If \(\tau\) and \(p\) denote intercept time and slowness, respectively, in the \(\tau-p\) diagram, then which one of the following is CORRECT for a P-wave propagating inside the Earth?
Show Hint
A smooth single τ-p branch means velocity rises monotonically; a break/offset between two branches signals a low-velocity zone sandwiched between two increasing-velocity regions.
Velocity initially increases then decreases and again increases with depth
Velocity initially decreases then increases and again decreases with depth
Show Solution
The Correct Option isC
Solution and Explanation
Think of it the other way round, starting from the travel-time curve rather than \(\tau(p)\) directly. If \(v(z)\) increased monotonically everywhere, \(dp/dx\) would never change sign and the \(x(p)\)/\(t(p)\) curves would be single-valued and smooth, so \(\tau(p)\) would trace one unbroken curve. A break in the plotted \(\tau-p\) curve means that over some depth interval \(dv/dz\) must have gone negative — i.e. a low-velocity zone — because that is the only mechanism that removes a range of turning depths (and hence a contiguous range of \(p\)) from the set of rays that actually return to the surface as first arrivals (this range instead becomes a shadow zone, filled only by weaker diffracted/head-wave energy).
Reconstructing the depth profile implied by the two branches of the figure: the upper branch corresponds to rays turning above the LVZ (velocity increasing with depth down to the top of the LVZ), the missing/discontinuous region corresponds to the LVZ (velocity decreasing), and the lower branch corresponds to rays turning below the LVZ, where velocity resumes its normal increase with depth. Hence the depth-velocity trend is increase → decrease → increase, matching option (C), consistent with classical Earth models (e.g., the asthenospheric low-velocity zone beneath the lithosphere) that produce exactly this kind of triplicated \(\tau-p\)/travel-time behaviour.
