# Distance, time, and velocity are related by distance = velocity x time Therefore, in a t…

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Distance, time, and velocity are related by distance = velocity x time Therefore, in a time t, a P-wave traveling at the P-wave velocity VP will move across a distance r, where r is given by (1) The time necessary for the P-wave to travel a distance r can be obtained by dividing equation (1) by VP: (2) r V t = p * € t = r VP EARTHQUAKE HYPOCENTER SEISMOMETER 1 surface of Earth EPICENTER r The seismic energy of the P-waves travels a distance r at a velocity of VP in a time t. Equivalently, a time t is required for the P-waves to reach a distance r from the epicenter if they travel at a velocity VP. SEISMIC STATION (seismometer) TP = time of P-wave arrival TS = time of S-wave arrival TS-P If a P-wave is generated from an earthquake at the origin time (the time the earthquake starts) T0, the first wiggle on the seismogram will arrive at the observation station labeled “seismometer 1”, at a distance r1 from the earthquake, at the time given by (3) Similarly, an S-wave from the same earthquake traveling at a velocity VS will arrive at the same seismometer at the time given by (4) Since S-waves travel more slowly than P-waves, > . Now we have a problem. Equations (3) and (4) both contain the unknown origin time T0. However, if we subtract equation (3) from equation (4) we eliminate T0 and obtain the following very useful result: (5) We can now define something called the S-P time (“S minus P time”) for the event that we just recorded at seismometer 1. We will use to represent the S-P time for this event at station 1. (6) 1 Tp P P V r T T 1 0 1 = + 1 TS S S V r T T 1 0 1 = + 1 TS 1 Tp 1 1 1 1 1 1 1 r V V V r V r T T S P S P S P ú û ù ê ë é – = – = – 1 TS-P 1 1 1 TS -P = TS -TP earthquake “start time” time needed for P-wave to travel to seismometer earthquake “start time” time needed for S-wave to travel to seismometer The S-P time depends on the distance from the earthquake to the seismic station and the relative times between the P and S wave, which can be variable based on 3D earth structure. During Lab 2 (Intro to Matlab and Ray Paths) you calculated P and S wave travel-time curves for an earthquake located 10 km below the surface. Your plot should have looked something like this: 1) What happens to the S-P travel time as you get farther away from the epicenter? 2) An earthquake is recorded at two seismic stations, station A and station B. If station A is 10 km from the epicenter (point on Earth’s surface directly above where the earthquake rupture began), and station B is 100 km from the epicenter, which station will exhibit a larger S-P time? **Extra Credit Question** How do you think S-P travel time could be useful for earthquake early warning (i.e. using earthquake arrival times to warn others about imminent ground shaking)

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