Synthesis of Directional Wave Packets from Shot Records

Using directional waves is advantageous in subsurface seismic imaging because such waves are localized in space and time. Hence, the recorded data contain information mostly about the illuminated targets. However, most seismic field data are physically generated by point sources that excite wavefield propagating into all directions and interact with all parts of the medium. How to convert point-source wavefields into a wavefield due to a directional wave packet without physically exciting it, is the subject of investigation here. In particular, we investigate the Gaussian wave packet (GWP) which is a directional wave packet localized in space and time. GWP is an exact solution of the wave equation and it differs from the widely used asymptotic solutions such as Gaussian Beams or Gaussian Packets. The spatial localization and propagation direction of GWP are controlled by parameters chosen by users. We propose a method to synthesize GWP field data in complex media using recorded shot records of point sources based on the reverse-time concept. To assess the quality of the synthesized GWP data, we study the influences from point-source wavelets and the spatial interval between point sources. Finally, we present the constructed GWP fields in two numerical examples. We also show one application of the GWP data in seismic imaging using multiples.