We formulate the Kirchhoff-Helmholtz representation theory for the combination of seismic interferometry signals synthesized by cross-correlation and by cross- convolution in acoustic media. The approach estimates the phase of the virtual reflec- tions from the boundary encompassing a volume of interest and subtracts these virtual reflections from the total seismic-interferometry wavefield. The reliability of the com- bination result, relevant for seismic exploration, depends on the stationary-phase and local completeness in partial coverage regions. The analysis shows the differences in the phase of the corresponding seismic interferometry (by cross-correlation) and virtual reflector (by cross-convolution) signals obtained by 2D and 3D formulations, with synthetic examples performed to remove water layer multiples in ocean bottom seismic (OBS) acoustic data.
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