Seismic Wave Arrival Time Analysis: Statements I & II

Statement I: Near-Surface Earthquake Phases

Statement I: ScP and PcS phases of a near-surface earthquake arrive at an observatory at different times.

Assessment: False.

• ScP (S-wave converts to P-wave at the Core-Mantle Boundary, CMB) and PcS (P-wave converts to S-wave at the CMB) involve distinct paths.
• For near-surface earthquakes, path lengths are relatively short. The arrival time calculation involves travel from the source to the CMB and then from the CMB to the station.
• Let $T_{S \to CMB}$ and $T_{P \to CMB}$ be the travel times of S and P waves from the source to the CMB, respectively. Let $T_{P \to Sta}$ and $T_{S \to Sta}$ be the travel times of P and S waves from the CMB to the station.
• The arrival time for ScP is $T_{ScP} = T_{S \to CMB} + T_{P \to Sta}$.
• The arrival time for PcS is $T_{PcS} = T_{P \to CMB} + T_{S \to Sta}$.
• Although $T_{S \to CMB} > T_{P \to CMB}$ (since S-wave speed is slower than P-wave speed in the mantle) and $T_{P \to Sta} < T_{S \to Sta}$ (since $v_p > v_s$ in the mantle), the specific path lengths for near-surface sources can cause $T_{ScP}$ to be very close to $T_{PcS}$.
• Therefore, their arrival times are often practically indistinguishable, making the statement that they arrive at definitively different times false in an observational context.

Statement II: Deep Focus Earthquake Phases

Statement II: ScP phase of a deep focus earthquake arrives earlier than PcS phase at the same observatory.

Assessment: True.

• Deep focus earthquakes originate deep within the Earth.
• Both ScP and PcS phases involve travel from the CMB to the seismic observatory.
• The ScP phase travels this final segment as a P-wave.
• The PcS phase travels this final segment as an S-wave.
• In the Earth's mantle, P-wave velocity ($v_p$) is greater than S-wave velocity ($v_s$), i.e., $v_p > v_s$.
• Consequently, the travel time for the P-wave segment from the CMB to the station ($T_{P \to Sta}$) is shorter than the travel time for the S-wave segment ($T_{S \to Sta}$) over the same distance.
• This ensures that the ScP phase arrives earlier than the PcS phase.

Conclusion on Statements

Statement I is false, and Statement II is true. This corresponds to Option D.