Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2014 / Paper 1 / 1 / d / Solution

Linearized arrivals contain $\delta t_i=\delta t_0+(\partial T_i/\partial z)\delta z+\cdots$. When the stations have similar depth sensitivities, a depth change shifts nearly all predicted times together and an origin-time change compensates it. Distant stations can also have very weak depth sensitivity. Improve the range of takeoff angles and station distances, especially with nearby or borehole stations, and include S–P or depth-phase differences such as pP–P that cancel origin time while retaining depth information. Accurate phase identification and the velocity model remain necessary.