Seismic P-Wave Travel Time to Antipodal Point

This solution details the approximate travel duration for a seismic P-wave originating from a surface focus earthquake to reach its diametrically opposite point on Earth, known as the antipodal point.

Earthquake P-Wave Properties

P-waves (Primary waves) are the fastest seismic body waves. They travel through the Earth's interior by compressing and expanding material.

Antipodal Point Definition for Earthquakes

The antipodal point is located directly opposite the earthquake's origin on the Earth's surface. For a surface focus, the shortest path through the Earth to this point is along its diameter.

Calculating P-Wave Travel Path Through Earth

The distance covered by a P-wave traveling through the Earth to the antipodal point approximates the Earth's diameter.

• Earth's mean radius ($R$): approximately 6371 km.
• Earth's mean diameter ($D$): $D = 2 \times R \approx 12742 \text{ km}$.

P-wave speeds vary within the Earth, generally ranging from 5 km/s in the crust to over 13 km/s in the deep mantle and core. An average speed suitable for this calculation is around 10.6 km/s.

The formula for travel time is:

$ \text{Travel Time} = \frac{\text{Distance}}{\text{Average Speed}} $

Using the calculated diameter and the average speed:

$ \text{Travel Time} \approx \frac{12742 \text{ km}}{10.6 \text{ km/s}} \approx 1197 \text{ seconds} $

Determining Approximate P-Wave Travel Duration

The computed travel time of approximately 1197 seconds closely matches the option of 1200 seconds.

Thus, the approximate travel time for a P-wave from a surface focus earthquake to its antipodal point through the Earth is 1200 seconds.