A seismograph station records the arrival of the first Primary (P) wave from an earthquake at exactly 10:05:20 AM. The first Secondary (S) wave arrives at the same station at 10:06:05 AM. Assuming a typical average crustal velocity multiplier ($k$) of $8 \text{ km/s}$, calculate the approximate distance ($d$) from the seismograph station to the earthquake's epicenter.

An earthquake epicenter is located $640 \text{ km}$ from a monitoring station. If the first P-wave arrives at the station at 14:30:00 (2:30:00 PM), at what exact time will the first S-wave arrive? Assume the regional crustal velocity multiplier ($k$) is $8 \text{ km/s}$.

A massive earthquake occurs offshore. A coastal seismograph station, located exactly $250 \text{ km}$ from the known epicenter, records a time difference of $33.5 \text{ seconds}$ between the arrival of the first P-wave and the first S-wave. Calculate the specific velocity multiplier ($k$) for the crustal rock in this specific region.

A major metropolitan city is situated in a deep, bowl-shaped valley completely filled with hundreds of meters of soft, unconsolidated alluvial clay and loose river sands. The city sits approximately $50 \text{ km}$ away from a major, active strike-slip fault system located in the surrounding hard-rock mountains.

A critical, multi-billion-dollar international airport is constructed entirely on an artificial island built by dumping millions of cubic meters of loose, uncompacted marine sand into a shallow bay (reclaimed land). The region is highly seismically active.