Pressure Normal Derivative Extraction for Arbitrarly Shaped Surfaces

The normal derivative of the pressure field at a recording surface has proven to be very useful information for deghosting and extrapolation of marine seismic data. The Kirchhoff Helmholtz integral with the Greens function source outside a (source free) closed surface relates the pressure field at the surface with its normal derivative. However, extracting the normal derivative of the pressure field 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 pressure measurement at notch frequencies are notoriously poor. In this paper, we present a method based on the Kirchhoff-Helmholtz integral equation for extracting the normal derivative of the pressure field (away from 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.