Wavefield Extrapolation Using the Wavelet Transform

A (spatial) wavelet transform is applied to the seismic data model in the space domain, such that a data model in the wavelet domain is obtained. The wavelet transform is a mathematical tool, which transforms a signal to the mixed space-wavenumber domain. Because. of their compact support wavelets are cut out for analyzing finite-length apertures. Moreover, wavelets can zoom in on local high wavenumber aspects. Subsequently a redatuming scheme (which is the heart of our migration scheme) is derived in the wavelet domain, corresponding to the redatuming scheme in the space domain. The important difference between the two domains is the fact that in the space domain redaturning can be carried out per point source experiment and in the wavelet domain redatuming can be carried out per scale experiment. Redatuming carried out per scale experiment is very advantageous. A remarkably small part of the extrapolation operators already reveals the correct structural information.