l1-norm regularization and wavelet transform: An improved plane-wave destruction method

Seismic diffractions are the specific responses of small-scale inhomogeneities or discontinuous structures in the subsurface, such as faults and cracks, and can be used for locating reservoirs of oil and gas. However, because diffraction energy is much weaker than reflection energy, separating diffractions against the background of strong reflections from seismic data is difficult. In this paper, we propose a regularization method based on the l1-norm constraint to extract seismic diffractions from seismic records in the common-offset gathers. Regularization is a practical method for ill-posed nonlinear problems. The proposed method considers wavelet transform and l1-norm regularization in the plane-wave destruction method, which enhances the stability and accuracy of reflection local slopes. Wavelet transform has multi-level and multi-scale analysis properties and thus it is an effective method for sparse transform. Further, the l1-norm can effectively constrain sparsity properties. Through a synthetic example, the stability of this regularization method is demonstrated to be stronger than that of the conventional plane-wave destruction (PWD) method. Both the numerical simulation and field data application indicate that the proposed regularization method for diffraction extraction is promising and feasible in removing specular reflections and strengthening diffractions.