Full-wave directional illumination analysis in the frequency domain

Directional illumination analysis based on one-way wave equations has been studied extensively; however, its inherent limitations, e.g., one-way propagation, wide-angle error, and amplitude inaccuracy, can severely hinder its applications for accurate survey design and true-reflection imaging corrections in complex media. We have analyzed the illumination in the frequency domain using full two-way wave propagators considering the extensive computation and huge storage required for time-domain methods, and the fact that the illumination is frequency dependent. This full-wave analysis can provide frequency-dependent full-angle true-amplitude illumination not only for the downgoing waves but also for the upgoing waves, including turning waves and reflected waves. Two methods were considered to decompose the full wavefield into the local angle domain: a direct full-dimensional decomposition and more efficient split-step decomposition composed of three lower-dimensional decompositions. The results of illumination analysis demonstrated the advantages of this method. The two decomposition methods produced similar results.