CONCLUSIONS

I have presented a method for solving the frequency-dependent eikonal equation by extrapolating the phase-slowness function along the frequency axis. When terms dependent on ray density are dropped from the extrapolation equation, the extrapolation turns out to be a frequency-dependent smoothing of the medium slowness. This smoothing is non linear, and it is consistent with the wave equation.

I tested the accuracy of the solution of the frequency-dependent eikonal both in presence of wavefield focusing and defocusing. In both cases the results of modeling using the proposed method match the result of modeling using the wave equation significantly better than the solution of the conventional eikonal equation.

Kirchhoff migration and seismic tomography are among the applications that I believe should gain from using my method of computing frequency-dependent traveltimes. But, more investigations are needed for determining the limitations and benefits of applying the new method to either problem.