Wave-equation-based seismic illumination analysis Xiao-Bi Xie 1 , Shengwen Jin 2 , and Ru-Shan Wu 1 ABSTRACT We present a wave-equation-based method for seismic il- lumination analysis. A one-way wave-equation-based, gen- eralized screen propagator is used to extrapolate the wave- fields from sources and receivers to the subsurface target. A local plane-wave analysis is used at the target to calculate lo- calized, directional energy fluxes for both source and receiver wavefields. We construct an illumination matrix using these energy fluxes to quantify the target illumination conditions. The target geometry information is used to manipulate the illumination matrix and generate different types of illumina- tion measures. The wave-equation-based approach can pro- perly handle forward multiple-scattering phenomena, in- cluding focusing/defocusing, diffraction, and interference effects. It can be directly applied to complex velocity models. Velocity-model smoothing and Fresnel-zone smoothing are not required. Different illumination measurements derived from this method can be applied to target-oriented or volu- metric illumination analyses. This new method is flexible and practical for illumination analysis in complex 2D and 3D velocity models with nontrivial acquisition and target geometries. INTRODUCTION The illumination of a subsurface target is affected by many fac- tors, e.g., the limited acquisition geometry, the complex overburden structure, and the reflector dip angle. An uneven illumination causes a distorted image. Seismic illumination analysis quantifies such im- age distortion and has many applications in seismic migration/imag- ing. The effect of acquisition geometry can be evaluated by calculat- ing illuminations of different shooting patterns. More accurate am- plitude variation with angle AVA or amplitude variation with offset AVO may be obtained if the observation is corrected with angle- dependent illumination. In the past, the illumination estimate was based simply on the ac- quisition geometry at the surface under the assumption of a homoge- neous velocity model, horizontal targets, and symmetric raypaths Hoffmann, 2001. These assumptions may be invalid for complex structures under realistic situations. To properly calculate the target illumination, we have to extrapolate the wavefield between sources, targets, and receivers. In order to calculate the angle-dependent illu- mination, we also need directional information from the wavefield. Traditionally, illumination and resolution analyses have used the ray-based method Schneider and Winbow, 1999; Bear et al., 2000. The ray-based method can provide both intensity and directional in- formation carried in the wavefield. Dynamic ray tracing is used to calculate energy propagation along the source-target-receiver path using the smoothed velocity model. The common reflection point CRP gathers ray amplitude, hit count, offset coverage, etc. on the target are used for the illumination measurements. A Fresnel-zone smoothing is usually applied to obtain smoothly distributed cover- age on the target horizon Muerdter and Ratcliff, 2001a, b. These procedures have been discussed by Muerdter and Ratcliff 2001a, b and Muerdter et al. 2001, who made a comprehensive demonstra- tion of the application of ray-based illumination analysis in the sub- salt region. Using common focusing point CFP analysis, Berkhout et al. 2001 and Volker et al. 2001 investigated the effect of acqui- sition geometry on target illumination and migration resolution. Hoffmann 2001 used the illumination information for resolution analysis. Based on the illumination analysis in the local-angle do- main, Gelius et al. 2002 and Lecomte et al. 2003 defined a resolu- tion function and discussed the effect of a complex velocity model on the illumination and resolution. Although the ray-based illumination analysis can handle both ir- regular acquisition geometry and laterally varying velocity models, the high-frequency asymptotic approximation and the caustics in- herent in ray theory may severely limit its accuracy in complex re- gions Hoffmann, 2001. While the ray-based method is relatively efficient for target-oriented analysis, it is still not a cost-effective ap- proach for full-volume 3D illumination analysis. Attempts have been made to apply the wave-equation-based method to seismic illu- mination and resolution analysis. Schuster and Hu 2000 derived an Presented at the 74th Annual Meeting, Society of Exploration Geophysicists, October 2004. Manuscript received by the Editor March 3, 2005; revised manu- script received January 24, 2006; published online August 28, 2006. 1 IGPP/CSIDE, University of California at Santa Cruz, 1156 High Street, Santa Cruz, California 95064. E-mail: xie@pmc.ucsc.edu; wrs@pmc.ucsc.edu. 2 Screen ImagingTechnology, Incorporated, 1322 Southwest Freeway, Suite 1508, Houston,Texas 77074. E-mail: jin@screenimaging.com. © 2006 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 71, NO. 5 SEPTEMBER-OCTOBER 2006; P. S169–S177, 10 FIGS., 1 TABLE. 10.1190/1.2227619 S169