Directional illumination analysis using beamlet decomposition and propagation

Abstract

We evaluate directional illumination (DI) and acquisition-aperture efficacy through wave theory-based beamlet decomposition of the wavefield. Beamlet decomposition (wavelet transform along spatial axis) provides localizations in both space and direction of a wavefield. We introduce the image conditions in beamlet domain and local angle domain and then define the local image matrix (LIM). We calculate the DI in the image space for a given source or a group of sources by decomposing Green’s functions into local angle domain at image points. Acquisition-aperture efficacy (AAE) matrix and acquisition dip-response (ADR) vector can be defined to quantify the efficacy of an acquisition configuration for a given subsurface point. As numerical examples, we calculate the DI maps and ADR maps for high- and low-velocity lens models and for the SEG-EAGE 2D salt model. We further investigate the influences of acquisition geometry and overlaying structures on the quality of prestack depth migration image for the subsalt area of the SEG-EAGE model. We find that the ADR maps for different dip angles have good correlation with the image qualities of the corresponding reflectors. DI analysis can be used in the aperture correction for image amplitude in local angle domain for wave theory-based migration methods.