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Several authors have noted problems when first-arriving traveltimes are used in prestack Kirchhoff migration. The method appears to fail when complex velocity models are used. A good example of this is the failure of first arrival traveltimes to image the Marmousi dataset [(Geoltrain and Brac,1993)]. This dataset was created specifically to test prestack velocity analysis and imaging algorithms [(Versteeg and Grau,1990)]. When the true velocity model was released, it became clear that the dataset could be imaged successfully with algorithms that used recursive extrapolation of the full wavefield but it was not well imaged by non-recursive Kirchhoff migration algorithms.There are two possible reasons for this:
1) Most Kirchhoff algorithms use first arriving traveltimes to approximate the full Green's function. The first arrivals may contain little energy. Imaging using these traveltimes does not coherently stack the most important parts of the wavefield.
2) The traveltimes are usually calculated in the high frequency limit. If the medium is dispersive these traveltimes will not be a good approximation to the traveltimes of the seismic wavefield.
In this paper I propose a method that addresses both of these limitations. As with most methods, the Green's functions are approximated by a single event model. The model is parameterized by a traveltime, amplitude and phase at each point. In my method the traveltime chosen is the traveltime of the maximum energy arrival not the first arrival. This is the best single event approximation to the full Green's function (in the L2 norm). The traveltime is not calculated from a solution to the eikonal equation. Instead the parameters are estimated from solutions to the Helmholtz equations at a few frequencies in the seismic frequency band. This ensures that the traveltimes chosen are representative of traveltimes for waves in that frequency band.