## ES 10 The Earth Homework 5 Geologic Time and Stratigraphy Due 9 March 1998 Greg Anderson

This homework set is worth a total of 100 points. Be sure to read the entire assignment carefully before beginning work on it. You should read Chapter 7 of The Blue Planet and the lecture notes from Lectures 10, 14, and 15, before you attempt this homework.

Please write your answers on paper other than this assignment, make sure your name is on each page, and staple your pages together. If you have problems with or questions about the homework, please come see me at the discussion section or send me an e-mail. My e-mail address is anderson@python.ucsd.edu; the discussion section will be held on Wednesday evening, 4 March, at 5:45 in Peterson 103.

### Stratigraphy

Let's assume you are a field geologist, hiking around with your notebook, compass, hammer, and backpack. You are trying to make a unified stratigraphic column from the various outcrops you have seen around you. You need to figure out how to stack the various rock layers in the outcrops so that they are in chronological order, with the oldest rocks on the bottom (remember the Principle of Superposition?). Fortunately, some of the same rock layers are seen in more than one outcrop. Unfortunately, sometimes there are unconformities, and you need to try to work around them.

#### Question 1 (4 points)

You have looked at three outcrops today, and you have sketched them in your notebook (see Figure 1), using rectangles to represent the rock layers, with different layers having different fill patterns. You have arbitrarily labeled the rock layers A-I, carefully noting that the labels do not necessarily correspond to the correct chronological order.

You're back at camp now and you are going to assemble the stratigraphic column. Write down the chronological order for the rock layers, with the oldest rock layer first. That is all you need to write down--just the order of the rock layers. If you decide that some of the layers are the same rock (just with different labels), write down both labels with a slash (``/'') between them, like ``A/B''.

Your answer should look something like: I, H, G, D/E, F, A, C, B. Note that this order is not the right one.

#### Question 2 (6 points)

It has been another long day in the field, and you have been looking at more rock outcrops, and making more notebook sketches (see Figure 2). Again, you have labeled the rock layers arbitrarily (A-L). You have also noted that there is an unconformity between layers ``A'' and ``B''.

It is again evening in camp, and you are trying to make sense of the order of rocks you have seen. Again, you are to write down the correct chronological order for the rock layers, just as in Question 1 (remember to write down the oldest layer first!).

### Stratigraphy and the ``History of Rocks''

The next three problems are more challenging. Here, you need to examine the sketches in your notebook and use the principles of structural geology (re-read your notes from Lectures 10, and 15) to unravel the complex history of the structures you have seen.

When you are asked to write down the geologic history of a region, what does that mean? It means you need to list all the important geologic events which you can deduce from the rock section you have. Some of the things you might have to list are the order in which rock layers were laid down, when intrusions or extrusive volcanics were made relative to the other events in the history, when layers were eroded or folded or faulted, etc.

#### Question 3 (10 points)

Today, you and the field crew have been exploring a river canyon. High up in the wall of one side of the canyon, you have seen (and sketched) what is Figure 3. Here, there are 4 rock layers (A-D) and a nice granitic batholith (E).

You need to write down (in chronological order) the geologic history of the region. You don't need to be long-winded. A simple list like:

1. First, this happened
2. Next, this happened
3. And then this happened
4. Finally, this happened
is fine!

#### Question 4 (10 points)

You are again doing the same sort of work. Look at Figure 4 and write down the geologic history of the area. Again, just a simple list (as in Question 3) is all you need to do - don't spend too much time being long-winded. You may assume for this question that layer D is the oldest layer.

#### Question 5 (20 points)

This time, things are really complicated. After a lot of work, you have sketched in your notebook Figure 5. Here, there are rock layers going in all sorts of directions and two faults.

Again, you need to write down the geologic history of the region. Make sure to tell me when the faults were formed relative to the rock layers (i.e. they formed before layer X and after layer Y). Also, you need to tell me what kinds of faults the two faults shown in your sketch are, and which fault formed first (the one between layers H and I or the one between layers K and L).

