Homework: Crater Counting on Mars

Astronomy 23/223 Homework:

HOTSPOTS AND PLATE MOTION
(Exercise courtesy of Amherst College Geology Department)

At a divergent plate boundary - or "spreading center" - asthenospheric mantle rises in a long linear belt along the plate boundary. In contrast, a hotspot is a point source of upwelling mantle, much like a fountain. Well known, presently active hotspots include Hawaii, Yellowstone, and Iceland. There are many other, less familiar hotspots, however, like the Marquesas and Austral hotspots in the Pacific. In all, there are 41 hotspots active today. Like the rising arms of convection cells, hotspot mantle decompresses as it ascends - undergoing partial melting and yielding basaltic magma to the surface.

If we examine Hawaii, as a typical hotspot, we see that a long chain of islands and seamounts (submerged oceanic peaks) trails off from the "Big Island" to the northwest, bending to a more northerly trend at Yuryaku seamount. Only the island of Hawaii is presently volcanically active; all the other islands are inactive. Each island was built from basaltic volcanism derived from the hotspot plume. The chain-like array of these islands results from the motion of the Pacific plate over the hotspot's point source of upwelling mantle; the plate motion carries each newly built island away from the hotspot over time. Hotspot island chains, therefore, preserve a record of the motion of the plate on which they are built.

THE HOTSPOT FRAME OF REFERENCE:

Look at the map below of the Hawaii Island-Emperor Seamount chain, the Line and Marquesas Islands chain, and the Marshall and Austral Islands chain in the Pacific. All three are presently active hotspot chains, and have been active for at least 60 Ma, based on the age of basalt flows in the island chains. Notice that all three chains trace out parallel tracks.

1) What can we hypothesize about the motion of these hotspots relative to each other?

2) What can we infer from this about the rigidity of the Pacific plate?

THE MOTION OF THE PACIFIC PLATE:

Evidence like that of the Marquesas, Austral, and Hawaiian hotspots demonstrates that hotspots stay fixed relative to each other for long periods of geologic time. This provides a frame of reference within which to analyze the motion of plates. In this exercise, you will use the Hawaiian hotspot to examine the motion of the Pacific plate over the time span during which that hotspot has been active.

Examine the following table. It shows the age of basaltic volcanism on each island in the Hawaiian-Emperor chain, the distance of the island from the active hotspot measured along the chain, and the elevation of the island or seamount above or below sea level, respectively.

	Age (Ma)	Distance from Hawaii
Hawaii	0	0
Maui	0.8	221
Lanai	1.3	226
Molokai	1.8	270
Oahu	2.6
Niihoa	4.9	565
Kauai	5.1	519
Nihoa		780
Necker	10.3	1058
French Frigate shoal	12	1209
Laysan	19.9
Pearl reef	20.6	2281
Midway	27.2	2432
Kammu
Daikokuji	42.2	3493
Yuryaku	43.4	3520
Kimmel		3668
Koko	48.1	3758
Ojin	55.2	4102
Jingu	55.4	4175
Nintoku	56.2	4452
Yamel
Sulko	59.6	4860

3) How long has the Hawaiian-Emperor hot spot been active?

Now, graph the distance of each island or seamount from Hawaii (vertical axis) versus the age of the island (horizontal axis). You can do this with a computer spreadsheet program if you wish). This is a distance/time graph and so the slope of any line on this graph represents velocity.

4) This graph represents the velocity of what?

Now, draw a best-fit line, or several line segments through the points. This is an interpretive exercise (you should not let a computer do this part). The slope of the line that you draw represents the velocity (distance/time) of the Pacific plate as it moves over a stationary hotspot, so your choice of a best fit line or line segments has real implications for what can be learned about plate motion. What makes a best fit line? You don't want to just connect each dot with innumerable tiny line segments. This would imply very jerky and variable plate motion. Some scatter of points off a line is acceptable; we expect both inherent variability in natural systems and error in measurement of the values being plotted. On the other hand, a scientist can discriminate between acceptable scatter and physically significant changes in value by knowing the amount of error included in the values being plotted. In this case, errors of +/-3 Ma in age dating, and +/-100 km in location are reasonable. Larger differences represent real changes in distance and time (changes in the rate of plate motion) and should plot on a new, different line segment.

5) Consider the map above and distance/time graph you have made. What changes have occurred in both direction and velocity of Pacific plate motion while the Hawaiian hotspot has been active?

6) Have changes in direction and speed of plate motion been synchronous or independent?

ELEVATION OF THE HAWAIIAN ISLANDS:

Plot a graph of the age of each island in the Hawaiian-Emperor chain (horizontal axis) versus the elevation of each island above or below sea level (vertical axis). Draw a single best fit curve through these points.

7) What can you say about the elevation of hotspot-produced islands as they move farther and farther away from the site of mantle upwelling?

8) Can you think of an explanation for this relationship?

9) The volcanic region around the Tharsis Bulge on Mars is the tallest in the solar system. Why do huge volcanoes form on Mars, and not on Earth?

This page was created by Darby Dyar and is maintained by Darby Dyar and Rebekah Robson-May.
Last updated on 4 November, 2002 .