Time migration velocity analysis by velocity continuation |

Velocity continuation is a process of transforming time migrated images
according to the changes in migration velocity. This process has wave-like
properties, which have been described in earlier papers
(Fomel, 2003,1994,1997). Hubral et al. (1996) and
Schleicher et al. (1997) use the term *image waves* to describe a
similar concept. Adler (2002,2000) generalizes the velocity
continuation approach for the case of variable background velocities, using
the term *Kirchhoff image propagation*. Although the velocity
continuation concept is tailored for time migration, it finds important
applications in depth migration velocity analysis by recursive methods
(Vaillant et al., 2000; Biondi and Sava, 1999).

Applying velocity continuation to migration velocity analysis involves the following steps:

- prestack common-offset (and common-azimuth) migration - to generate the initial data for continuation,
- velocity continuation with stacking and semblance analysis across different offsets - to transform the offset data dimension into the velocity dimension,
- picking the optimal velocity and slicing through the migrated data volume - to generate an optimally focused image.

In this paper, I demonstrate all three steps, using both synthetic data and a North Sea dataset. I introduce and exemplify two methods for the efficient practical implementation of velocity continuation: the finite-difference method and the Fourier spectral method. The Fourier method is recommended as optimal in terms of the accuracy versus efficiency trade-off. Although all the examples in this paper are two-dimensional, the method easily extends to 3-D under the assumption of common-azimuth geometry (one oriented offset). More investigation may be required to extend the method to the multi-azimuth case.

It is also important to note that although the velocity continuation result could be achieved in principle by using prestack residual migration in Kirchhoff (Etgen, 1990) or frequency-wavenumber (Stolt, 1996) formulation, the first is inferior in efficiency, and the second is not convenient for the conventional velocity analysis across different offsets, because it mixes them in the Fourier domain (Sava, 2000). Fourier-domain angle-gather analysis (Sava et al., 2001; Sava and Fomel, 2003) opens new possibilities for the future development of the Fourier-domain velocity continuation. New insights into the possibility of extending the method to depth migration can follow from the work of Adler (2002).

Time migration velocity analysis by velocity continuation |

2013-03-03