Directional illumination analysis using the local exponential frame

Abstract

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.