Question

a seismic station records a travel time difference between p-wave arrival and s-wave arrival of 3 minutes. how far away was the earthquake epicenter from this location?

Answer 1

To calculate the distance to an earthquake epicenter from a seismic station that records a 3-minute difference between P-wave and S-wave arrivals, one can use the travel time curve and known speeds of the P-waves and S-waves in a specific equation.

Step-by-step explanation:

To find the distance to an earthquake epicenter using the difference in arrival times of P-waves and S-waves, seismologists use the travel time curve. The principle is that P-waves travel faster than S-waves and this difference in speed can be utilized to calculate the distance to the epicenter. If a seismic station records a travel time difference of 3 minutes (180 seconds) and we know the speeds of the P-waves and S-waves for the area (which are usually derived from seismological data), we can determine the distance to the epicenter.

For instance, if P-waves travel at 6 km/s and S-waves at 3.5 km/s (typical values), the travel time difference (t) can be plugged into the equation t = d/vp - d/vs, where d is the distance to the epicenter, vp is the speed of the P-wave, and vs is the speed of the S-wave. Solving for d, you would find that d = t / (1/vp - 1/vs). Substituting the values, d = 180 / (1/6 - 1/3.5) would give us the distance to the epicenter.

Answer 2

Using the travel time difference of 3 minutes and the average speed of P-waves (6 km/s) and S-waves (3.5 km/s), the distance to the earthquake epicenter is calculated to be approximately 1512 km.

Step-by-step explanation:

To determine the distance to an earthquake epicenter based on the travel time difference between P-waves and S-waves, we can use the speeds of the waves and the formula Distance = Speed × Time. Given that a seismic station records a travel time difference of 3 minutes (180 seconds) between P-wave arrival and S-wave arrival, we need to know the speeds of P-waves and S-waves for the specific region to calculate the distance.

Let's assume the average speeds of P-waves are 6 km/s and S-waves are 3.5 km/s. This is a rough average as the speeds can vary based on the Earth's material they travel through. The time difference (Δt) between the arrival of P-waves and S-waves is given by the equation Δt = Distance / Vp - Distance / Vs. By rearranging the formula to Distance = Δt / (1/Vs - 1/Vp), we can find out our final answer.

Calculating the distance:

Δt = 180 seconds (3 minutes),
Vs = 3.5 km/s,
Vp = 6 km/s,
Distance = 180 / (1/3.5 - 1/6),
Distance = 180 / (6/21 - 3.5/21),
Distance = 180 / (6 - 3.5) × 21,
Distance = 180 / 2.5 × 21,
Distance = 72 × 21 km,
Distance = 1512 km.

Therefore, the epicenter of the earthquake was approximately 1512 km away from the seismic station.