Discussion
The difference in arrival times of P and S wave increases with distance while the ratio of P and S wave velocities :
Answer: A
The ratio of P and S wave velocities remains same.
Both waves travel through the same rock, and the ratio of their speeds depends on its elastic properties, through Poisson's ratio. For most crustal and mantle rocks Vp/Vs is close to \(\sqrt{3}\), about 1.73. Because the S-wave is always slower by a nearly fixed proportion, the lag between P and S arrivals grows steadily with distance, which is how the S-P time is used to find the distance to an earthquake.
The ratio does not decrease logarithmically or linearly, nor increase periodically, with distance.
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