Depth extrapolation of seismic wavefields using cubic spline approximation

Depth extrapolation equation used for seismic migration is often solved by finite-difference technique. The most commonly used migration method is based upon the Crank-Nicolson implicit scheme. Some modifications to this scheme are in practice which improve the impulse response of the migration operator. In this paper we propose a different approach where the wavefield is approximated by cubic spline function. The approximation to second derivative resulting from this approach is similar to that of the 1/6th trick of Claerbout. There is another spline parameter θ which controls the nature of impulse response. The scheme is unconditionally stable for 0 5 1 0.. ≤ ≤θ. As the value of θ increases the dispersed evanescent energy gets more and more attenuated. The method is demonstrated by calculating the impulse response and by applying it to a synthetic data set