Diffraction Imaging Method Using Curvelet-Domain Cascade Filter

Diffraction separation is crucial for high-resolution imaging of small-scale and discontinuous geological bodies, which are associated with oil and gas migration paths, reservoir spaces, or geological hazards in engineering. Diffraction and reflection show different geometric forms in the seismic common-offset domain, where reflection shapes are linear and diffractions are in the form of hyperbolic curves. One main challenge in diffraction separation technology lies in effectively suppressing reflected energy while preserving the diffraction energy. Curvelet is a sparse transformation with angle classification. After applying the curvelet transformation, reflections tend to be concentrated in a few coefficient matrices, while diffractions exhibit the opposite behavior. Based on the significant difference between reflections and diffractions in the curvelet domain, a diffraction separation and imaging method using cascaded filters in the curvelet domain is proposed that includes adaptive high-pass and median filters. Previous methods have encountered challenges in effectively separating reflected waves from diffracted waves, often struggling to simultaneously suppress reflected energy and preserve diffraction energy. These limitations can lead to difficulties in accurately identifying small-scale geological features and discontinuities. In contrast, the proposed method overcomes these limitations by leveraging the advantages of the curvelet transform and the cascaded filtering approach in the curvelet domain. The curvelet transform's sparse representation and angle classification properties enable effective concentration of reflections and diffractions in separate coefficient matrices. By employing adaptive high-pass and median filters, we achieve enhanced suppression of reflected energy and preservation of diffraction energy. Numerical experiments demonstrate that the proposed method not only eliminated high-slope and horizontal reflections but also preserved the energy-level and polarity-reversal of diffractions. Field application further confirms its potential value in accurately identifying complex stratigraphic structures and small-scale discontinuities.