This lesson will last one week. In it, we'll explore some basic points about faults and earthquakes. We will also see how archaeology and solid Earth geoscience are linked.
By the end of Lesson 7 you should be able to:
Lesson 7 will take us one week to complete: 22 - 28 Jul 2020.
The chart below provides an overview of the requirements for Lesson 7.
Requirement | Submitted for Grading? | Due Date |
---|---|---|
Reading discussion: Read articles and discuss them with the class | Yes - Your discussion board participation counts toward your discussion grade. | ongoing participation in the Canvas discussion "Delphic Oracle" 22 - 28 Jul 2020 |
Problem set: Greek earthquake problem set | Yes - This exercise will be submitted to the "Greek earthquake problem set" assignment in Canvas. | 28 Jul 2020 |
If you have any questions, please post them to our Questions? Discussion Forum (not e-mail). I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.
This lesson's Neat-o Interdisciplinary Idea is that solid Earth geoscience can be linked with archaeology. We are going to begin this lesson on faults and earthquakes by reading two related papers about how a team that consisted of a geologist, an archaeologist, a toxicologist, and a chemist worked together to find out whether ancient writings about the Temple of Apollo at Delphi were true. Two-thousand-year-old texts claimed that noxious vapors and springs came out of the ground at the site of the Temple of Apollo at Delphi and that the oracle of the temple got her powers of divination from breathing them. In the early 1900s, geologists and archeologists thought those writings were complete fiction because they found no evidence of any vapors. However, a more thorough recent investigation of the tectonic setting at Delphi, done by the authors of the papers we'll read, supports the ancient writings and even makes a reasonable claim about the probable composition of the gas.
Once you have finished the readings, engage in a class discussion as described below.
This discussion will take place over the first week of this lesson and will require you to participate multiple times during that period.
You will be graded on the quality of your participation. See the grading rubric [2] for specifics on how this assignment will be graded.
In the articles you just read, the authors assume you know something about faults: how they are classified, what kind of motion they experience, what sense of stress they feel, and how to recognize them on a map. Therefore, it is time to step back a little and review some basic material about faults and earthquakes.
A fault is formed in the Earth's crust as a brittle response to stress. Generally, the movement of the tectonic plates provides the stress, and rocks at the surface break in response to this. Faults have no particular length scale. If you whack a hand-sample-sized piece of rock with a hammer, the cracks and breakages you make are faults. At the other end of the spectrum, some plate-boundary faults are thousands of kilometers in length.
The sense of stress determines the type of fault that forms, and we usually categorize that sense of stress in three different ways:
Handily, these three senses of stress also correlate with the three types of plate boundaries.
In terms of faulting, compressive stress produces reverse faults, tensional stress produces normal faults, and shear stress produces transform faults. *Terminology alert: Geoscientists refer to faults that are formed by shearing as transform faults in the ocean, and as strike-slip faults on continents. Otherwise, these two types of faults are basically the same thing. Check out the sketches below to see a cartoon of what each of these fault types look like in cross-section.
Here we have a basic cross-section consisting of three rock layers: brown, pink, and granite. You can tell it's a cross-section because I drew a little tree (Bob Ross-style!) and a couple of birds and the sun.
Now we'll apply some tensional stress to this terrain. Tension has the effect of pulling and elongating. If this material were ductile, it would stretch and get thinner, but we are dealing with brittle rocks here, so instead they will break. The way this typically happens is by forming a fault at some angle to the bedding. Then the whole package of rocks slides along this fault. The type of fault formed here is called a normal fault. This terminology came from miners in Germany who noticed that most of the faults where they were working were of this nature, so they called them "normal," meaning typical.
As you can see, the fault has had the effect of dropping the block on the right with respect to the block on the left. If you saw something like this in the field, you'd be able to tell how much offset there was on the fault by measuring how much the layers had moved across the fault.
If we instead apply compressive stress, this has the effect of squeezing and shortening the terrain. A fault will form that looks an awful lot like the normal fault in the previous example, but the motion on this fault is in the opposite direction. This fault is called a reverse fault because it is the "reverse," meaning opposite, of normal. Reverse faults tend to form scarps--a scarp is the piece of rock that has been thrust up higher than the original surface level.
The third typical fault type is the strike-slip fault. Strike-slip faults are distinct from the previous two because they don't involve vertical motion. They form via shear stress. These are not as easy to recognize in cross-section unless there has been so much movement on the fault that there are completely different rock types on either side of the fault. Most strike-slip faults are close to vertical with respect to the bedding.
