Fresnel aperture pre-stack depth migration

We investigate possible improvements in seismic imaging. We discuss how the Fresnel zone relates to the migration aperture and introduce the concept of the Fresnel aperture, which is the direct time-domain equivalent, at the receivers’ surface, of the subsurface Fresnel zone. Through these concepts we propose a new and efficient method for optimal aperture selection and migration. For complex media, multipathing will occur and multiple Fresnel apertures can exist for a given image point. In practice, due to inaccuracies and smoothing of the background velocity macromodel, inaccuracies in the ray-tracing method used for Green’s function computations and possible noise corruption of the data, the true Fresnel apertures will, in many cases, be replaced by ‘false’ ones, with apparently new Fresnel apertures being added. Hence, contributions from these ‘false’ Fresnel apertures cause a noise-corrupted image of the subsurface. It is now assumed that the single-scattered events are quite robust with respect to the above-mentioned distortions, and that their corresponding Fresnel apertures will remain essentially undistorted, with the strongest amplitudes. Based on this main assumption, we propose a method, analogous with velocity analysis, where the strong-amplitude Fresnel apertures can be picked interactively and at least semi-automatically. However, as in velocity analysis, a certain amount of user interaction has to be assumed. When this technique is combined with a prestack Kirchhoff-type depth-migration method, we call it Fresnel-aperture PSDM. This imaging method has been applied to data from both the Marmousi model and the North Sea. In both cases the improvements, when compared to conventional imaging, were considerable. Introduction Improving the resolution of seismic images is one of the most challenging topics in geophysics. In the study presented here, we investigate the consequences of the band-limited nature of seismic data when forming images of the subsurface. We propose a new and efficient method for the so-called specular-ray selection which we denote Fresnel-aperture selection. Previous work based on the so-called projected Fresnel zone (Schleicher et al. 1997; Vanelle & Gajewski 2001) reported an improvement in the S/N ratio only for data of rather poor quality. Moreover, these works imply some knowledge of the reflectors, including computation of curvature information, which can be both cumbersome and difficult in complicated media. Other authors (Tygel et al. 1993) used the so-called multiple-weights diffraction stack. This method, based on the work of Bleistein (1987), selects only the specular source–receiver pairs, leaving the estimation of the Fresnel aperture size to the user. The method presented here does not require any knowledge apart from the conventional traveltime table and includes geometry and nature of all the scattering objects (i.e. reflectors and diffractors). It is also perfectly stable whatever the complexity of the medium under consideration. In the case of an accurate and simple velocity model, high-quality data and a negligible multiple-contribution conventional Kirchhoff diffraction stack, employing the complete data set gives very much the same result as our optimized aperture selection. However, for complex models and noise-contaminated data, we demonstrate the possibility of significantly improving the image quality with the help of the Fresnel aperture concept underlying the specular-ray selection. Note that, if a wavefront-orientated ray-tracing method is being used (Coman & Gajewski 2002), multivalued traveltime tables can be computed with great accuracy but this is still time-consuming. However, we believe that in general cases involving complex media, multipathing imaging is not an easy task, due to imprecisions in the velocity macromodel, inaccuracies in the ray tracing and the problem with noisy data including possible multiples. Furthermore, in multipathing imaging, the entire multichannel data set must be processed at one time (Operto et al. 2000), and applications to individual common-offset gathers may provide spurious artefacts in the individual migrated images (Xu et al. 1998). This phenomenon can be explained in our terminology by the so-called ‘false’ Fresnel apertures. Specular rays and Fresnel zones In the high-frequency limit, the approximate solution to the wave equation is described by ray theory. The high-frequency condition is in fact equivalent to assuming that the velocity within the medium of propagation is piecewise smooth compared to the wavelength of the source pulse. Local discontinuities between continuous blocks or layers can be handled kinematically by the reflection/transmission conditions. The trajectory of the wave energy between a given source–receiver pair is then described by geometrical optics obeying Fermat’s principle of stationarity, which also governs the reflection/transmission paths or the so-called specufirst break volume 22, March 2004 Fresnel aperture prestack depth migration Hocine Tabti*, Leiv-J. Gelius**, and Thomas Hellmann** * Formerly University of Oslo, Department of Geology, Blindern, Oslo; presently PGS Geophysical AS, Strandveien 4, P.O. Box 290, N-1326, Lysaker, Norway. E-mail: Hocine.Tabti@pgs.com ** University of Oslo, Department of Geology, P.O. Box 1047 Blindern, N-0316, Oslo, Norway.