Identify Given Seismic Phase Travel Times

The problem provides the following travel times for seismic phases recorded near an earthquake epicentre:

• $T_{PcP} = 9.0$ minutes
• $T_{ScS} = 15.5$ minutes
• $T_{PKiKP} = 16.5$ minutes

Calculate Additional Travel Time for P-wave Phase

The difference between the travel times of the $PKiKP$ phase (a P-wave reflecting off the inner core boundary) and the $PcP$ phase (a P-wave reflecting off the core-mantle boundary) represents the additional travel time for the P-wave phase associated with the path segment involving the inner core boundary reflection.

Calculate this additional time ($\Delta T_P$): $ \Delta T_P = T_{PKiKP} - T_{PcP} $ $ \Delta T_P = 16.5 \text{ min} - 9.0 \text{ min} = 7.5 \text{ min} $

Determine Additional Travel Time for S-wave Phase

In problems of this nature, it's often observed that the additional travel time for the corresponding S-wave phase ($SKiKP$ relative to $ScS$) is equivalent to the additional travel time calculated for the P-wave phase.

Assume the additional time for the S-wave phase ($\Delta T_S$) is the same: $ \Delta T_S = \Delta T_P = 7.5 \text{ min} $

Calculate SKiKP Travel Time

The travel time of the $SKiKP$ phase is found by adding this additional travel time ($\Delta T_S$) to the travel time of the $ScS$ phase.

Calculate the travel time of $SKiKP$ ($T_{SKiKP}$): $ T_{SKiKP} = T_{ScS} + \Delta T_S $ $ T_{SKiKP} = 15.5 \text{ min} + 7.5 \text{ min} = 23.0 \text{ min} $

Therefore, the travel time of the $SKiKP$ phase is 23.0 minutes.