A prestack basis pursuit seismic inversion

Resolving thin layers and clearly delineating layer boundaries in inverted seismic sections are very important goals for exploration and production. Many seismic inversion methods based on a least-squares optimization approach with Tikhonov-type regularization can lead to unfocused transitions between adjacent layers. A basis pursuit inversion (BPI) algorithm based on the L₁ norm optimization method can, however, resolve sharp boundaries between layers. We have formulated a BPI algorithm for amplitude-versus-angle inversion and investigated its potential to improve contrasts between layers. Like the BPI for poststack case, the sparse layer constraint, rather than the sparse spike constraint, is used to construct the model space as a wedge dictionary. All the elements of the dictionary are bed reflectivities, which include solutions consisting of thin beds as well. With this dictionary, we use an L₁ norm optimization framework to derive three reflectivities, namely, R_p, R_s, and R_ρ Although BPI does not require a starting model, highresolution absolute velocities (V_P, V_S) and density (ρ) can be obtained by incorporating initial models in the BPI derived reflectivities. Tests on synthetic and field data show that the BPI algorithm can indeed detect and enhance layer boundaries by effectively removing the wavelet interference.