A THEORY OF ACOUSTIC DIFFRACTORS APPLIED TO 2‐D MODELS*

A bstract Finite‐offset seismic reflection modeling of acoustic waves, propagating in a two‐dimensional depth section of arbitrary complexity, is discussed. The procedure developed employs the principles of simplified (far‐field) diffractor theory and ray tracing. Each reflector is represented by a set of discrete secondary sources or diffractors and the wavefield associated with each diffractor is calculated directly in the time domain by ray tracing. Reflections and diffractions are subsequently built up by the numerical superposition of these wavefields. This superposition is nondispersive for all frequencies for which the Fresnel zones are large compared with the diffractor separation. All primary travel paths connecting the shot to diffractor and diffractor to geophone are accounted for together with phase changes induced by focal events. The method allows the modeling of arbitrary trace gathers for energy originating from selected reflectors. The nonsequential nature of the algorithm makes it suited to machines capable of carrying out many similar operations in parallel or concurrently. Diffractor theory also provides physical insight into wave scattering and focusing. In particular, the half‐differential waveform associated with a line diffractor leads to an explanation of the 90° phase lead induced by a cylindrical focus and, similarly, the full differential waveform of a point diffractor can be used to explain the 180° phase shift induced by a point focus.