why is the arrival time for the p - wave earlier that the arrival of the s-wave the same seismograph station?
P waves travel faster than S waves.
http://www.seismo.unr.edu/ftp/pub/louie/class/100/seismic-waves.html
explains the difference
The arrival time of the P-wave is typically earlier than the arrival time of the S-wave at the same seismograph station because P-waves are faster than S-waves. P-waves, short for Primary waves, are a type of seismic wave that are the first to be recorded at a seismograph station after an earthquake occurs. S-waves, also known as Secondary waves, are the second type of seismic wave that arrive at the seismograph station.
To understand why the P-wave arrives before the S-wave, it's important to know the characteristics of each wave. P-waves are compression waves, meaning they cause particles to move back and forth in the same direction as the wave propagation. They can travel through solid rock, liquid, and gas. P-waves are faster than S-waves, with an average speed of around 6 kilometers per second in the Earth's crust.
On the other hand, S-waves are shear waves, which means particles move perpendicular to the direction of wave propagation. Unlike P-waves, S-waves cannot travel through liquid or gas, only through solid materials. They are slower than P-waves, with an average speed of around 3.5 kilometers per second in the Earth's crust.
When an earthquake occurs, P-waves reach the seismograph station first because they can travel through both solid and liquid layers of the Earth's interior. As a result, the P-waves arrive earlier, creating the primary signal on the seismograph record. S-waves, being slower and restricted to traveling through solids, take longer to reach the seismograph station. Therefore, the arrival of the S-wave occurs after the P-wave, resulting in a time delay between the two waves on the seismogram.
By observing the time difference between the arrivals of the P-wave and S-wave on a seismogram, scientists can calculate the distance between the seismograph station and the epicenter of the earthquake, using a method called earthquake triangulation. This, in turn, helps determine the location of the earthquake's epicenter.