Diffraction Imaging Method Based on Morphological Component Analysis

Diffraction imaging is beneficial for characterizing the distribution of small-scale structures. Traditional diffraction imaging methods highlight diffractions by applying various energy suppression techniques within migrated dip-angle gathers to attenuate reflections in the Fresnel zone. However, these methods not only suppress reflected waves but also remove diffracted waves within the Fresnel zone, which may degrade the focusing of discontinuities in the diffraction image. We develop a diffraction imaging technique using morphological component analysis (MCA). We first use high-resolution linear Radon transform (LRT) to focus diffracted waves, thereby better preserving them during separation. In the Radon domain, diffracted waves appear as point-like features, whereas reflected waves exhibit curved events. Accordingly, we employ the stationary wavelet transform (SWT) and seislet transform as sparse representation dictionaries for diffracted and reflected waves, respectively. Based on these two sparse representation dictionaries, MCA can effectively extract the diffraction component. The proposed method is a non-Fresnel-zone-muting diffraction imaging technique that better preserves the diffracted waves within the Fresnel zone, thereby improving the focusing of discontinuities. Tests on the Sigsbee 2B model demonstrated that the proposed method effectively removed reflected waves while preserving diffracted waves within the Fresnel zone. Applications to field data indicate the effectiveness of the technique in highlighting deep-seated high-angle fractures, facilitating the detailed characterization of discontinuous features.