Geologic Mapping C

[hippo9]

1. Subduction zones occur at what type of plate boundary?

2. What type of crust is "subducted" during subduction?

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1. Subduction zones occur at what type of plate boundary?

2. What type of crust is "subducted" during subduction?

Click to Show Answer

1) Convergent (oceanic-continental or oceanic-oceanic)

2) Oceanic

[hippo9]

Click to Show Answer

1) Convergent (oceanic-continental or oceanic-oceanic)

2) Oceanic

Yep your turn

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Suppose there are three drills going through a layer of rock underground. Assume all of the drills start at the same elevation. The first drill is pointed straight down and hits the layer at 1.1 km along its path. The second drill is 83 km north and 3 km east of the first drill. It is also pointed straight down. It hits the layer at 2.4 km along its path. The third drill is 75 km west of the first drill. It is angled at 85 degrees below horizontal pointing towards east and hits the layer at 1.9 km along its path. Find the strike and dip of the layer.

Bonus: If the first drill exits the layer at 1.2 km directly under it, what is the thickness of the layer?

[Reeeee-o-mapping]

I did this problem by drawing it out as opposed to just doing the math so my answer might be off.
Strike: N57°E, Dip: 11.2°NW, Thickness: 1.18 km

[UTF-8 U+6211 U+662F]

In the general ballpark of what I got

(Sorry I wasn't quite clear with the wording for the thickness problem... the drill exits the layer at 1.2 km below the ground, not 1.2 km below the point where it entered the layer. If it exited the layer at 1.2 km below the point where it entered the layer, your answer would be correct.)

My mathematical solution for completeness (Click to Show Hidden Text)

Part 1:

Represent the information as three coordinates (x, y, z) and let (0, 0, 0) be the position of the first drill at ground level.
Positive x represents east, and negative x represents west.
Positive y represents north, and negative y represents south.
Positive z represents up, and negative z represents down.

First: (0, 0, -1.1)
Second: (3, 83, -2.4)
Third: (-75 + 1.9cos(85°), 0, -1.9sin(85°)) or (-74.8, 0, -1.89)

Now, we can solve for the equation of the plane.
In 2 dimensions, a possible equation for the line would be [math]y = mx + y_0[/math].
In 3 dimensions, a possible equation for the plane would be [math]z = m_xx + m_yy + z_0[/math].
Plugging in our values, we get these three equations:
[math]-1.1 = m_x\cdot 0 + m_y\cdot 0 + z_0[/math]
[math]-2.4 = m_x\cdot 3 + m_y\cdot 83 + z_0[/math]
[math]-1.89 = m_x\cdot -74.8 + m_y\cdot 0 + z_0[/math]

Part 2:

Now, we have three linear equations in three variables. Solve this however you like! Here, I'll use Cramer's rule (best used with a calculator that supports matrices), but you can use any method you want:

[math]m_x = \frac{\begin{vmatrix}-1.1 & 0 & 1 \\ -2.4 & 83 & 1 \\ -1.89 & 0 & 1\end{vmatrix}}{\begin{vmatrix}0 & 0 & 1 \\ 3 & 83 & 1 \\ -74.8 & 0 & 1\end{vmatrix}} = 0.0106[/math]

[math]m_y = \frac{\begin{vmatrix}0 & -1.1 & 1 \\ 3 & -2.4 & 1 \\ -74.8 & -1.89 & 1\end{vmatrix}}{\begin{vmatrix}0 & 0 & 1 \\ 3 & 83 & 1 \\ -74.8 & 0 & 1\end{vmatrix}} = -0.160[/math]

[math]z_0 = \frac{\begin{vmatrix}0 & 0 & -1.1 \\ 3 & 83 & -2.4 \\ -74.8 & 0 & -1.89\end{vmatrix}}{\begin{vmatrix}0 & 0 & 1 \\ 3 & 83 & 1 \\ -74.8 & 0 & 1\end{vmatrix}} = -1.1[/math]

So we get the equation [math]z = 0.0106x - 0.160y - 1.1[/math]

Part 3:

The strike (measured clockwise from north) is [math]\arctan\frac{0.160}{0.0106} = 86.2\degree[/math]

(For those that understand calculus notation, [math]\frac{0.160}{0.0106} = \frac{\partial x}{\partial y}[/math])

So, the dip direction is either 176.2° or -1.8°. In this case, it is -1.8°. Using the apparent dip equation, the dip is [math]\arctan\frac{\tan{AD}}{\sin(90\degree - 1.8\degree)} = \arctan\frac{0.160}{\sin{88.2\degree}} = 9.09\degree\textrm{NW}[/math]

([math]\tan{AD} = \frac{-\partial z}{\partial y}[/math])

The thickness is [math]0.1\cos{9.09\degree} = 0.0987\ \textrm{km}[/math]

Your turn!

Edit: Just to be clear, you don't need matrices to solve it, and simply drawing it out without solving any systems of equations is a perfectly valid way of doing it.

[Reeeee-o-mapping]

In each of the following pairs, state the one that would be more likely to experience ductile deformation and explain why:

Rock at Low/High temperature

Rock under a 10m Igneous/Sedimentary layer

Rock experiencing a Low/High strain rate

Rocks rich in Feldspars/Micas with a Low/High water content

[linzhiyan]

In each of the following pairs, state the one that would be more likely to experience ductile deformation and explain why:

Rock at Low/High temperature

Rock under a 10m Igneous/Sedimentary layer

Rock experiencing a Low/High strain rate

Rocks rich in Feldspars/Micas with a Low/High water content

Attempt (Click to Show Hidden Text)

1) high
2) Sedimentary
3) High
4) Micas, High

[Reeeee-o-mapping]

Almost!
1. High temperature is right!
2. It's actually igneous (igneous rocks are denser, which means they're heavier, which would create more pressure and thus lead to ductile deformation)
3. Low strain rate is actually more conducive to ductile deformation than high strain rate, as quick and sudden stresses don't give the rock time to deform and often lead to fracture.
4. Micas with high water content is right! Your turn!

[linzhiyan]

Sorry, I completely forgot about this...

1. List the following geologic time periods from the oldest to the most recent.
Pliocene, Jurassic, Triassic, Mississipian, Pleistocene, Silurian, Pennsylvanian.

2. State the process of the formation of a metamorphic rock. (In general.)

3. How are plate tectonics formed?