Removal of surface-related wave phenomena - The marine case

Removal of the effects of the free surface from seismic reflection data is an essential preprocessing step before prestack migration. The problem can be formulated by means of Rayleigh's reciprocity theorem which leads to an integral equation of the second kind for the desired pressure field that does not include these free-surface effects. This integral equation can be solved numerically, both in the spatial domain and in the double Radon domain. Solving the integral equation in the double Radon domain has the advantage of reducing the computation time significantly since the kernel of the integral equation becomes dominant diagonally. Two methods are proposed to solve the integral equation: direct matrix inversion and a recursive subtraction of the free-surface multiples using a Neumann series. Both methods have been developed and tested on a synthetic data set, which was computed with the help of an independent forward-modeling scheme.