Time-space modeling of receiver ghost in the native acquisition coordinates: a step toward a non-Fourier-based deghosting

We provide a new theoretical contribution to the geophysical signal processing on how the ghost operator can be approximately analytically modeled. We derive a time-space-domain receiver ghost modeling operator for a wavefront traveling under a flat sea surface. The operator can be used to model the ghost wavefront on the native acquisition geometry without going into the temporal or spatial Fourier domain. We demonstrate the ghost operator with a multivariate generalization of the Gaussian function in conjunction with a hyperbolic traveltime function and compared it with modeled Green’s functions. This multivariate special function was specifically conceived for seismic data decomposition and promotes the signal cone of the data. Its composition with the hyperbolic traveltime function also ensures signal cone preservation and stable ghost operator computation. The ghost model derived is valid independent of streamer depth, i.e., for shallow as well as deep towed-streamer geometry, and it can also be extended to the source ghost. The proposed method, when combined with an appropriate data decomposition approach, provides a step toward developing deghosting algorithms in the native acquisition geometry with minimal user-defined parameters.