See in the animation below how the various fault types move. Animation is silent and comes from IRIS [3].
Each of these three types of faults is marked in a standard way on a geologic map. I've sketched those symbols below.
Can you identify the type of faulting occurring at each plate boundary in the map below? Check your answer here [4]. (and a captioned version [5]).
Have another look at Figure 1 from de Boer et al., 2001 (reproduced below). What type of faulting is being depicted on that map? Can you picture in three dimensions how the lithosphere is moving in that map? Think about it and compare your idea to my sketch [7] (and a captioned version [8]).
When an earthquake happens, the main quantity of interest is its magnitude. How big was the earthquake? Over the years, scientists have developed various ways to measure earthquake size and strength. Here's an overview of the most common magnitude measurements.
This scale is a qualitative measure of the amount of felt shaking caused by an earthquake. This scale goes from I (not much of anything) to XII (total destruction). The amount of felt shaking is generally measured by interviewing witnesses to find out how much shaking they felt. Sometimes the interviews can be supplemented by observing any earthquake damage to buildings. For earthquakes in the historic record that happened before the advent of seismometers, Mercalli intensities are often assigned by checking out old newspaper reports and examining the foundations of old buildings. Mercalli intensities are generally depicted on maps by several concentric rings around the epicenter of the earthquake that give some idea of the severity of the felt shaking at various distances away from the earthquake. The Mercalli is not a very useful scale for science because it can't tell us much about big earthquakes that are not felt by people--earthquakes that occur at a great depth, or in the ocean, for example.
Charles Richter developed a magnitude scale in the 1930s because he wanted to be able to characterize the seismicity he had been measuring in California with some kind of numbering system that would encompass all the earthquakes, from ones that had hardly been felt at all, up to really big ones. The way he did this was to pick a reference earthquake and measure its maximum ground motion. Then all the other earthquakes he had recorded could be compared to the reference, after correcting for distance. Each integer increase represented a factor of 10 increase in ground motion amplitude. This scale worked because he always used the same type of seismometer and all his earthquakes were in southern California, so there didn't have to be any extra corrections for different depth or rock type. Today, scientists don't use the Richter scale the way he did because not all earthquakes of interest happen in California, and also because the type of seismometer he used is out of date now. For all measurements recorded on a different type of instrument or that measured amplitudes of different wavetypes, you'd have to make a conversion to get your number to be in line with Richter's scale. The handy thing about the Richter scale is that for most earthquakes of interest, the magnitudes end up being numbers that range from about 3 - 9 and these are numbers easily understood by people. (In fact the scale itself does not set an upper or lower limit; limits of earthquake size are set by the Earth).
Today scientists calculate the seismic moment of an earthquake when they want to talk about how big it was. Seismic moment (M0) is simply the product of the average amount of slip that happened, the area of the fault that slipped, and the rigidity of the rock. The equation is :
M0 = rigidity x area x slip
The rigidity of rock is a constant number based on the rock type. It has units of pressure. Typical assumptions are on the order of 3 x 1010 N/m2. Slip is a length and it is on the order of centimeters (meters for a great earthquake). Area is in units of length2 and is often on the order of km2. The units for seismic moment are then Nm (newton meters). As an example, the 2004 26 December Sumatra-Andaman earthquake had the following dimensions as reported by Lay et al. (2005): Its slip averaged about 5 m, its rupture length was about 1300 km and the fault width was between 160 - 240 km. Assuming a rigidity of 3 x 1010 N/m2 gives us a seismic moment of 3.9 x 1022Nm. See a pencast calculation of this earthquakes's seismic moment [9].
Now, the problem with seismic moment is that regular people who watch the news or read the papers don't really know what to make of a number like 4.4 x 1022Nm, and even scientists are smart enough to realize this, so we convert seismic moment to a magnitude scale called "moment magnitude," usually symbolized Mw or sometimes just M. This scale is designed purposely to be about equal to Richter's scale so that people will have a feel for what it means. Hiroo Kanamori at Caltech derived the formula for the conversion of seismic moment to moment magnitude as follows:
Mw = (2/3)*logM0 - 6.05
Using Kanamori's formula to convert seismic moment to moment magnitude, what was the magnitude of the 2004 Dec 26 Sumatra-Andaman earthquake? Try it yourself and then check your work by clicking below:
Click here for my answer for the magnitude of the Sumatra-Andaman earthquake.
The answer is 9.05. Here is how I got that answer:
The seismic moment was 4.4 x 10^22 Nm.
