Kirchhoff elastic prestack depth migration

The first important part of the m/i is the elastic prestack depth migration. This step attempts to produce true relative amplitude estimates of elastic specular reflectivity. Presently, I have developed the theory and algorithm, in conjunction with my good friend and colleague Dr. Wafik Beydoun at ARCO Research, to estimate the $\grave{P}\!\acute{P}$ reflectivity, R_pp, as a function of the specular angle $\theta_{pp}$ (Lumley et al., 1991). Other components of the full nine-component elastic reflectivity matrix ${\bf R}$, such as the $\grave{P}\!\acute{S}$ and $\grave{S}\!\acute{S}$ depth images, are included in the theory but not yet implemented.

The R_pp and $\theta_{pp}$ depth images are both estimated simultaneously in the Kirchhoff prestack depth migration algorithm, directly from the observed reflection data. Heterogeneous migration velocity models, including dipping structure, are accommodated by the use of WKBJ Green's tensors, which must be raytraced through a ray-valid medium. The migration is implemented in a constant offset manner to preserve reflectivity amplitudes as a function of specular angle. The method has been tested on synthetic and marine field data with very encouraging results (Lumley and Beydoun, 1991).

Details are in manuscript preparation for journal publication, and will appear in subsequent SEP reports. Anticipated difficulties include near surface variations in structure and elastic properties, which will likely make land data a challenging problem. Also, raytracing Green's function components in laterally variable velocity models can be very computationally intensive. Perhaps the CM can be of help here, in implementing an idea that Wafik and I have had for fast paraxial raytracing of Green's function traveltimes, WKBJ amplitudes, and various other necessary ray properties.