Virtual signals combination - phase analysis for 2D and 3D data representation (acoustic medium)

We formulate the Kirchhoff-Helmholtz representation theory for the combinationof 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 virtualreflections from the total seismic-interferometry wavefield. The reliability of the com-bination result, relevant for seismic exploration, depends on the stationary-phase andlocal completeness in partial coverage regions. The analysis shows the differencesin the phase of the corresponding seismic interferometry (by cross-correlation) andvirtual reflector (by cross-convolution) signals obtained by 2D and 3D formulations,with synthetic examples performed to remove water layer multiples in ocean bottomseismic (OBS) acoustic data.