Directional illumination analysis using the local exponential frame

We have developed an efficient method of directional illumination analysis in the local angle domain using local exponential frame beamlets. The space-domain wavefields with different shot-receiver geometries are decomposed into the local angle domain by using the local exponential beamlets, which form a tight frame with the redundancy ratio two and are implemented by a linear combination of local cosine and local sine transforms. Because of the fast algorithms of the local cosine/sine transforms, this method is much more efficient than the previously used decomposition methods in directional illumination analysis, such as the local slant-stacking method and the Gabor-Daubechies frame method. The results of directional illumination (DI) maps and the acqui-sition dip responses (ADR) for the 2D SEG/EAGE salt model and the 45-shot 3D SEG/EAGE model demonstrated the validity and feasibility of our method. Compared with the illumination results using local slant-stacking decomposition, the new method produces illumination maps of similar quality, but it does so a few times faster. Furthermore, because of its high computational efficiency and saving in memory usage, the new method makes the 3D directional illumination analysis readily applicable in the industry.