Take the log (base 10) of that number and get 22.64
Multiply that by 2/3 and get 15.10
Subtract 6.05 and get 9.05
Another way to think about earthquake size is in terms of the energy released by an earthquake. It is actually not terribly easy to measure all the energy released by an earthquake because you have to integrate over time and space and include the broadest possible spectrum of frequencies to make sure you are recording all the energy. Therefore, direct measurements usually underestimate the energy. If they aren't trying to measure it instrumentally, most seismologists just use the following empirical formula, developed by Båth (1966) to relate magnitude to energy (in units of joules):
log E = 5.24 + 1.44M
This relationship was only meant to work for fairly big (M > 5) earthquakes. Plug magnitude values of 5.0, 6.0, and 7.0 into the equation above. The energy released by an M5 earthquake is about 2.8 x 1012 joules. An M6 earthquake releases 7.8 x 1013 joules, and an M7 radiates 2.1 x 1015 joules. If you don't have a sense for what these numbers mean, the bomb dropped on Hiroshima released about 7.4 x 1012 joules. Even though all of these are large numbers, what I want you to see here is that the difference between these values is huge. A magnitude 7 releases almost 30 times as much energy as a magnitude 6.
Using the formula to relate magnitude to energy, how much energy was radiated by the Sumatra-Andaman earthquake? Try it yourself and then check your work by clicking below:
Click here for my answer to how much energy was radiated by the Sumatra-Andaman earthquake.
The answer is 1.84 x 10^18 joules. Here is how I got that answer:
The magnitude is 9.05. We already knew that.
Multiply magnitude by 1.44 and get 13.03.
Add 5.24 and get 18.27
Raise 10 to the power of 18.27 and get 1.84 x 10^18 joules
A 60-watt incandescent light bulb uses 60 joules of energy per second. The rupture of the Sumatra-Andaman earthquake lasted about 500 seconds. So,this earthquake released enough energy during its rupture to light up how many 60-watt lightbulbs? Try it yourself and then check your work by clicking below:
Click here for my answer to how many 60-watt lightbulbs the energy would light up.
The answer is 6.14 x 10^13 60-watt lightbulbs. Here is how I got that answer:
The earthquake radiated 1.84 x 10^18 joules. We knew that already.
Multiply 60 by 500 and get 30000 joules used by one lightbulb in 500 seconds
Divide that into 1.84 x 10^18 joules and get 6.15 x 10^13 lightbulbs
Wow, that's a lot of light bulbs! In fact, if you assume they are all about 4 inches in diameter, then if you put this many lightbulbs side by side you would have a trail that goes farther than the distance from the Sun to Neptune. That's a long way.
That was a really big earthquake.
Large earthquakes trigger seismicity dynamically from shaking as well as statically, from changing the surrounding stress field. Aftershocks are a specific class of triggered seismicity whose spatial and temporal properties have been well characterized by many empirical observations. By "empirical" I mean that the laws that govern the timing and size of aftershocks are not based on any kind of physics; instead they are merely fits to many observations. However, the observations have been so numerous that we know these fits are robust, hence we call them "laws." I hesitate to use the word "prediction" when talking of earthquakes, but in the case of aftershocks, their timing and areal extent can be estimated fairly accurately just from knowing the size and location of the mainshock.
This empirical law states that the largest magnitude aftershock will be between 1.1 and 1.2 magnitude units smaller than the mainshock. This observation is independent of the size of the mainshock. Now is a good time to digress and mention that some of this categorization is definition dependent. What I mean is that, because of the way we define them, aftershocks can never be bigger than the mainshock. If an aftershock bigger than the mainshock were to occur, we'd just reclassify that one as the mainshock and call the previous biggie a foreshock. This may seem conveniently circular, but, logically, there's no other way to do it. The biggest earthquake in a sequence has to be called the mainshock.
The Japanese seismologist after whom this law is named formulated his empirical observation about the temporal decay of aftershocks in the 1890s. (See Lesson 2 for more about his life and times!) He realized that the rate of aftershocks decays with time after the mainshock and that this decay happens to be inversely proportional to the time after the main shock. The modified version of his law is written like this:
N(t) ∝ (c+t)-p
in which N is the number of aftershocks as a function of time t after the mainshock and c and p are constants. In practice c is a very small number and p is somewhere around 1. In the case of c = 0 and p = 1, the equation above just simplifies to Omori's original law:
N(t) ∝ 1/t.
