Deconvolution-Homomorphic or Predictive?

Both the methods of predictive as well as homomorphic deconvolution require an assumption about the phase characteristic of the source pulse. In the case of predictive deconvolution, the difficulty lies in the specification of the dispersive all-pass filter that converts the minimum-phase pulse estimate into the "correct" pulse estimate. In the case of homomorphic deconvolution, the difficulty arises in the specification of the cepstral cutoff quefrencies that produce the "correct" pulse estimate. Both approaches work up to a point, but neither yields a complete solution to the seismic-source pulse-estimation problem.