Post-Stack velocity analysis by separation and imaging of seismic diffractions

Small geological features manifest themselves in seismic data in the form of diffracted waves, which are fundamentally different from seismic reflections. Using two field data examples and one synthetic example, we demonstrate the possibility of separating seismic diffractions in the data and imaging them with optimally chosen migration velocities. Our criterion for separating reflection and diffraction events is the smoothness and continuity of local event slopes that correspond to reflection events. For optimal focusing, we develop the local varimax measure. The objectives of this work are velocity analysis implemented in the post-stack domain and high-resolution imaging of small-scale heterogeneities. Our examples demonstrate the effectiveness of the proposed method for highresolution imaging of such geological features as faults, channels, and salt boundaries. INTRODUCTION Diffracted and reflected seismic waves are fundamentally different physical phenomena (Klem-Musatov, 1994). Most seismic data processing is tuned to imaging and enhancing reflected waves, which carry most of the information about subsurface. The value of diffracted waves, however, should not be underestimated (Khaidukov et al., 2004). When seismic exploration focuses on identifying small subsurface features (such as faults, fractures, channels, and rough edges of salt bodies) or small changes in seismic reflectivity (such as those caused by fluid presence or fluid flow during reservoir production), it is diffracted waves that contain the most valuable information. In this paper, we develop an integrated approach for extracting and imaging of diffracted events. We start with stacked or zero-offset data as input and produce timemigrated images with separated and optimally focused diffracted waves as output. The output of our processing flow can be compared to coherence cubes (Bahorich and Farmer, 1995; Marfurt et al., 1998). While the coherence cube algorithm tries to enhance incoherent features, such as faults, in the migrated image domain, we perform the separation in unmigrated data, where these features appear in the form of diffracted waves. Fomel, Landa, & Taner 2 Diffraction imaging We also introduce diffraction-event focusing as a criterion for migration velocity analysis, as opposed to the usual “flat-gather” criterion used in seismic imaging. Focusing analysis is applicable not only to multi-coverage prestack data but also to post-stack or single-coverage data. The idea of extracting information from seismic diffractions is not new. Harlan et al. (1984) used forward modeling and local slant stacks for estimating velocities from diffractions; Landa and Keydar (1998) used common-diffraction-point sections for imaging of diffraction energy and detecting local heterogeneities; Soellner and Yang (2002) simulated diffraction responses for enhancing velocity analysis. Sava et al. (2005) incorporated diffraction imaging in wave-equation migration velocity analysis. The novelty of our approach is in integration of two essential steps: 1. Separating diffracted and reflected events in the data space, 2. Focusing analysis for automatic detection of migration velocities optimal for imaging diffractions. We explain both steps and illustrate their application with field and synthetic datasets. SEPARATING DIFFRACTIONS The underlying assumption that we employ for separating diffracted and reflected events is that, in a stacked data volume, background reflections correspond to strong coherent events with continuously variable slopes. Removing those events reveals other coherent information, often in the form of seismic diffractions. We propose to identify and remove reflection events with the method of plane-wave destruction (Claerbout, 1992; Fomel, 2002). Plane-wave destruction estimates continuously variable local slopes of dominant seismic events by forming a prediction of each data trace from its neighboring traces with optimally compact non-stationary filters that follow seismic energy along the estimated slopes. Minimizing the prediction residual while constraining the local slopes to vary smoothly provides an optimization objective function analogous to differential semblance (Symes and Carazzone, 1991). Iterative optimization of the objective function generates a field of local slopes. The prediction residual then contains all events, including seismic diffractions, that do not follow the dominant slope pattern. An analogous idea, but with implementation based on prediction-error filters, was previously discussed by Claerbout (1994) and Schwab et al. (1996). Although separation of reflection and diffraction energy can never be exact, our method serves the practical purpose of enhancing the wave response of small subsurface discontinuities. Fomel, Landa, & Taner 3 Diffraction imaging IMAGING DIFFRACTIONS How can one detect the spatially-variable velocity necessary for focusing of different diffraction events? A good measure of focusing is the varimax norm used by Wiggins (1978) for minimum-entropy deconvolution and by Levy and Oldenburg (1987) for zero-phase correction. The varimax norm is defined as