3 Point Problem

Here is our original map. We want to find the strike and dip of a thin limestone bed that outcrops at the three X's.

Step 1

Draw a line between the outcrop at the highest elevation and the outcrop at the lowest elevation. If you have two outcrops at the same elevation (which does not apply to this particular problem), then draw a line between them instead. That is your strike line and you can skip ahead to step 4.

Measure the map distance of that red line with your ruler (I get about 1600m). Set up a triangle with the map distance and elevation difference at two ends to calculate the apparent dip. The apparent dip tells you that the true dip has to be at least that value, it cannot be less.

tan(θ) = (opp/adj)
tan(θ) = (400m/1600m)
tan-1(400m/1600m) = θ = 14° = apparent dip

Step 2

Now, along the red line you drew, you want to find out where the elevation of the third point, for this case 300m, would lie (ignore the elevation contours along the red line). Take the difference of elevation between the third point and one of the other given points, we'll use the outcrop at 200m (300m outcrop - 200m outcrop). Set up another triangle using the apparent dip angle.

tan(14°) = (100m/X)
X = (100m/tan(14°)) = 401m

Step 3

Now, measure 401m along the red line away from the outcrop at 200m (if you used the outcrop at 600m as one of your other given points in step 2, then X = 1199m and you would move 1199m along the red line from the outcrop at 600m and end up at the same place) and make a mark (the blue square).

Now, connect that line to the third given outcrop point which is also at 300m - that is your strike line (the green line).

Step 4

The dip is orthogonal (at a right angle) to the strike line. The dip direction will be in the general direction of the lower elevation. To help understand this, just picture a cross section in your head. With a high point on the left side and a low point on the right side, the bed would have to be dipping from the left to the right (or be an incredibly thick bed, but we are told it is a thin limestone bed).

So, in this case, the dip is in the SE direction (the pink line).

Step 5

To figure out the true dip angle, extend the 300m strike line. Connect that strike line to the 200m outcrop so that the line is orthogonal to the 300m line. Measure the distance of that purple line with your ruler (I get about 240m).

Set up another triangle with the elevation difference being 100m (300m strike line - 200m outcrop elevation). The tan of that angle is the true dip.

tan(θ) = (opp/adj)
tan(θ) = (100m/240m)
tan-1(100m/240m) = θ = 23° = true dip

Step 6

To figure out the outcrop pattern, continue making strike lines with 100m contours. Set up another triangle with the elevation 100m and the dip angle 23° to solve for side adjacent to the angle. That is how far apart your strike lines should be spaced. After you draw in all of your strike lines (they should be equally spaced, mine are not because I suck), make a mark (the orange marks) everytime a strike line at a certain elevation comes in contact with an elevation contour of the same value. Then, roughly connect the dots and you have your outcrop pattern!

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