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.

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In marine seismic acquisition, the free surface generates seismic events in our recorded data that are often categorized as noise because these events do not contain independent information about the subsurface geology. Ghost events are considered as such noise because these events are generated when the energy generated by the seismic source, as well as any upgoing wavefield propagating upward from the subsurface, is reflected downward by the free surface. As a result, complex interference patterns between up-and downgoing wavefields are present in the recorded data, affecting the spectral bandwidth of the recorded data negatively. The interpretability of the data is then compromised, and hence it is desirable to remove the ghost events from the data. Rayleigh's reciprocity theorem is used to derive the relevant equations for wavefield decomposition for multisensor and single-sensor data, for depth-varying and depth-independent recordings from marine seismic experiments using a single-source or dual-source configuration. A comparison is made between the results obtained for a 2D synthetic example designed to highlight the strengths and weaknesses of the various acquisition configurations. It is demonstrated that, using the proposed wavefield decomposition method, multisensor data (measurements of pressure and particle velocity components, or multidepth pressure measurements) allow for optimal wavefield decomposition as independent measurements are used to eliminate the interference patterns caused by the free surface. Single-sensor data using constant-depth recordings are found to be incapable of producing satisfactory results in the presence of noise. Single-sensor data using a configuration with depth-varying measurements are able to deliver better results than when constant-depth recordings are used, but the results obtained are not of the same quality when multisensor data are used.

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