Velocities within the earth can be determined from body wave time-distance (T-D) data by the Herglotz-Wiechert method provided the velocity does not decrease too rapidly with depth. Until the present time, the properties of T-D curves for rapid decreases of velocity with depth have been considered only qualitatively.
This paper presents a technique for calculating a T-D curve for any velocity distribution, including continuous and discontinuous increases and decreases of velocity with depth. Some properties of T-D curves are quantitatively studied by systematically varying the characteristics of a single model and noting the corresponding variations in the calculated T-D curves. From this it is concluded that a significant low-velocity channel may not be evidenced by a shadow zone but rather by an overlapping of two distinct branches of the T-D curve. It is further concluded that the presence of a shadow zone implies a very gentle velocity gradient below the low-velocity channel.
By fitting a calculated T-D curve to observed data one can determine velocity as a function of depth even when the velocity decreases rapidly with depth, when a low-velocity channel exists. Observed T-D data for two underground nuclear explosions (gnome and bilby) measured in four different azimuths were fitted with T-D curves calculated for assumed velocity distributions. It is concluded that these data can be satisfied by a low-velocity channel for P waves in the upper mantle. The character of this channel (depth, thickness and velocity) was determined in each azimuth. The depth to its top was shallow (70 ± km) in the western U.S. and deep (125 ± km) in the eastern U.S. The velocity gradient below the channel is sharp enough to produce no prominent shadow zones. There are significant lateral changes in upper mantle velocities in the western U. S.