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How do I find the depth?

Hi,

I've made a quick sketch on photoshop for this problem.



4 holes are drilled into the ground and coal is found at points A, B, C and D; at depth A = 50m, B = 90m, and C = 150m

How would I be able to determine the depth at D?


I'm very desperate for an answer! It will come up in my exam in geology.
(edited 12 years ago)
Reply 1
Bump, anyone? My exam is tommorw. :frown:
Original post by Geiger
Bump, anyone? My exam is tommorw. :frown:


Couple of options:

Assuming the underlying coal lies in a plane, using Da for the depth at A, etc. you have:

Db-Dc = Da-Dd

This works because you have a rectangular grid.


However if that is too terse and assumes too much, you'll need to use the equation of a plane. Equally if you get a question where the grid isn't rectangular, nor something else nice, you'll need this method.

So slap a set of co-ordinates on the grid - I'd base it at D.

Then at any point the depth is givan by H = ax + by +c, where a,b,c constants, as yet unknown, H is the depth of the coal at the hole, and x,y are the co-ordinates of the hole.

Set up three equations for the three known holes, and solve. You're only interested in the value of c, as that will be the depth as the origin, the hole D.
(edited 12 years ago)
Reply 3
Original post by ghostwalker
Couple of options:

Assuming the underlying coal lies in a plane, using Da for the depth at A, etc. you have:

Db-Dc = Da-Dd

This works because you have a rectangular grid.


However if that is too terse and assumes too much, you'll need to use the equation of a plane. Equally if you get a question where the grid isn't rectangular, nor something else nice, you'll need this method.

So slap a set of co-ordinates on the grid - I'd base it at D.

Then at any point the depth is givan by H = ax + by +c, where a,b,c constants, as yet unknown, H is the depth of the coal at the hole, and x,y are the co-ordinates of the hole.

Set up three equations for the three known holes, and solve. You're only interested in the value of c, as that will be the depth as the origin, the hole D.


Thanks for your answer! Yes, it's a plane. Using your equation would mean the depth of Dd is 150m, and we don't have to use the 400m and 300m, right? It seems abit bizzare that it's that simple because we get 4 marks for it, it's geology for engineers.

Could it be that you meant,
Dd-Dc = Da-Db? Because then the answer would be 110m.
(edited 12 years ago)
Original post by Geiger
Thanks for your answer! Yes, it's a plane. Using your equation would mean the depth of Dd is 150m


Have another go.

and we don't have to use the 400m and 300m, right?


That's correct, as it's a rectangular grid.


It seems abit bizzare that it's that simple because we get 4 marks for it, it's geology for engineers.


Depends what you've covered in your course; I don't know what they're expecting. The second method is more general.


Could it be that you meant,
Dd-Dc = Da-Db? Because then the answer would be 110m.


That method works as well; mathematically it's the same thing.
Reply 5
Original post by ghostwalker
Have another go.

That's correct, as it's a rectangular grid.

Depends what you've covered in your course; I don't know what they're expecting. The second method is more general.

That method works as well; mathematically it's the same thing.


Ah wonderful. Thanks again, it's 110m for bothd equation. Haven't had much sleep in the last days.

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