Traveltime inversion of both direct and reflected arrivals in vertical seismic profile data

Abstract

Traveltimes from both direct and reflected arrivals in a VSP data set (Bridenstein no. 1 well in Oklahoma) are inverted in a least‐squares sense for velocity structure. By comparing the structure from inversion to the sonic log, we conclude that the accuracy of the reconstructed velocities is greater than that found when only the direct arrivals are used. Extensive tests on synthetic VSP data confirm this observation. Apparently, the additional reflection traveltime equations aid in averaging out the traveltime errors, as well as reducing the slowness variance in reflecting layers. These results are consistent with theory, which predicts a decrease in a layer’s slowness variance with an increase in the number and length of terminating reflected rays. For the Bridenstein data set, 130 direct traveltimes and 399 primary reflection traveltimes were used in the inversion.