Extraction of the Normal Component of the Particle Velocity for Arbitrarly Shaped Surfaces

The normal component of the particle velocity (or the normal derivative of the pressure field) at the recording surface is an indispensable information when deghosting or extrapolating marine seismic data. However, the pressure field at the recording surface is related to the normal component of the particle velocity based on Kirchhoff-Helmholtz integral equation. Nevertheless, extracting the normal component of the particle velocity from the recorded pressure is not a trivial task. This is because; first, the Greens function containing the scattering information from a spatio-temporally varying sea surface must be known; and second, the signal-to-noise ratio of the pressure measurement at the notch frequencies are notoriously poor. We present a method based on Kirchhoff-Helmholtz integral equation for extracting the normal component of the particle velocity (away from the pressure notch locations for any arbitrarily shaped sea surfaces. The validity of the method is demonstrated using both synthetic and field datasets obtained using a dual-sensor streamer.