprocity and representations: Geoph. J. Int., Vol. 216, 560-583

(14) Frijlink, M., and Wapenaar, K., 2010, Reciprocity theorems for one-way wave fields in curvilinear coordinate systems: SIAM Journal on Imaging Sciences, Vol. 3 (3), 390-415

(13) Wapenaar, K., 2007, General representations for wavefield modeling and inversion in geophysics: Geophysics, Vol. 72, SM5-SM17

(12) Wapenaar, K., 2006, Nonreciprocal Green's function retrieval by cross correlation: J. Acoust. Soc. Am., Vol. 120 (1), EL7-EL13.

(11) Wapenaar, K., Slob, E., and Fokkema, J., 2004, Reciprocity and power balance for piecewise continuous media with imperfect interfaces: Journal of Geophysical Research - Solid Earth, Vol. 109, B10301-1-B10301-9

(10) Wapenaar, K., and Fokkema, J., 2004. Reciprocity theorems for diffusion, flow and waves: A.S.M.E. Journal of Applied Mechanics, Vol. 71, p 145-150

(9) Wapenaar, K., Dillen, M., and Fokkema, J., 2003, Reciprocity theorems for electromagnetic one-way wave fields in 2-D inhomogeneous media: Subsurface Sensing Technologies and Applications, Vol. 4, p 101-115

(8) Wapenaar, K., 2003, Reciprocity theorems for seismoelectric waves: J. Seism. Expl., Vol. 12, p 103-112

(7) Wapenaar, C.P.A., Dillen, M.W.P., and Fokkema, J.T., 2001, Reciprocity theorems for electromagnetic or acoustic one-way wave fields in dissipative inhomogeneous media: Radio Science, Vol. 36 (5), 851-863.

(6) Wapenaar, K., Dillen, M., and Fokkema, J., 2001, Applying one-way reciprocity theorems in time-lapse seismic imaging: J. Seism. Expl., Vol. 10, 165-181.

(5) Wapenaar, K., and Fokkema, J., 2001, Reciprocity violated?: The Leading Edge, Vol. 20 (9), 1073.

(4) Wapenaar, K., 1998, Reciprocity properties of one-way propagators: Geophysics, Vol. 63, 1795-1798.

(3) Wapenaar, C.P.A., 1996, One-way representations of seismic data: Geoph. J. Int., Vol. 127, 178-188.

(2) Wapenaar, C.P.A., and Grimbergen, J.L.T., 1996, Reciprocity theorems for one-way wave fields: Geoph. J. Int., Vol. 127, 169-177.

(1) Wapenaar, C.P.A., 1996, Reciprocity theorems for two-way and one-way wave vectors: a comparison: J. Acoust. Soc. Am., Vol. 100 (6), 3508-3518.

Powerpoint presentations

Wapenaar, C.P.A., Slob, E.C., and Fokkema, J.T., 2004, Reciprocity and power balance for partially coupled interfaces: 66th annual EAGE meeting, Paris, H-039 abstract / presentation

Wapenaar, C.P.A., Dillen, M.W.P. and Fokkema, J.T., 2001, Elastodynamic reciprocity theorems for time-lapse seismic methods: 71st annual SEG meeting, San Antonio, 2053-2056 abstract / presentation

Wapenaar, C.P.A., Fokkema, J.T., Dillen, M.W.P. and Scherpenhuijsen, P., 2000, One-way acoustic reciprocity and its applications in multiple elimination and time-lapse seismics: 70th annual SEG meeting, Calgary, 2377-2380 abstract / presentation

Page last modified: November 2022