Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009geoji.179..319d&link_type=abstract
Geophysical Journal International, Volume 179, Issue 5606, pp. 319-332.
Astronomy and Astrophysics
Astronomy
1
Interferometry, Theoretical Seismology, Wave Scattering And Diffraction, Wave Propagation
Scientific paper
In this paper, generalized representation theorems for acoustic wavefields in perturbed media are derived from convolution- and correlation-type reciprocity theorems. These theorems allow calculation of the total wavefield in perturbed media from boundary integrals involving knowledge of the impulse responses due to monopole and dipole sources at the boundary only. The presented derivation makes explicit the close connection between the convolution-type reciprocity theorem and the Lippmann-Schwinger integral equation for the scattered field. The derivation of the correlation-type representation theorem leads to an expression for the total wavefield analogous to the Lippmann-Schwinger equation, but expressed in terms of the time-advanced Green's function instead. The generalized correlation-type representation theorem provides an alternative method to obtain virtual-source time-lapse seismic wavefields compared to the current method of differencing base and monitor virtual-source wavefields, while the convolution-type theorem has potential applications in non-linear inversions and time-lapse seismic feasibility studies for reservoir monitoring.
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