Amplitude and phase in DMO and MZO algorithms

Alexander M. Popovici

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ABSTRACT

In constant velocity, the sequence Dip Moveout (DMO), Normal Moveout (NMO), Stacking and Zero-Offset Migration (ZOM) is equivalent to Prestack Migration. In this context the Dip-Moveout correction can be expressed in two ways. First, DMO can be defined kinematically in time-space domain and implemented in Fourier domain (Hale 1983). Second, DMO can be defined as a process separated out of Prestack Migration, after eliminating the NMO, Stacking and ZOM steps.

I simplify the comparison between the two methods by incorporating the sequence DMO, NMO and Stacking into a single process named Migration to Zero-Offset (MZO). MZO is a kinematic process than can be implemented in a manner similar to Hale's and Zhang's DMO, by adding the NMO step as a time shift in the Fourier domain. Second, I define MZO as the process separated out of Prestack Migration, after eliminating the Zero-Offset Migration step. I compare the amplitude and phase output of the two MZO algorithms together with Hale's and Zhang's DMO algorithms for three simple models. The results suggest that the two methods are not equivalent.