Day Two -- How Deep is this Glacier?

Ask Students to remember from the last time:

• We talked about how you can determine the distance between you and another place by sending a runner - whose speed you know - running to the destination of interest and back. You must also time how long the runner takes.
  
  • Remember you need to divide your runner's round trip time by two to find out the one-way time it takes to run to the destination.
  • Remember also that this is essentially what glacier seismologists do to determine the depth of glaciers.
• Seismologists place a series of "geophones" or "shot-receivers" (phones that listen to the earth) on a glacier and then set off an explosion or "shot" at the surface of the glacier some distance away from the phones. Then they "listen" for the "echo" that comes back up to the surface off the bottom of the glacier. It really is an echo because sound is bouncing off the bottom of the glacier.

Figure 4
• Just like timing your friends running to some destination and back to determine how far away their homes are, glacialogists time the sound wave made by their explosion on the surface of the glacier and count how many seconds elapse between the exposion and their picking up the sound of the explosion back at the surface again through their phones.
• Remember, this sound wave is traveling through the ice of the glacier. Don't think this is strange, sound waves actually travel better and faster through denser media like ice, than they do through less dense media, like air.
• Let's actually look at what a sound wave is like. A sound wave is the same as a seismic wave through rock, like in an earthquake, and is the same as a pressure wave or compression wave in a toy Slinky. A pressure wave is not an up and down wave like you see in the ocean but rather an in and out wave. Click on the video to see what a pressure wave looks like.

Pressure Wave

Seismologists studying Black Rapids Glacier actually did set off an explosion on the surface of the glacier 16 km from the head, where the glacier begins flowing. This location can be seen on the map of Black Rapids Glacier in Figure 2 (Day 1) as being due north of Meteor Peak. Figure 5 below is a side view of the glacier showing the path of the explosion sound wave from the surface to the bottom and back to the surface again. The Y-axis (side axis) represents the depth in meters and the X-axis (bottom axis) the distance along the surface of the glacier with 0 being the location of the phones.

The glacier is flowing from left to right with the phones placed "upstream" from the site of the explosion. Multiple phones are not necessary to determine the depth of a glacier with a flat bottom such as are found in Antarctica but are helpful for imaging the shape and texture of glacier with curved bottoms. Most glaciers are valley glaciers and have curved or u-shaped bottoms.

Figure 5

The Black Rapids Glacier is flowing left to right. This shows an explosion on the right, or "downstream" side of the glacier generating sound waves traveling down to the bottom of the glacier and then bouncing off the bottom back to the surface of the glacier and picked up by multiple phones, all located between 600 and 700 meters "upstream" from the site of the explosion. The depth of the glacier at this location is about 600 meters.

Formative Assessment:

• Have students describe qualitatively in words, written or orally, how one could determine the depth of a glacier.

Day Three -- How Deep is this Glacier?

More Sound Waves!
In actual fact, sound waves from an explosion bounce off - reflect - off all surfaces underneath the ice. The phones will pick up echos of the explosion for quite some time after the explosion. Figure 6 shows just a few of the many possible reflection paths taken by the sound waves. While this may appear to present a severe complication to determining the distance to the bottom of the glacier, it does not. All one needs to do is pick up the first, or earliest, reflection wave and ignore all the others. Getting back to the running friend analogy, it is as if you sent hundreds of your friends running in all directions, running to their respective homes and back. All you are interested in is the closest home. After you have timed the arrival of your first friend, you can ignore the rest, even though they may be still arriving hours later.

Figure 6

Figure 6 is the same as Figure 5 (Day Two) except showing reflections off a few different surfaces underneath the ice. There is one other fact one needs to be aware of in interpreting the seismogram from the explosion. The explosion produces a sound wave traveling in all directions. This means the wave heads down through the ice into the glacier and also through the ice on the surface of the glacier. Clearly, the wave along the surface travels the shortest distance to get to the phones since it does not have to reflect off any surfaces. There is no analogy to this wave in the running friend situation. The surface wave is useful, however, in that it tells you how fast the wave is traveling through the ice, since this is a distance you do know; you could actually lay a very long measuring tape along the surface of the glacier to determine the distance from the explosion to the phones.

The actual seismogram for Black Rapids Glacier recording the seismic waves produced by the explosion at the location north of Meteor Peak is shown in Figure 7.

