why is the arrival time for the p wave always earlier thsn the ariivsl of the same seismograph station?

Not exaclty sure what you are asking but the P waves travel the faster than the other earthquake waves.

oops - I put an extra "the" in that sentence. I wanted to say at first that "the P" waves are the fastest" and then changed the sentence and left the extra THE in by mistake.Sorry!

The arrival time for the P-wave is typically earlier than the arrival of the same seismograph station because of the difference in travel speed between P-waves and S-waves.

When an earthquake occurs, it generates different types of seismic waves that travel through the Earth's interior. P-waves (primary waves) are the fastest seismic waves and are the first to be detected by seismograph stations. They travel through solids, liquids, and gases and cause the ground to compress and expand in the direction that the waves are traveling.

On the other hand, S-waves (secondary waves) are slower than P-waves. They travel only through solids and cause the ground to move up and down or side to side perpendicular to the direction of wave propagation. S-waves follow P-waves and are recorded on seismographs after the initial arrival of the P-waves.

The reason why P-waves arrive earlier than S-waves at the same seismograph station is because P-waves travel faster through the Earth's interior. As a result, they take less time to reach the seismograph station compared to S-waves, which have to travel a longer distance through the Earth.

To determine the time difference between the arrival of the P-waves and S-waves at a specific seismograph station, seismologists use the difference in the arrival times recorded on the seismogram. By analyzing these time differences, scientists can gather valuable information about the earthquake's location, depth, and magnitude.