Methodology for Processing Seismograms Containing Total Internal Reflections

A very common problem encountered in downhole seismic testing (DST) and crosshole seismic testing (CST) is the processing of seismograms that contain total internal reflections (TIRs). TIRs arise when the incident angle exceeds the critical angle, and they are associated with reflected source wave distortions due to the fact that the reflection coefficients become complex. TIRs are typical in CST investigations (since horizontally traveling source waves have high angles of incidence on bounding stratigraphic layers), whereas in DST investigations, TIRs are encountered whenever there are significant man-made structures (piles, stone columns, and deep underground structures such as deep basements, parking garages, and dam structures). To process seismograms containing TIRs, time-variant blind seismic deconvolution (BSDtv) techniques are required, and this paper outlines a new formulation of a previously published concept in blind seismic deconvolution referred to as principle phase decomposition (PPD). This new PPD filter formulation allows for BSDtv where the direct source wave is isolated from the reflected source waves. The BSDtv PPD filter formulation is referred to as BSDSolver-tv.