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Math Help - Maths Earthquake Problem!?

  1. #1
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    Question Maths Earthquake Problem!?

    I've been assigned a task to find the epicenter of an earthquake:

    "3 of the Australian government seismic measurements stations have reported the following data -

    Difference between arrival times in seconds (S and P waves*)
    Gold Coast - 97.8
    Townsville - 71.1
    Mt Isa - 54.5

    *You may assume that the speed of a P-Wave is 7.5km/s & the speed of an S-Wave is 4.5km/s"

    It then gives a suggested method to be followed:
    - Find distance from each 3 place to the epicente
    - Build diagram that uses longitude and latitude as its co-ordinate system
    - Define any further variables
    - Develop vector relationships between each of the cities and the epicenter of the earthquake and use these to find the epicentre
    - Generalise model for any 3 seismology centres and arrival times

    OKAY so I'm kind of confused about how I'm supposed to find the epicentre and also how I am supposed to incorporate vectors and latitude/longitude into the solution
    Any help would be greatly appreciated!!!!
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  2. #2
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    Re: Maths Earthquake Problem!?

    Quote Originally Posted by monicaisobel View Post
    I've been assigned a task to find the epicenter of an earthquake:

    "3 of the Australian government seismic measurements stations have reported the following data -

    Difference between arrival times in seconds (S and P waves*)
    Gold Coast - 97.8
    Townsville - 71.1
    Mt Isa - 54.5

    *You may assume that the speed of a P-Wave is 7.5km/s & the speed of an S-Wave is 4.5km/s"
    Suppose the time it took for the P wave to arrive was T seconds. Then the distance would be X= 7.6 km/s* T. The time for the S wave to arrive is T+ 97.8s so we have 4.5 km/s*(T+ 97.8)= X also. Setting those equal, 7.6T= 4.5(T+ 97.8)= 4.5T+ 440.1. Then (7.5- 4.5)T= 3T= 440.1 so that T= 146.7 s. The distance then is 146.7*7.5= 1100.25 km. Do the same thing for the other two places.

    It then gives a suggested method to be followed:
    - Find distance from each 3 place to the epicente
    - Build diagram that uses longitude and latitude as its co-ordinate system
    Place these cities on a "diagram" or, better, map, and be sure to put the cities at the correct relationship to one another using, as it says, the longitue and latitude of each. The draw a circle around each city using the distances found as the radii. Those three circles should all intersect at least close to a single point.

    - Define any further variables
    - Develop vector relationships between each of the cities and the epicenter of the earthquake and use these to find the epicentre
    - Generalise model for any 3 seismology centres and arrival times

    OKAY so I'm kind of confused about how I'm supposed to find the epicentre and also how I am supposed to incorporate vectors and latitude/longitude into the solution
    Any help would be greatly appreciated!!!!
    The "latitude/longitude" of each city is used to put each city on your map. If you can identify a point where all three circles at least come close to intersecting, that will be the epicenter. The vectors will be from each city to the epicenter.
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