Final answer:
The difference in arrival time between P-waves and S-waves is used to calculate the distance to an earthquake's epicenter. By knowing the speeds of these waves, seismologists can estimate how far the earthquake occurred from the seismograph station.
Step-by-step explanation:
The relationship between the difference in arrival time of the first P-wave and the first S-wave to a seismograph station and the distance to the epicenter of an earthquake is a key concept in seismology. P-waves, being faster, arrive before the S-waves. By measuring the time interval between the arrivals of these two types of waves and knowing their speeds, seismologists can calculate how far away the earthquake occurred.
The calculation involves multiplying the time difference by the average velocity difference between the two wave types. If the speeds of P-waves and S-waves are known in a given region of the Earth, the distance D to the epicenter can be estimated using the formula D = (v₁ - v₂) × Δt, where v₁ and v₂ are the velocities of the P-waves and S-waves respectively, and Δt is the observed time difference.