1. ## 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!!!!

2. ## Re: Maths Earthquake Problem!?

Originally Posted by monicaisobel
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.