VSP INTERVAL VELOCITIES FROM TRAVELTIME INVERSION*

A bstract A principal use of the vertical seismic profile (VSP) is to determine the variation of seismic velocity with depth. Presented here is a discussion of the errors involved with the time picks of a VSP survey and several methods currently used to calculate a velocity section from these time picks. Another technique is proposed, based on the least‐squares inversion of the traveltimes, to arrive at a better estimate and statistical description of the velocity section. This technique uses the Levenberg‐Marquardt damped least‐squares formulation and ray tracing through a horizontally‐layered medium to iteratively refine the velocity section. The accuracy and robustness of the procedure are investigated by inverting noisy traveltime curves and comparing these results to the original model velocity section. Agreement is found to be good. One interesting feature of the inverse procedure is that, for certain geometries, it can resolve a few velocity layers, even though there are no measurements made inside those layers. Three actual VSP surveys are analyzed and compared to their corresponding sonic logs. In two of the surveys, it appears that there is some velocity dispersion. Velocity changes associated with gas saturation are evident on one of the surveys.