Try plugging in some numbers to this equation with any units you want for time, such as days. You will see that the number of aftershocks drops off rapidly at first and then decays more slowly. Once the number of aftershocks has dwindled to whatever the normal background seismicity rate is for the region, we say the aftershock sequence is over. Having trouble picturing this concept? See my screencast explanation of Omori's Law [11]. Click here for a close-captioned explanation of Omori's Law [12].
People often get confused and think that this law governs both the size and timing of aftershocks. In fact, Omori's law says nothing about the size of aftershocks. The often-observed fact that bigger aftershocks usually happen pretty soon after the main shock is just a mathematical coincidence. Because there are fewer and fewer aftershocks at all as time gets farther from the main shock, the likelihood of one of them being big is also less. This is simply because there are always many more small earthquakes than big ones in any region for any period of time. (If you took EARTH 501, you will remember this from the frequency-magnitude plots you made in the New Madrid lesson.)
A third useful observation about aftershocks is that they usually cluster around the edges of the area ruptured by the main shock. I think this makes intuitive sense. You can think of an earthquake rupture as getting rid of all the built-up stress over the patch that breaks. However, maybe some of the excess stress at the edges where the earthquake stops is still there. As the fault gets used to the new stress field, little earthquakes happen at the boundary between what broke and what didn't. This feature of aftershocks comes in handy because it helps for estimating hazard and risk associated with aftershocks if you know approximately where they are going to be. It is also useful scientifically because it provides a check on the calculated size of the rupture area that seismologists normally derive from theoretical models. The map below shows aftershock locations following the 26 December 2004 Sumatra-Andaman earthquake. This earthquake ruptured the longest segment of a fault ever recorded, somewhere between 1300 and 1600 kilometers. You can see what a huge areal extent the aftershocks cover. Each little colored circle on the map below is an aftershock.
Now you are going to use the USGS Web site to find out some earthquake parameters using their database of publicly available earthquake data. Since we started out this lesson by discussing the particulars about an interesting tectonic regime in ancient Greece, let's stay in Greece and find out some things about its more recent tectonic activities.
Go to the USGS Latest Earthquakes Map [13]and follow my directions below. We are looking for a magnitude 6.4 earthquake that happened in Greece on June 8, 2008.
Click the settings icon, which looks like a bike sprocket in the upper right corner of the page.
Scroll down in the settings menu to the Search Earthquake Catalog bar and click it
Under Magnitude, click the Custom button and enter 6 as the minimum magnitude
Under Date & Time, enter 2008-06-08 as the start date and 2008-06-09 as the end date
Under Geographic Region, select World
Don't change anything else.
Scroll down and click Search
There's your earthquake. It should be the only one on the map. Click the circle on the map where your earthquake is located. Now a pop-up box appears in the bottom left corner of the page with a link that says M 6.4 - southern Greece. Click that link.
You'll be taken to a page that has lots of scientific information about this earthquake. All the questions I ask you in this part of the problem set are found there, or can be figured out from information that is there.
Create a word processing document (Microsoft Word, Macintosh Pages, Google Docs, or PDF) to record your work for this problem set.
1.1 What was the location of this earthquake (latitude, longitude, depth)?
For 1.2 and 1.3 you should look at the ShakeMap and Did You Feel It? links.
1.2 About how far was this earthquake from Delphi? (See Figure 1 in the de Boer et al. Geology paper for a map showing the location of Delphi.)
1.3 What was the estimated intensity of ground shaking that was felt at Delphi from this earthquake?
1.4 Calculate energy released for this event
I want you to learn to use the various earthquake search features that the USGS provides. If you took EARTH 501, then you know something about this already. In this part of the activity, we'll use the search feature to find aftershocks of the mag 6.4 event we found in Part 1.
Go to the USGS Latest Earthquakes Map [13]and follow my directions below.
2.1 How many earthquakes did this search find?
2.2 What was the biggest event (not including the mag 6.4 main shock), and how many are there of this size? Does this observation support Båth's Law?
For 2.3, you will want to download the list of earthquakes. Do so by clicking 'Click for more information' at the top of the list.
2.3 Make a plot that compares the aftershock data you found for this earthquake to Omori's law. Note: I think the easiest way to do this will be to count the number of aftershocks each day and plot that number vs. time. Then put another line on your plot that shows the ideal Omori relationship. That way you can compare the two. (If you have trouble getting started with this, post to the "Questions" discussion board.)
2.4 Does the number of earthquakes in this region decay with time as Omori's Law predicts? Discuss the observations suggested by your plot. If you did not find an Omori-type relationship, what are some possible reasons?
2.5 What assumptions did we make that may or may not have been valid when we looked for aftershocks using this search feature?
