Marine seismic imaging involves reconstructing subsurface reflectivity from some scattered acoustic data generally observed near the ocean surface. The procedure can be framed as a linearized inverse scattering problem and is often called least-squares migration (LSM). LSM has been shown to be effective in optimizing the reconstruction of subsurface reflectivity, particularly in cases of missing or undersampled data or uneven subsurface illumination.
In standard LSM, the reflectivity model parameters are usually defined as a grid of point scatterers over the area or volume to be migrated. We propose an approach to pre-stack LSM using the Dual Tree Complex Wavelet Transform (DT-CWT) as a basis for the reflectivity.
Wavelet bases have a reputation for decorrelating or diagonalizing a range of non-stationary signals. In LSM, diagonalization of the model space affords a more accurate but practical representation of prior information about the subsurface reflectivity model parameters. The DT-CWT is chosen for its key advantages compared to other wavelet transforms. These include shift invariance, directional selectivity, perfect reconstruction, limited redundancy and efficient computation.
A complex wavelet based LSM algorithm, derived in a Bayesian framework, is presented. Minimization of the least-squares cost function is performed in the wavelet domain rather than the standard reflectivity model domain.