Diffraction imaging of high-resolution 3D P-cable data from the Gulf of Mexico using azimuthal plane-wave destruction

Abstract

We review in historical order the key contributions to the development of the theory of diffractions. The work of Grimaldi, Huygens and Young provides the first part of this story, giving an understanding of diffraction and interference phenomena. Huygens was able to explain the laws of reflection and refraction, but lacked a deeper understanding of interference. This was provided by Young who used it to show how diffraction could arise from the interference of two waves. Fresnel, Helmholtz and Kirchhoff chose a different path and developed a full mathematical expression of Huygens’ principle, incorporating wave phase and interference. Sommerfeld and his students were able to reformulate the Huygens-Helmholtz-Kirchhoff integral as the sum of an incident geometrical-optics wave and a diffraction integral, which is interpretable as the contribution of the diffracted rays from the boundary. From our modern vantage point, this provides a rather pleasing analogy to Young’s early attempts at a theory of diffraction, using just two rays. A full ray-theoretical theory of diffraction, the Geometrical Theory of Diffraction, was given by Keller and extended by Klem-Musatov and Aizenberg to the case of seismic diffraction analysis.