The distance between the epicenter of an earthquake and a seismic station can be determined using the time difference between the arrival of the P-wave and the S-wave at the station. The P-wave is the first wave to arrive and is a compressional wave, while the S-wave is the second wave to arrive and is a shear wave. The time difference between the P-wave and the S-wave can be used to calculate the distance to the epicenter using the following formula:
$$ L = (t_S - t_P) \cdot v_P $$
Where:
- $$L$$ is the distance from the epicenter to the seismic station
- $$t_S$$ is the arrival time of the S-wave
- $$t_P$$ is the arrival time of the P-wave
- $$v_P$$ is the velocity of the P-wave
The velocity of the P-wave is approximately 5 km/s, and the velocity of the S-wave is approximately 3 km/s. Solving the equation for $$L$$, we get:
$$ L = (t_S - t_P) \cdot v_P = 16.9 \text{ s} \cdot \left(\frac{5 \text{ km}}{\text{s}}\right) = 84.5 \text{ km} $$
Therefore, the distance between the epicenter and the seismic station is approximately 84.5 km.
