Open AccessSymplectic structure of wave‐equation imaging: a path‐integral approach based on the double‐square‐root equation
Author(s) -
De Hoop Maarten V.,
Le Rousseau Jérôme H.,
Biondi Biondo L.
Publication year - 2003
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.2003.01877.x
Subject(s) - square root , mathematical analysis , wave equation , mathematics , wavefront , operator (biology) , integral equation , physics , geometry , optics , biochemistry , chemistry , repressor , transcription factor , gene
SUMMARY We carry out high‐frequency analyses of Claerbout's double‐square‐root equation and its (numerical) solution procedures in heterogeneous media. We show that the double‐square‐root equation generates the adjoint of the single‐scattering modelling operator upon substituting the leading term of the generalized Bremmer series for the background Green function. This adjoint operator yields the process of ‘wave‐equation’ imaging. We finally decompose the wave‐equation imaging process into common image point gathers in accordance with the characteristic strips in the wavefront set of the data.