Step 1: Understanding P–wave propagation.
Seismic phases are named according to the path a wave takes through the Earth’s internal layers:
- \(P\): propagation through mantle.
- \(K\): propagation through the outer core (since it is liquid).
- \(I\): propagation through the inner core.
Step 2: Analyze the given ray path.
From the figure:
- The P–wave originates at the earthquake focus.
- It travels through the mantle.
- It enters and passes through the outer core.
- It emerges back through the mantle and reaches the surface.
This corresponds to the seismic phase notation \(\mathbf{PKP}\).
Step 3: Elimination of incorrect options.
- PcP: A P–wave reflected at the core–mantle boundary (does not go through the core).
- PKP: A P–wave that travels through mantle, outer core, and back into mantle.
- PPP: A P–wave that reflects within the mantle multiple times, never enters the core.
- PmP: A P–wave reflected at the Moho discontinuity.
Final Answer:
\[
\boxed{\text{PKP}}
\]