Figure 7

Actual seismogram for the explosion at km 16 from the head - west end - of Black Rapids Glacier just north of Meteor Peak. Each vertical trace in the Figure corresponds to one particular phone, called a shot-to-receiver and the X-axis indicates the phone's distance from the explosion. There are 12 separate phones. The Y-axis indicates the time of travel of the sound or seismic wave from the time of the explosion to the reception of the sound wave at the phone. The first blip on each trace, seen just below the upper diagonal line is the surface wave. The next blip on each trace, seen just below the lower diagonal line is the reflection off the closest surface to the explosion - taken to be the bottom of the glacier. All the other blips below this one are reflections off of other surfaces beneath the glacier which are further away than the closest surface depicted in Figure 5.

Formative Assessment:

• What is the first sound wave to reach a phone from the surface explosion?
  
  • The surface wave.
• Why are there several waves recorded on each phone trace?
  
  • The phone picks up reflections off all surfaces under the glacier, not just the surfaces directly underneath the explosion. The greater the distance away from the explosion, the greater the time to reflect to the phone.
• The sound wave from an experimental explosion on a glacier travels 850 meters to a phone on the surface of the glacier. The sound wave travels at 3650 meters/second. How many seconds should elapse between the time of the explosion and its detection at the phone?
  
  • 850 meters/(3650 meters/second) = 0.23 seconds

Day Four -- How Deep is this Glacier?

The fifth trace from the left in Figure 7 represents the sound wave received by the phone located approximately 1460 meters from the explosion. The time for the wave to travel along the surface, directly in a straight line from the explosion is about 0.4 seconds. 1460 meters/0.4 seconds = 3650 meters per second. This is equivalent to determining the speed of your friends running to their homes. This, therefore, is the speed of a sound wave through ice. Using the same trace, the time of travel of the sound wave off the bottom of the glacier - the first wave of reflection - is approximately 0.49 seconds. Remembering that this is the time to travel to the bottom and back, the wave required 0.245 seconds (0.49 seconds/2) to reach the bottom. This is a distance of, rounding off a bit:

(3650 meters /second) x 0.25 seconds = 910 meters

Is this the distance between the surface of the glacier and the bottom directly underneath the explosion? No, because the wave followed an angled path as shown in Figure 5. To determine the actual vertical depth of the glacier one draws the sound wave path triangle as shown below in Figure 8 and then bisects that triangle to form two right triangles.

Figure 8

Schematic diagram of the path taken by the sound wave producing trace #5 in Figure 7 above. The sound wave travels from the explosion down through the ice, hits bedrock and then bounces back up to the phone. The surface distance traveled by the wave is 1460 meters, the total through-the-ice distance traveled by the wave is 910 + 910 = 1820 meters.

Figure 9

Schematic diagram depicting how the triangle in Figure 8 is bisected to show how the glacier depth is related to the surface distance - 730 meters - and the through-the-ice distance - 910 meters.

You are almost done! You simply need to determine the value of the unknown leg of the triangle in Figure 9. There are several ways to do this. Graphically, one can draw a right triangle, measure a distance of 7.3 cm (representing 730 meters) along one side, make a mark, and then lay a ruler down connecting this mark with the other side of the right triangle intersecting it at 9.1 cm (representing 910 meters) and then drawing this line. Simply lay the ruler down along the unknown side and determine its length. This crude method produced a length of 5.4 cm. Since 7.3 cm represented 730 meters, 5.4 cm would represent 540 meters. That's the depth of Black Rapids Glacier at the location of the explosion! The Pythagorean theorem may also be used:

Pythagorean Theorem

The Pythagorean theorem states:

a² + b² = c²

a, the depth of the glacier,

rounding off, again, gives 540 meters.

Formative Assessment:

Use the last seismic trace in Figure 7, the one for the phone most distant from the explosion, to determine the depth of Black Rapids Glacier.

The distance to the bottom from phone 12 is, with rounding again:

0.535 seconds/2 x (3650 meters/second) = 976 or 980 meters

The surface distance from the site of the explosion to the phone is 1650 meters.

Constructing the right triangle again as in Figure 9, gives sides of 980 and 825 meters.

a, the depth of the glacier,

You expect the depth of a round-bottomed glacier to vary as you move across glacier.

Day Five -- How Deep is this Glacier?

Figure 10 below shows a cross section of Black Rapids Glacier at the site of the explosion chosen by glaciologists. Black Rapids Glacier is an example of a valley glacier. Valleys carved by glaciers have a U shape. It is possible for the first sound wave to hit the shot-to-receiver phone to be a reflection off the side of the valley instead of the bottom because the side of the valley may be closer to the phone than the bottom.

Figure 10:
Cross section of the Black Rapids Glacier as determined by glaciologists

Formative Assessment:

Have students communicate through writing, drawing, tape recording or by other means, how one determines the depth of a glacier. Students will evaluate each other's work on the basis of whether they can understand how the process is explained by the author.