Analysis of Seismic Data in the -p Domain

Abstract

Densely sampled surface seismic data can be transformed to the 7-p domain to derive information about subsurface propagation velocities and to develop images of the subsurface that depend upon the angle of incidence. For one dimensional earth structures this plane wave decomposition of the observational data makes it possible to derive interval velocities estimates using pre- and post-critical reflections and refractions with little or no limiting assumptions. Once the velocity structure is obtained, it can be used to correct the seismic arrivals to their two-way normal incidence travel time in a manner analogous to that employed in traditional seismic processing, but without limiting assumptions. Amplitude dependence as a function of incidence angle can also be preserved. 1D acoustic and elastic synthetic seismic data can also be computed in this domain and require a similar transformation that superimposes the individual plane wave response functions. Numerical difficulties encountered in computing both transforms illustrate the need for fine two dimensional sampling. These aliasing artifacts occur because of finite spatial and temporal sampling and limited receiving aperture. They can be minimized by employing modern data acquisition systems but can often be reduced by simple windowing procedures during the transformation. But, in many applications such as velocity analysis and imaging, these artifacts will not be coherent along the imaging trajectories and their impact is minimal.