GATE-2018 (24) :Wyllie – Time average equation

CSIR-NET 2013

1. Consider a 80 km thick crust of, Vp-6 km/s overlying the mantle with P-velocity 8.0 km/s. If an earthquake occurs near surface, at which epicenter distance the Pn will be first recorded on seismogram?

(1) 280 km

(2) 320 km

(3) 390 km

(4) 430 km

 

Solution:

Beyond about 200 km there were two arrivals; the $P_g$ event was overtaken by another arrival $(P_n)$ which had evidently travelled at higher speed. Mohoroviçiç identified $P_g$ as the direct wave from the earthquake and $P_n$ as a doubly refracted wave (equivalent to a head wave) that travelled partly in the upper mantle. Mohoroviçiç calculated velocities of 5.6 km/s for $P_g$ and 7.9 km/s for $P_n$

At Crossover distance the Direct wave and refracted waves cross each other in t-x plot, and reach at same time.

Crust thickness z = 80km

Velocity of the first layer $V_1$= 6 km/s

Velocity of the second layer $V_2$= 8 km/s

$x_{cross}= 2z \sqrt{\frac{V_2+V_1}{V_2-V_1}}$

$x_{cross}= 2*80 \sqrt{\frac{8+6}{8-6}}$

$x_{cross}= 2*80 \sqrt{\frac{14}{2}}$

$x_{cross}= 2*80 \sqrt{7}$

$x_{cross}= 423.32km$

Reference : Fundamental of Geophysics, William Lowrie.