Fast Kirchhoff migration in the wavelet domain

We present results of the application of the wavelet transform method to seismic imaging. The objective of this research is to develop 3D seismic Kirchhoff imaging in the wavelet-transform domain, making use of the time-frequency property of wavelets. We propose to migrate the wavelets as units rather than single samples as in conventional Kirchhoff migration implementation. In practice, the wavelet transform of each trace from a seismic section is carried out, then the significant wavelet coefficients are migrated according to their time location in a manner similar to the conventional migration of samples. These operations are then followed by a proper reconstruction. Since the number of significant wavelet coefficients is much fewer than the number of samples in the time domain, and the migration procedure in fact does not change, computation time is significantly reduced. We conducted a series of 2D and 3D experiments with artificial and real data to check whether the migration of significant wavelet coefficients leads to a correct result. Results from synthetic data as well as field data have shown that the migration in the wavelet domain significantly reduces computation time while maintaining good image quality.