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?
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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
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The Correct Option isC
Solution and Explanation
In \(\tau-p\) (intercept time vs ray parameter) analysis, each ray parameter \(p = \sin i/v\) corresponds to one turning depth, and \(\tau(p)\) is built from \(\tau(p)=\int (\eta)\,dz\) type integrals along the ray. For a velocity structure that increases smoothly and monotonically with depth, \(\tau(p)\) is a single, smooth, continuously decreasing curve with no breaks — every value of \(p\) in the observed range maps to exactly one turning point.
The plotted curve here instead shows two separate, offset branches: a steeper branch at smaller \(p\) (shallower turning depth) is followed, after a visible break/step, by a second, flatter branch at larger \(p\) sitting at a lower \(\tau\). A clean break of this kind in the \(\tau(p)\) curve is the classic signature of a low-velocity zone (LVZ) at depth: rays that would turn inside the LVZ cannot do so (velocity has locally decreased, so they instead refract more efficient below it), which removes a contiguous band of ray parameters from the observed branch and creates a shadow zone in the travel-time curve and a corresponding jump/offset in \(\tau(p)\).
Physically this requires the P-wave velocity to (i) increase with depth down to the top of the low-velocity zone, (ii) decrease through the LVZ itself, and (iii) increase again with depth below the LVZ once normal compaction/pressure effects resume. This three-stage behaviour — increase, then decrease, then increase again — is exactly option (C).
\(\boxed{\text{Velocity initially increases, then decreases, then increases again with depth}}\)
