Travel-time depth

Conceptually, the output of a migration program is a picture in the (x,z)-plane. In practice the vertical axis is almost never depth z; it is the vertical travel time $\tau$. In a constant-velocity earth the time and the depth are related by a simple scale factor. The meaning of the scale factor is that the $(x, \tau$)-plane has a vertical exaggeration compared to the (x,z)-plane. In reconnaissance work, the vertical is often exaggerated by about a factor of five. By the time prospects have been sufficiently narrowed for a drill site to be selected, the vertical exaggeration factor in use is likely to be about unity (no exaggeration).

The travel-time depth $\tau$ is usually defined to include the time for both the wave going down and the wave coming up. The factor of two thus introduced quickly disappears into the rock velocity. Recall that zero-offset data sections are generally interpreted as exploding-reflector wavefields. To make the correspondence, the rock velocity is cut in half for the wave analysis:  

$$\tau \ \ =\ \ {2\,z \over v_{\rm true} } \ \ =\ \ {z \over v_{\rm half} }$$ (15)

The first task in interpretation of seismic data is to figure out the approximate numerical value of the vertical exaggeration. It probably won't be printed on the data header because the seismic velocity is not really known. Furthermore, the velocity usually increases with depth, which means that the vertical exaggeration decreases with depth. For velocity-stratified media, the time-to-depth conversion formula is  

$$\tau (z) \ \ =\ \ \int_0^z \ {dz \over v (z) } \ \ \ \ \ \ \... ...m or} \ \ \ \ \ \ \ \ { d \tau \over dz }\ \ =\ \ {1 \over v }$$ (16)