A model of the mantle has a smooth speed gradient down to depth
PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics · Seismology, tectonics and geodynamics
The Solid Earth, Ch Rays and travel times: from arrivals to a layered planet
Problem
A model of the mantle has a smooth speed gradient down to 900km depth, where vP jumps rapidly from 10.4 to 11.0kms−1 across a thin layer, resuming a smooth gradient below.
((a)) Describe, in words (a sketch is not required to be submitted, but describe what it would show), the shape of the T(Δ) curve produced by rays that pass near this jump: how many branches appear, and how they overlap in distance.
((b)) Describe the corresponding τ(p) curve over the same range of p, and explain why it does not show the same folding as T(Δ).
((c)) Take the Earth's radius as a=6371km and treat the jump as thin, at radius rj=a−900km. For rays that just graze the top and the bottom of the jump the turning condition gives p=rj/v. Give the range of the spherical ray parameter associated with this feature, in srad−1 and in sdeg−1.