Imaging of rough surfaces for impulsive and continuously radiating sources

Synthetic experiments are employed to investigate the possibility of using focused imaging to reconstruct the subsurface structure. The technique of focusing two arrays of receivers on a subsurface point and cross correlating the outputs is known as the split array cross correlation (SACC) processing. Each point in a subsurface grid is assumed to be the source of scattered Huygens wavelets. The SACC processing gives the relative strengths of the scatterers. A correlation image is constructed from diffracted and reflected signals using the SACC processing. It shows the locations and the strengths of the Huygens sourcelets. Post correlation stack results show the diffraction pattern is enhanced relative to that of the reflection. The SACC processing works for known impulsive sources and continuously radiating random sources. Numerical model experiments were made for an assemblage of wedges, which gives rise to reflections from the facets and diffractions from the apexes and the ‘‘V’’ bottoms. The synthetic seismograms are computed based on the impulse solution for reflection and diffraction from a rigid wedge, adapted from the Biot–Tolstoy impulse theory of diffraction. The controlled source correlation image shows the diffractors and the portions of plain surfaces where reflections occur. The correlation image region is bounded by the ellipse of constant travel time from source to scatterer to receiver. The source and the receiver are at the foci of the ellipse. The correlation image of continuously radiating sources shows high intensities at the diffractors and the mirror images of the sources in the reflecting planes.