2.6 Make an educated guess about the background rate of seismicity in this area. How did you decide?
Let's look at the aftershock sequence of the Mw 9.0 earthquake of 11 Mar 2011. If you want to check it out, I made an animation of a two-month time window centered on the earthquake [14], using an exponential scale for symbol size since that is closer to accurate. Let's go through a similar exercise as with the Greek earthquake and see how well Omori's Law works in this case.
Go back to the USGS Latest Earthquakes Map [13] and follow my directions.
3.1 When did you decide to end your search (how many days had elapsed after the mainshock)? How many earthquakes did your search find? Do you think you found all the earthquakes in this aftershock sequence? More? Fewer? Why?
3.2 Make a plot that compares the aftershock data you found for this earthquake to Omori's law.
3.3 Does the number of earthquakes in this region decay with time as Omori's Law predicts? Discuss the observations suggested by your plot. If you did not find an Omori-type relationship, what are some of the reasons?
3.4 Can you tell what the background seismicity rate is for this area? Why or why not?
3.5 Compare the aftershock sequence for this event to the one you observed for the Greek earthquake. Does this sequence merely look exaggerated (because the mainshock was so much bigger) but otherwise the same or are there other significant differences? What I am driving at is for you to try to decide whether you can verify the idea that aftershock sequences are scale independent. I know we are only comparing two sequences instead of a statistically meaningful number, but it is still worth thinking about.
The point of this part of the problem set is for you to learn how you can adapt the catalog search features offered by the USGS for your own use. What better way to do this than to find the most recent earthquake closest to where you live? Here's how:
Go back to the USGS Latest Earthquakes Map [13] and follow my directions below.
If your search returns nothing, choose a bigger region or else make the start time a few years earlier. If your search turns up a huge number of earthquakes you may want to do it again with a smaller region or a shorter time window.
Choose the earthquake closest to where you live, or a different one that looks exciting, and answer the Part 4 questions.
4.1 What was the date of your earthquake?
4.2 What was the location (latitude, longitude, depth) of your earthquake?
4.3 What was the magnitude of your earthquake?
4.4 How close was this earthquake to where you actually live? Did you feel it? If there is a DYFI map, check it out and see if anybody else near you felt it.
Save your word processing document and name it like this:
L7_greek_earthquake_AccessAccountID_LastName.doc (or your file extension).
For example, former Cardinals right fielder and hall of famer Enos Slaughter would name his file "L7_greek_earthquake_ebs9_slaughter.doc"
Upload your file to the Lesson 7 - Greek earthquake problem set assignment in CANVAS by the due date indicated on the first page of this lesson.
I will use my general grading rubric for problem sets [15] to grade this activity.
I am not a social scientist by training, but I still think it is pretty interesting to think about how much the Earth has shaped the course of human history. I guess that shouldn't be too surprising, since this planet is our home, but I think it can be overlooked. In this lesson we just touched on one small aspect. Think about how much the Oracle at Delphi affected political decisions in ancient Greece. The placement of the Temple of Apollo over a particular type of fault made it all possible. Cool, no?
You have reached the end of Lesson 7! Double-check the list of requirements on the table on the first page of the lesson to make sure you have completed all of the activities listed there.
If you have anything you'd like to comment on or add to the lesson materials, feel free to post your thoughts in our next Teaching/Learning discussion!
Links
[1] https://commons.wikimedia.org/wiki/File:The_Temple_of_Apollo_at_Delphi.jpg
[2] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/discussion_rubric_0.pdf
[3] https://www.iris.edu/hq/inclass/animation/asperities_on_a_strikeslip_fault
[4] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/video/fault_quakes/globalPlateBoundaryExpl.mp4
[5] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/video/fault_quakes/globalPlateBoundaryExplCC.mov
[6] http://volcano.oregonstate.edu/
[7] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/video/fault_quakes/deBoerFig1Xsec.mp4
[8] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/flash/fault_quakes/deBoerFig1XsecCC.mov
[9] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/video/fault_quakes/calculateSeismicMoment.mp4
[10] http://www.rcquakes.com/community/book/
[11] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/video/fault_quakes/omoriPlot.mp4
[12] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/video/fault_quakes/omoriPlotCC.mov
[13] http://earthquake.usgs.gov/earthquakes/map/
[14] https://www.e-education.psu.edu/earth520/sites/www.e-education.psu.edu.earth520/files/video/fault_quakes/tohokuAftershocks.mp4
[15] https://www.e-education.psu.edu/1686