Time-shift imaging condition in seismic migration |

**Paul Sava and Sergey Fomel**

Seismic imaging based on single-scattering approximation
is based on analysis of the match between the
source and receiver wavefields at every image location.
Wavefields at depth are functions of space and time and are
reconstructed from surface data either by integral
methods (Kirchhoff migration) or by differential methods
(reverse-time or wavefield extrapolation migration).
Different methods can be used to analyze wavefield matching,
of which cross-correlation is a popular option.
Implementation of
a simple imaging condition requires time cross-correlation
of source and receiver wavefields, followed by extraction
of the zero time lag.
A generalized imaging condition operates by cross-correlation
in both space and time, followed by image extraction at
zero time lag.
Images at different spatial cross-correlation lags are indicators of
imaging accuracy and are also used for image angle-decomposition.

In this paper, we introduce an alternative prestack imaging condition in which we preserve multiple lags of the time cross-correlation. Prestack images are described as functions of time-shifts as opposed to space-shifts between source and receiver wavefields. This imaging condition is applicable to migration by Kirchhoff, wavefield extrapolation or reverse-time techniques. The transformation allows construction of common-image gathers presented as function of either time-shift or reflection angle at every location in space. Inaccurate migration velocity is revealed by angle-domain common-image gathers with non-flat events. Computational experiments using a synthetic dataset from a complex salt model demonstrate the main features of the method.

- Introduction
- Imaging condition in wave-equation imaging
- Space-shift imaging condition
- Time-shift imaging condition
- Space-shift and time-shift imaging condition

- Angle transformation in wave-equation imaging

- Moveout analysis
- Time-shift imaging in Kirchhoff migration
- Examples
- Discussion
- Conclusions
- Acknowledgment
- Bibliography
- About this document ...

Time-shift imaging condition in seismic migration |

2007-04-08