A spatiotemporal ghost model and its action on the spatiotemporal special function C-Gaussian

The C-Gaussian function is a spatiotemporal multivariate special function whose Fourier transform is dominantly supported within a cone with its axis is centered along frequency, the dual of time with respect to Fourier transform. Its explicit analytic nature enables straight forward spatiotemporal differentiation as well as extrapolation. Unlike plane waves, which has infinite spatial extent, C-Gaussian function decays in space and time eliminating additional introduction of multiplicative windowing functions to control their support. Furthermore, C-Gaussian function in higher spatial dimensions can be obtained using its representation in lower spatial dimensions which makes it a candidate not only for data decomposition at acquisition but also for wavefield decomposition and wave propagation. Motivated by this, we derived a time-space-domain receiver ghost modeling operator for a wavefront propagating under a flat sea surface and computed its action on the C-Gaussian function composed with a hyperbolic traveltime function. The ghost operator can be used to model the ghost wavefront on the native acquisition geometry without going into the frequency-wavenumber domain, the dual of time-space with respect to Fourier transform. We compared our results with the analytically modeled Green’s functions.