Diffraction imaging point of common-offset gather: GPR data example J.J.S. de Figueiredo ∗ (DEP/UNICAMP, Brazil), F. Oliveira (CPGF/UFPA and FACEN/UFPA, Brazil), E. Esmi (IMECC/UNICAMP, Brazil), L. Freitas (Geoprocessados, Mexico), S. Green (University of Houston), A. Novais and J. Schleicher (IMECC/UNICAMP and INCT-GP, Brazil) SUMMARY Hydrocarbon traps are generally located beneath complex geo- logical structures. Such areas contain many seismic diffractors that carry detailed structure information in the order of the seis- mic wavelength. Therefore, the development of computational resources capable of detecting diffractor points with a good resolution is desirable, but has been a challenge in the area of seismic processing. In this work, we present a method for the detection of diffractor points in the common-offset gathers do- main. In our approach, the diffraction imaging is based on the diffraction operator, which can be used in both the time and depth domains, in accordance with the complexity of the area. This method, which does not require any knowledge apart from the migration velocity field (i.e., rms velocities or interval velocities) applies pattern recognition to the amplitudes along the diffraction operator. Numerical examples using synthetic and real data demonstrate the feasibility of the technique. INTRODUCTION It is well known that hydrocarbon reservoirs commonly are located in geological stsructures that are difficult to image with seismic methods and obtain high resolution. This structures include common hydrocarbon traps, such as faults, pinch-outs, unconformities, salts domes, and other structures the size of which is of the order of the wavelength (Trorey, 1970). Because of the importance of these types of structures, sev- eral methods for imaging diffractions have been developed in the recent past. The first authors to look into the topic were Landa et al. (1987) and Landa and Keydar (1998), who pro- posed and refined a detection method related to specific kine- matic and dynamic properties of diffracted waves. Another approach (Moser and Howard, 2008) is based on suppressing specular reflections to image diffractions in the depth domain. Most recently, Zhu and Wu (2010) developed a method based on the local image matrix (LIM), which uses an image con- dition in the local incident and reflection angles for source- receiver pairs to detect diffractions. In this work, we propose a diffraction detection method based on an amplitude analysis along the elementary diffractions (Tabti et al., 2004). This method does not require any knowl- edge apart of from the migration velocity field, i.e., rms ve- locities or interval velocities depending on the complexity of the area. It applies pattern recognition to the amplitudes along the diffraction operator. Numerical examples on synthetic and ground penetrating radar (GPR) field data demonstrate the fea- sibility of the method. METHOD Diffraction operator Tabti et al. (2004) introduced amplitude analysis along ele- (a) (b) (c) Figure 1: (Illustration of the diffraction operator for (a) a re- flection point and (b) a void image point. Top: amplitude along the diffraction operator; center: diffraction traveltime and seis- mic event; bottom: image point and ray family. (c) Illustration of the diffraction operator for a diffraction point. Top: ampli- tude along the diffraction operator; center: diffraction travel- time and seismic event; bottom: image point and ray family. mentary diffractions for Fresnel aperture specification. As il- lustrated in Figure 1a, the traveltime of an elementary diffrac- tion associated with a reflection point is tangent to the reflec- tion traveltime at the stationary point (location of the specular reflection event). More specifically, in limited bandwidth sit- uations, this tangential point becomes a tangential contact re- gion, which defines the minimum aperture for true-amplitude Kirchhoff migration (Schleicher et al., 1997). (Tabti et al., 2004) named it the Fresnel aperture due to its close relation- ship to the Fresnel zone. For image point off any reflectors or diffractors, below referred to as “void image points”, there is no such region. The traveltime of the elementary diffraction associated with a void image point may cross some reflection events, but won’t be tangential to any events (see Figure 1b), except for extremely rare coincidental situations. Tabti et al. (2004) described amplitude analysis along elemen- tary diffractions by means of a diffraction operator D. This operator derives from the Kirchhoff depth migration integral (Schleicher et al., 1993) I (M)=  A f d 2 ξ W (M, ξ )∂ t U (ξ , t )| t =τ D (M,ξ ) (1) where U (ξ , t ) is the seismic data measured at ξ , τ D (M, ξ ) is the traveltime of the elementary diffraction of M, A f is the Fresnel aperture, and W (M, ξ ) is a weight function. For sim- plicity, we omit the weight function in the present study, i.e. W (M, ξ )= 1. Integration variable ξ is the horizontal coordi- nate of the seismic section to be migrated, for instance the mid- point coordinate for a common-offset section or the receiver coordinate for a common-shot section. Instead of performing the summation, the diffraction operator D(M) at an image point M collects a single valued curve (or surface, in the 3D case), defined as a function of the integra- tion variable ξ . Its value at ξ is the amplitude the stack in © 2011 SEG SEG San Antonio 2011 Annual Meeting 4399 Downloaded 29 Feb 2012 to 143.106.96.234. 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