EARTH 501
Controversies in the Earth Sciences

Problem Set Part 2: Analyzing tide gauge records and DART data

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Part 2: Calculating the speed of a tsunami using DART data from 2011

On 2011/3/11 near Honshu Island, Japan (38.322°N, 142.369°E) at 5:46:23 (UTC), a magnitude 9 earthquake occurred. You will inspect the records of 13 DART stations that recorded the tsunami, use them to calculate the speed of the tsunami, plot the stations and the earthquake on a world map, and then answer a set of questions about the data and your observations. For this part of the problem set, I downloaded the freely available data and made the plots for you. Later on in this class you'll have to do the data processing yourself, but not this time. If you want to check the raw data out and see a nice map, this is where to go: 2011 Tohoku Japan DART Data

cartoon eliza alerts you that there are directions coming

Use "Part 2" of your problem set worksheet to record your work. View the DART station records for this activity. You can also click on the thumbnails in the table below to see each station's data separately.

In general you don't have to write a whole page of calculations for each station like I do in my examples, I just wanted to be thorough so you can see my procedure. On the other hand, if you don't show any work it is harder for me to give you partial credit if you make a mistake (see my grading rubric, below).

2.0 Using Google Maps, make a map of the location of both earthquakes, the tide gauge stations from Part 1, and the DART stations from Part 2. When you are done with your map, save it, make a link to it, and paste the link into your worksheet. Or you can take a screenshot of your map and insert that into your worksheet.

How to make a map with Google maps and share it with me (and a transcript)

2.1 You already worked with Julian days in Part 1. Now we are going to work with time as expressed in fractions of a day. The earthquake happened on 2011/3/11 at 5:46:23. What is the Julian day of this time, exactly, as expressed in decimal form?

My tutorial for calculating Julian days with fractional parts. (and a transcript)

2.2 Look at each station record and pick the arrival time of the tsunami. I have done the first one for you. Make sure you pick the arrival time of the tsunami and not the arrival time of the seismic waves. Fill in your answers in the table.

My tutorial for picking the arrival of the tsunami. (and a transcript)

2.3 Calculate the tsunami travel time to each station by subtracting the origin time from the arrival time. (Now aren’t you glad you converted the origin time to decimals!!). I’ve done the first one for you. Your answers will be in fractions of a day, so convert to hours. Fill in your answers in the table.

My tutorial for calculating the travel time. (and a transcript)

2.4 Calculate the epicenter-to-station distance along the great circle path between the two locations. We use the great circle path formula because we are calculating distance on the surface of a sphere. Here is the formula for great circle distance: cos(d) = sin(a)sin(b) + cos(a)cos(b)cos|c| in which d is the distance in degrees, a and b are the latitudes of the two points and c is the difference between the longitudes of the two points. Multiply the answer by 111.32 to get from degrees to kilometers. Jean-Paul Rodrigue, at Hoftstra University, gives an excellent explanation and tutorial of how to calculate distance along a great circle path. I’ve done the first one for you. Fill in your answers in the table.

My tutorial for calculating the distance along a great circle path. (and a transcript)

A nice website that will calculate great circle distance for you.

2.5 Calculate the tsunami speed. To get the speed, you use the formula speed = distance/time. I’ve done the first one for you. Fill in your answers in the table.

Let's think about why the speed seems a little too fast for station 21418 (and a transcript)

DART stations in Part 2 of Tsunami Data problem set
station station lat (ºN) station lon (ºE) tsunami arrival time (Jday) tsunami travel time (hr) earthquake to station distance (km) tsunami velocity (km/hr)
21418

38.7110

148.6940

70.26 0.468 551.9 1179
21413

30.5150

152.1170

       
21415

50.1762

171.8486

       
52402

11.8830

154.1100

       
46402

51.0683

-164.0053

       
51407

19.6169

-156.5106

       
51425

-9.5044

-176.2297

       
46411

39.3238

-126.9910

       
51426

-22.9911

-168.1031

       
51406

-8.4800

-125.0270

       
43413

10.8372

-100.0842

       
32413

7.4003

-93.4989

       
32412

-17.9865

-86.3887

       

2.6 I want you to think about the uncertainties in the calculations you performed in determining tsunami velocity. One obvious source of uncertainty is measurement precision at each tide gauge station. For example, let’s say that you are working with a DART station that takes a measurement every 15 minutes. This means that picking the arrival time of the tsunami can't be more precise than this. Go back and change the arrival time pick for Station 21418 and for Station 32412 each by 15 minutes. Now recalculate the speed of the tsunami for each of those two stations. How much has your answer changed for each one? Which one is affected more by the uncertainty in arrival time and why?

2.7 What are some other sources of uncertainty in these calculations?

2.8 Calculate the mean speed for the tsunami. Are you surprised by this speed? How does this speed compare to a jet airplane? an Indy car? a bullet fired from a gun? an earthquake P wave? a major league fastball? Pick several items that interest you (they don't have to be any of the examples above if you don't like those) and compare them to the speed of the tsunami.

2.9 Tsunami speed is controlled by water depth. In fact tsunami speed equals the square root of the product of water depth and g, the gravitational constant (9.8 m/s2). Calculate mean water depth of the Pacific Ocean. To do this, use the mean speed of the tsunami that you calculated in 2.8, convert it from km/hr to m/s, then plug into the equation speed=sqrt(depth*g).

2.10 I want you to think about approaching the question of tsunami speed from a different perspective. What if you wanted to determine how fast a hypothetical tsunami could get from point A to point B? List what would you need to know to make this calculation.

2.11 Now try it! Let's say a large earthquake happens in the Pacific northwest, approximately at the location of Seattle, generating a tsunami. Determine how long it would take the tsunami to arrive in Hilo, Hawaii.

2.12 What are the sources of uncertainty in the calculation you just did in the previous question?

2.13 There are definitely tide gauge stations on the west coast of Japan and they recorded the tsunami as well. However, we did not use any data from those stations to calculate the speed of the tsunami or to calculate the mean water depth between the earthquake and those stations. Why not? (In order to answer this question you will need to look at the map you made and think about what assumptions we made to do our calculations.)

Submitting your work

Save your worksheet as a Microsoft Word, PDF, or Pages file in the following format:
L2_TsunamiData_AccessAccountID_LastName.doc (or .pdf or .pages).
For example, Cardinals' shortstop Jhonny Peralta's file would be named "L2_TsunamiData_jap27_peralta.doc"

Upload your worksheet to the Tsunami Data problem set assignment in Canvas by the due date on the first page of this lesson.

Grading rubric

I will use my general grading rubric for problem sets when I grade this activity.