Locating Epicenter

Locating EpicenterLecture-61Locating an Earthquakes Epicenter Seismic wave behaviorP waves arrive first, then S waves, then L and RAfter an earthquake, the difference in arrival times at a seismograph station can be used to calculate the distance from the seismograph to the epicenter (D).

2

If average speeds for all these waves is known, use the S-P (S minus P) time formula: a method to compute the distance (D) between a recording station and an event.3

Global Travel Time Curve4Source: google images

Seismic Travel-time Curve: If the speeds of the seismic waves are not known, use Travel-Time curve for that region to get the distance1. Measure time between P and S wave on seismogram2. Use travel-time graph to get distance to epicenter53-circle method:Steps:1) Read S-P time from 3 seismograms.2) Compute distance for each event/recording station pair (D1, D2, D3) using S-P time formula.3) Draw each circle of radius Di on map.4) Overlapping point is the event location.

Assumption: Source is relatively shallow; epicenter is relatively close to hypocenter.

northD1D2D36If you gather this information from three or more points, you can figure out the location of the focus through the process of trilateration. Basically, you draw an imaginary sphere around each seismograph location, with the point of measurement as the center and the measured distance (let's call it X) from that point to the focus as the radius. The surface of the circle describes all the points that are X miles away from the seismograph. The focus, then, must be somewhere along this sphere. If you come up with two spheres, based on evidence from two different seismographs, you'll get a two-dimensional circle where they meet. Since the focus must be along the surface of both spheres, all of the possible focus points are located on the circle formed by the intersection of these two spheres. A third sphere will intersect only twice with this circle, giving you two possible focus points. And because the center of each sphere is on the earth's surface, one of these possible points will be in the air, leaving only one logical focus location.Locating an Earthquakes Epicenter: Deep Source7

Locating an Earthquakes Epicenter: Deep Source8Assuming P and S wave traveled through the crust at 6 km/sec and 3 km/sec respectively, estimate the epicentral location (latitude and longitude) of the hypothetical earthquake whose characteristics are given below:

Example Problem9Diameter of earth = 12720 km360o = p 127201o = 111 km (latitude)At latitude of 37.5o, longitude 1o = 111 cos 37.5 = 88 km

D = [(VpVs)/(Vp-Vs)] Dt1037o37.5o38o121.5o122.5o122o55.5 km55.5 km44 km44 kmScale 1mm: 1 kmLongitudeLatitude11Scale 1mm: 1 kmSeismograph 1 is at latitude 37.375o , 0.375o from 37o latitude line Seismograph 1 is at 0.375*111 = 41.625 km from 37o latitude line Seismograph 1 is at longitude 121.875o , 0.375o from 121.5o longitude line Seismograph 1 is at 0.375*88 = 33 km from 121.5o longitude line 19.9937o37.5o38o121.5o122.5o122o41.2544 mm55 mm41.3627.523119.9937o37.5o38o121.5o122.5o122o29.341.62544 mm41.3627.523133123737.538121.5122122.5Distance of epicenter from 37.5o latitude line = 28 mm 111 mm = 1oLatitude of epicenter = 37.5+28/111 = 37.7522o= 37o 458Distance of epicenter from 122o longitude line = 8.5 mm88 mm = 1oLongitude of epicenter= 122+8.5/88 =122.0966o= 122o54813Exercise ProblemsAssuming P and S wave traveled through the crust at 6 km/sec and 3 km/sec respectively, estimate the possible location of the epicenter P of a shallow earthquake if P forms an equilateral triangle with two points A (10,10) and B (35, 10) on the ground surface. What is the difference in the arrival time of P and S waves at A and B?

Two Seismographic stations A and B are located 200 km apart on level ground. An earthquake occurred between these two stations and the epicenter is located exactly on the line joining these two stations. The difference in time between P and S wave arrivals was 10 seconds at A and 15 seconds at B. Determine the location of epicenter from these two stations.

14Kramer, S.L. (1996) Geotechnical Earthquake Engineering, Prentice Hall. http://www.youtube.com/watch?v=cN2FtHY3LyA (Demo video)http://www.youtube.com/watch?v=UsIn3CzggpgActivity: http://serc.carleton.edu/NAGTWorkshops/geophysics/activities/25073.html (Accessed on 27 March, 2012)

References15SeismographArrival Time

LatitudeLongitudeP- waveS-wave

37(2230121(523006:11:18.9306:11:26.9

37(4500122(200006:11:14.8406:11:18.71

37(5233121(433806:11:17.2606:11:23.53

SeismographDifference in arrival time of P and S wavesDistance from epicenter

LatitudeLatitudeLongitudeLongitudet (sec)D (km)

37(223037.375(121(5230121.875(7.9747.8

37(450037.75(122(2000122.333(3.8723.2

37(523337.876(121(4338121.7272(6.2737.6