Moveout correction for irregular topography has been a longstanding challenge in processing seismic exploration data. Irregular topography usually results in large moveout among traces, a low signal-to-noise ratio (S/N), and difficulty in modeling near-surface velocities. Conventional normal moveout (NMO) corrections and elevation static methods are imprecise and tend to introduce significant errors for large offsets. Over the past two decades, several multiparameter time corrections and stacking techniques to reduce noise and improve resolution have been proposed in place of the classic NMO and common-midpoint stack. These include the common-reflection-surface (CRS), common-offset CRS, nonhyperbolic CRS, implicit CRS, multifocusing (MF), irregular surface MF (IS-MF), spherical MF (SMF), and common-offset MF methods. Various CRS-type operators that consider the top-surface topography have been proposed. For MF-type operators, only IS-MF can be applied directly to the irregular topography with no elevation statics required. In this study, we have developed a new MF formulation, modifying the SMF method to consider nonzero elevations of sources and receivers and we corrected moveout of nonplanar data directly without prior elevation static corrections. The proposed extension combines the sensitivity to spherical reflectors of SMF with the applicability of the IS-MF method to irregular topography. We investigated the behavior of the new operator using a physical model data set and compared the results with those from the conventional IS-MF method. The results revealed that the new operator is more robust over a wide range of source and receiver elevations and has advantages on strongly curved interfaces. We also confirmed the potential of the proposed approach by comparing stacking results for a real-land data set with a low S/N.

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