You may assume for this question that layer M is the oldest layer. Also note that the arrows in Figure 5 are meant to show relative motion of the two sides of each fault, not the absolute motions of the bodies of rock on either side of each fault.

### Dating Rocks Using Radioactive Decay

You will want to read the lecture notes from Lectures 14 and 15 before attempting these problems. You will find the notes from David Sandwell's Lecture 14 particularly helpful; in fact, all the equations you will need are given in the notes for that lecture. Read them.

For all the questions in this part, you must show your work in order to get any credit. If you do not show your work, you will get no credit for the work you do. It's also important to show your work so I can give you partial credit; unless I can see where you went wrong (if you did), I cannot give you credit for the parts you did correctly.

#### Question 6 (10 points)

A scientist in a lab somewhere has measured the number of atoms in a sample over time. The sample starts out as pure Polonium-218 (Po-218) and decays radioactively to Lead-214 (Pb-214). The scientist has made the measurements shown in Table 1. Using Table 1, answer the following questions.

1. Compute the half-life of Po-218 to the nearest minute.
2. Compute the decay constant () for the decay of Po-218 to Pb-214. Give your answer in units of 1/min.
3. I give you a sample of material which contains both Po-218 and Pb-214. I tell you that there are 1185 atoms of Po-218 and 537 Pb-214 atoms. Assuming that the material was originally 100% pure Po-218, how old is the sample I've given you, to the nearest minute?

#### Question 7 (40 points)

Look at Figure 1). As part of your mapping effort, you've taken samples of layer C from Outcrop 1 and layers D and F from Outcrop 2. You want to find out how old the rocks are, so you take them to the lab to date them using radioactive decay.

In the lab, you are looking at the rock from layer C. You are going to date this rock using the Rubidium-87 (Rb-87) to Strontium-87 (Sr-87) decay method. You find 15000 atoms of Rb-87 and 323 atoms of Sr-87 in your sample. Given that Rb-87 decays to Sr-87 with a half-life of 48.8 billion years, and assuming that all the strontium in the sample comes from decay of rubidium, answer the following questions:

1. Compute the decay constant () for the decay of Rb-87 to Sr-87 Give your answer in units of 1/year.
2. How old is layer C in years?

Next, you look at the rock from layer D. You are going to date this rock using the Potassium-40 (K-40) to Argon-40 (Ar-40) decay method. You note that there are 1500 atoms of K-40 and 500 atoms of Ar-40 in the sample. Given that K-40 decays to Ar-40 with a half-life of 1.25 billion years, and assuming that all the argon in the sample comes from decay of potassium, answer the following questions:

1. Compute the decay constant () for the decay of K-40 to Ar-40. Give your answer in units of 1/year.
2. How old is layer D in years?

Finally, you look at the rock from layer E. You are going to date this rock using the Thorium-232 (Th-232) to Lead-208 (Pb-208) decay method. You note that there are 10000 atoms of Th-232 and 302 atoms of Pb-208 in the sample. Given that Th-232 decays to Pb-208 with a decay constant decay constant of 4.9511 × 10-11 1/year, and assuming that all the lead in the sample comes from decay of thorium, answer the following questions:

1. Compute the half-life for the decay of Th-232 to Pb-208. Give your answer in units of years.
2. How old is layer E in years?

Given your answers to (b), (d), and (f) above, and your answer to Question 1, how old are layers A, B, E, G, and I in Figure 1? Note that you might not be able to give exact answers for some of those layers; simply be as accurate as you can be.

Table 1: Radioactive Decay of Polonium-218

Time
(min)
Po-218 atoms
(parent)
Pb-214 atoms
(daughter)
0 1000 0
1 794 206
2 630 370
3 500 500
4 396 604
5 314 686
6 250 750
7 198 802
8 157 843
9 125 875
10 99 901