2D Green's theorem receiver deghosting in the (x-omega) domain using a depth-variable cable towards on-shore and ocean bottom application with variable topography

摘要

Green's theorem derived deghosting methods in the (x-ω) domain using flat cables have been successfully applied to synthetic and field data. Based on Green's theorem wavefield separation concepts, this paper derives a 2D acoustic receiver deghosting formula for a depth-variable cable assuming the shape of the cable is known. In numerical tests, the air-water boundary is assumed to be horizontal. We use the Cagniardde Hoop method to generate synthetic data on parabolic cables and on periodically semicircular cables, respectively. The normal derivative of the total field on the cable is assumed to be known and is estimated by finite difference. Numerical results show that current Green's theorem up/down separation formula for a constant depth cable remains useful for a mildly depth-variable cable. When the actual cable deviates significantly from horizontal, the horizontal cable formula produces serious errors and artifacts whereas the new formula produces an effective and satisfactory result. While the analysis and tests in this paper are based on nonhorizontal towed streamers, the motivation (and future work) is for on-shore and ocean bottom acquisition. Under these circumstances, the deviation from horizontal acquisition can be significant and the ability to accommodate a variable topography can have a considerably positive impact on subsequence processing and interpretation objectives.