Diffraction

Key Takeaways

• The mathematical relationship between a diffractor and its hyperbolic signature on an unmigrated seismic record is given by the diffraction equation, which states that the arrival time t at an offset x from the diffractor apex is t(x) = sqrt(t0^2 + x^2/v^2), where t0 is the two-way travel time to the diffractor at zero offset and v is the root-mean-square velocity above the diffractor; this equation is the basis of seismic migration, because migration is essentially the process of searching along these hyperbolic trajectories in the unmigrated data, summing the amplitudes along each hyperbola, and placing the summed energy at the apex — the process called diffraction summation or Kirchhoff migration; the migration velocity (which determines the shape of the summation hyperbola) must match the actual subsurface velocity for the diffraction energy to sum constructively at the apex; using too low a velocity produces undermigrated images where diffraction hyperbolae are not fully collapsed, while too high a velocity produces overmigrated images where energy is smeared beyond the true diffractor position; velocity model accuracy is therefore directly tied to the quality of diffraction imaging.
• Diffraction imaging, as a standalone processing and interpretation technique distinct from conventional reflection imaging, has emerged as a valuable tool for detecting and characterizing sub-resolution geological features that generate diffractions but not coherent reflections: small faults with throws below the seismic resolution limit (typically a quarter wavelength of the dominant frequency), fracture zones, karst collapse features, reef edges, and channel margins all produce diffraction energy that is suppressed or ignored in conventional processing oriented toward imaging flat-lying reflectors; dedicated diffraction separation algorithms (such as plane-wave destruction or local slope estimation methods that separate the diffraction wavefield from the specular reflection wavefield in the dip-angle domain) extract the diffraction energy that conventional processing treats as noise and image it separately, potentially revealing fracture corridors and fault systems that are invisible on the conventional reflection image; the application of diffraction imaging to fractured carbonate reservoir characterization and to fault seal analysis has generated significant interest in both the exploration and production phases of field development.
• The Huygens-Fresnel principle provides the physical foundation for understanding both reflection and diffraction: it states that every point on a propagating wavefront acts as a source of secondary spherical wavelets, and the observable wavefront at a later time is the envelope of all these secondary wavelets; for a smooth, planar reflector, the secondary wavelets from adjacent points on the reflector interfere constructively only in the specular reflection direction and cancel in all other directions, producing the familiar planar reflection event; at the edge of a reflector or at a point scatterer, the secondary wavelets from the edge point radiate in all directions without the canceling interference from adjacent reflector points, producing the observable diffraction hyperbola; this framework explains why diffraction imaging is intrinsically sensitive to edges and discontinuities — it is detecting the radiation pattern of point scatterers that are the end-points of specular reflectors, which by definition mark the boundaries of geological bodies.
• The imaging of salt body edges in depth presents one of the most challenging diffraction problems in seismic processing because the large acoustic impedance contrast at the salt-sediment interface generates very strong reflections and diffractions, and the salt body itself has complex 3D geometry that creates multi-path propagation complications; where the salt flank transitions from a steep face to a salt overhang or salt weld, the edge geometry generates diffractions that propagate down into the sediments below the salt (sub-salt), and correctly imaging these sub-salt diffractions is critical for mapping the reservoir geometry beneath the salt in deepwater Gulf of Mexico, Brazilian pre-salt, and North Sea salt plays; reverse time migration (RTM) has become the standard algorithm for sub-salt imaging in part because it correctly handles the multi-arrival wavefield near salt edges (including both reflections and diffractions) by numerically solving the full wave equation bidirectionally in time rather than using the ray approximation that breaks down near the complex salt geometry.
• In well seismic applications, vertical seismic profiles (VSP) provide an opportunity to image diffractions that are invisible on surface seismic because the downgoing direct wave from the surface source illuminates the formation from above while the receivers in the well capture upgoing reflected and diffracted energy from both the formation above and below the geophone positions; VSP diffraction imaging can detect and locate fractures, faults, and other scatterers within tens of meters of the wellbore that are beyond the resolution of the surface seismic survey, providing a bridge between the wellbore-scale information from cores and image logs and the field-scale information from 3D surface seismic; the tube wave — a borehole-guided wave that propagates along the fluid-filled wellbore — can be generated by the interaction of the direct P-wave with fractures intersecting the wellbore, and the amplitude and character of tube wave generation at different depths provides a direct indicator of open (hydraulically conductive) fractures that complements the wellbore imaging from resistivity or acoustic image logs.