Final answer:
Seismic waves' property of travelling at different speeds depending on the rigidity of the material they move through, combined with the fact that P-waves travel faster than S-waves, allows scientists to calculate the distance to an earthquake's epicenter.
Step-by-step explanation:
The wave property that enables scientists to locate the source of an earthquake is that seismic waves travel uniformly outward from the wave source. Both longitudinal waves, known as compressional or P-waves, and transverse waves, known as shear or S-waves, travel at different speeds through the Earth's crust. This speed variation is due to the rigidity of the materials they pass through. P-waves and S-waves are faster in more rigid materials like granite and slow down in less rigid materials such as sediments. Since P-waves travel faster, they arrive first at the seismic stations followed by S-waves. The time difference between their arrivals at various seismograph locations is used to calculate the distance to the earthquake's epicenter. This property of waves allows for seismic imaging, akin to an ultrasound, to visualize Earth's interior and identify both the epicenter of earthquakes and the structure of the Earth's core.