The free surface assumption for marine data-driven demultiple methods

In the past, integral formulations for marine data-driven demultiple methods have been derived from reciprocity theorems. Two fundamental assumptions in these derivations were that the sea-surface is flat and has a known reflection coefficient, often taken to be minus one. In this paper, we show that for dual sensor data these assumptions can be relaxed. The sea-surface has to obey the same conditions as any other reflecting boundary in the subsurface: it must be constant in time but shape and reflection strength can vary in space. For both surface-related multiple elimination, and multiple attenuation by multi-dimensional deconvolution, we derive integral equations that depend only on the measured pressure and particle velocity fields. Finally, we show there is an intimate connection between the integral equations for the methods.