Green's function interpolations for prestack imaging

A new interpolation method is presented to estimate the Green's function values, taking into account the migration/inversion accuracy requirements and the trade-off between resolution and computing costs. The fundamental tool used for this technique is the Dix hyperbolic equation (DHE). The procedure, when applied to evaluate the Green's function for a real source position, uses the DHE to derive the root-mean-square velocity, v _RMS, from the precomputed traveltimes for the nearest virtual sources, and by linear interpolation generates v _RMS for the real source. Then, by applying the DHE again, the required traveltimes and geometrical spreading can be estimated.
The inversion of synthetic data demonstrates that the new interpolation yields excellent results which give a better qualitative and quantitative resolution of the imaging sections, compared with those carried out by conventional linear interpolation. Furthermore, the application to synthetic and real data demonstrates the ability of the technique to interpolate Green's functions from widely spaced virtual sources. Thus the proposed interpolation, besides improving the imaging results, also reduces the overall CPU time and the hard disk space required, hence decreasing the computational effort of the imaging algorithms.