Reciprocity theorems for One-way wave fields in curvilinear coordinate systems

SIAM Journal on Imaging Sciences

Volumn 3, Issue 3, 2010, Pages 390-415

  Frijlink, Martijn ^a,b   Wapenaar, Kees ^b  

^a PGS   (Netherlands)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Curvilinear coordinates; One way wave fields; Reciprocity theorems

Indexed keywords

BASIS VECTOR; CARTESIAN COORDINATE; CARTESIANS; CO-ORDINATE SYSTEM; COVARIANT; CURVILINEAR COORDINATE; CURVILINEAR COORDINATE SYSTEMS; LOCAL PROPERTY; MULTIPLE REFLECTIONS; ONE WAY WAVE EQUATIONS; ONE-WAY WAVE FIELDS; ORTHOGONAL DIRECTIONS; PROPAGATION EFFECT; PSEUDO-DIFFERENTIAL OPERATOR; RAPID VARIATION; RECIPROCITY THEOREM; TRANSVERSE DIRECTIONS; WAVEFIELDS;

MATHEMATICAL OPERATORS; VECTORS; WAVE PROPAGATION;

WAVE EQUATIONS;

EID: 78651543710     PISSN: None     EISSN: 19364954     Source Type: Journal    
DOI: 10.1137/080739185     Document Type: Article

References (34)

1. L. Amundsen, Elimination of free-surface related multiples without need of the source wavelet, Geophysics,66 (2001), pp. 327-341.
2. Y. M. Berezansky, Z. G. Sheftel, and G. F. Us, Functional Analysis, Vol. I, Oper. Theory Adv.Appl. 85, Birkhäuser Verlag, Basel, 1996.
3. Y. M. Berezansky, Z. G. Sheftel, and G. F. Us, Functional Analysis, Vol. II, Oper. Theory Adv.Appl. 86, Birkhäuser Verlag, Basel, 1996.
4. J. W. Evans, Splitting methods and invariant imbedding for time-independent wave propagation in focusingmedia and wave guides, J. Math. Phys., 29 (1988), pp. 97-102.
5. J. T. Fokkema and P. M. van den Berg, Seismic Applications of Acoustic Reciprocity, Elsevier,Amsterdam, 1993.
6. M. O. Frijlink, R. G. van Borselen, and W. Sollner, On the free surface assumption for marinedata driven demultiple methods, in Extended Abstracts, 71st EAGE Conference and Exhibition,Amsterdam, 2009.
7. M. Frijlink and K. Wapenaar, Migration with correction for transmission losses in arbitrary homogeneousmedia, in SEG Expanded Abstracts, Vol. 32, Society of Exploration Geophysicists, 2004, pp.1029-1032.
8. Y. C. Fung and P. Tong, Classical and Computational Solid Mechanics, World Scientific, Singapore,2001.
9. M. Gustafsson, Wave Splitting in Direct and Inverse Scattering Problems, Ph.D. thesis, Lund University,Lund, Sweden, 2000.
10. A. J. Haines and M. V. de Hoop, An invariant imbedding analysis of general wave scattering problems,J. Math. Phys., 37 (1996), pp. 3854-3881.
11. M. V. de Hoop, Generalization of the Bremmer coupling series, J. Math. Phys., 37 (1996), pp. 3246-3282.
12. B. L. N. Kennett, Seismic Wave Propagation in Stratified Media, Cambridge University Press, Cambridge,UK, 1983.
13. W. A. Mulder, Rigorous redatuming, Geophys. J. Int., 161 (2005), pp. 401-415.
14. M. Reed and B. Simon, Methods of Modern Mathematical Physics. I. Functional Analysis, AcademicPress, New York, 1972.
15. M. Reed and B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness, Academic Press, New York, 1975.
16. M. Reed and B. Simon, Methods of Modern Mathematical Physics. III. Scattering Theory, AcademicPress, New York, 1979.
17. M. Reed and B. Simon, Methods of Modern Mathematical Physics. IV. Analysis of Operators, AcademicPress, New York, 1978.
18. P. Sava and S. Fomel, Riemannian wave field extrapolation, Geophysics, 70 (2005), pp. T45-T56.
19. G. T. Schuster, J. Yu, J. Sheng, and J. Rickett, Interferometric/daylight seismic imaging, Geophys.J. Int., 157 (2004), pp. 838-852.
20. R. Snieder, J. Sheiman, and R. Calvert, Equivalence of the virtual-source method and wave-fielddeconvolution in seismic interferometry, Phys. Rev. E, 73 (2006), 066620.
21. J. W. Strutt (Baron Rayleigh), The Theory of Sound, Vol. II, 2nd ed., Macmillan, New York, 1896.
22. Z. Sun, Reconstruction of source and medium parameters via wave-splitting and Green function equations,SIAM J. Appl. Math., 56 (1996), pp. 1146-1163.
23. B. Ursin, Review of elastic and electromagnetic wave propagation in horizontally layered media, Geophysics,48 (1983), pp. 1063-1081.
24. R. G. van Borselen, J. T. Fokkema, and P. M. van den Berg, Surface-related multiple elimination,Geophysics, 61 (1996), pp. 202-210.
25. P. M. van den Berg and A. T. de Hoop, Reflection and transmission of electromagnetic waves at arough interface between two different media, IEEE Trans. Geosci. Remote Sensing, GE-22 (1984), pp.42-52.
26. D. J. Verschuur, A. J. Berkhout, and C. P. A. Wapenaar, Adaptive surface-related multiple elimination,Geophysics, 57 (1992), pp. 1166-1177.
27. C. P. A. Wapenaar, Reciprocity theorems for two-way and one-way wave vectors: A comparison, J.Acoust. Soc. Am., 100 (1996), pp. 3508-3518.
28. C. P. A. Wapenaar, One-way representations of seismic data, Geophys. J. Int., 127 (1996), pp. 178-188.
29. C. P. A. Wapenaar and J. L. T. Grimbergen, Reciprocity theorems for one-way wave fields, Geophys.J. Int., 127 (1996), pp. 169-177.
30. K. Wapenaar, Reciprocity properties of one-way propagators, Geophysics, 63 (1998), pp. 1795-1798.
31. K. Wapenaar, E. Slob, and R. Snieder, Seismic and electromagnetic controlled-source interferometryin dissipative media, Geophys. Prosp., 56 (2008), pp. 419-434.
32. K. Wapenaar, J. Thorbecke, and D. Draganov, Relations between reflection and transmission responsesof three-dimensional inhomogeneous media, Geophys. J. Int., 156 (2004), pp. 179-194.
33. V. H. Weston, Factorization of the wave equation in a nonplanar stratified medium, J. Math. Phys., 29(1988), pp. 36-45.
34. V. H. Weston and S. He, Wave splitting of the telegraph equation in R3 and its application to inversescattering, Inverse Problems, 9 (1993), pp. 789-812.