MOTION OF THE PACIFIC PLATE: Determination of velocity from analysis of the Hawaiian Islands

 Ó January 2001, Douglas A. Fowler

Introduction

Geologists almost universally agree that the volcanoes of the Hawaiian Island chain result from a hot spot resulting from a mantle plume. Mantle plumes are thought to be relatively narrow columns of hot, plastically-flowing, solid mantle-rock rising from the base of the Earth's mantle (Plummer and McGeary, 1996). When the mantle plume reaches the base of the crust-mantle boundary, melting occurs that results in volcanism. In general, plate motion overrides this activity. The moving plate moves horizontally over the plume like a sheet of paper moved from right to left over a candle flame.  We get a series of burn marks that trace the motion of the paper relative to the flame. We interpret the Hawaiian Islands in a similar way: the Pacific moves over the mantle plume leaving a series of increasingly younger volcanic islands toward the plume's present location. The newest and most volcanically active island is directly over this plume. John McPhee (1998) provides excellent and very readable descriptions of this picture of plate movement over a hot spot that was generated by a mantle plume.

We can make a fairly reliable estimate of the velocity, both speed and direction, by combining distances and direction obtained from maps with radiometric ages for the basalts of the various islands

Any good map, along with rulers and protractors, can be used to determine distances and directions. Some of the most useful maps are those produced by the National Geographic Society (1960, 1976, 1983).

Harris, Tuttle, and Tuttle (1997) provide radiometric ages for the major islands of the Hawaiian chain. These are given in the following table:

From Geology of National Parks,

5th ed., Harris, Tuttle, & Tuttle

We note that these ages get progressively younger southeast toward Hawaii, the largest, most active island of the group. This is indeed consistent with our model of the Pacific Plate moving over a stationary mantle plume.    

Problem

From data for the Hawaiian Islands, determine the velocity  vector, i.e., direction as well as speed, for the Pacific Plate. We assume the mantle plume is stationary in the sense that we can use to define our frame of reference. Also determine the direction of motion as a  bearing, in degrees, relative to the north-south, east-west grid on the map. Show all steps in your calculations. Units and unit conversions should all be recorded. For help with units, see any good physics text, for example, Giancoli (1999).

References

Giancoli, D. C. (1998). Physics: principles with applications (5th ed.). Upper Saddle

          River, NJ: Prentice Hall.

Harris, A. G., Tuttle, E., & Tuttle, S. D. (1997). Geology of national

          parks (5th ed.). Dubuque, IA: Kendall/Hunt.

McPhee, J. (1998). Annals of the former world. New York: Farrar, Straus and Giroux.  

National Geographic Society (1960). Hawaii. Map supplement from

          National geographic magazine, July 1960, Washington:

          National Geographic Society.

National Geographic Society (1976). Close-up: U.S.A. Hawaii. Map

          supplement from National geographic magazine, April 1976,

          Washington: National Geographic Society.

National Geographic Society (1983). The making of America:

          Hawaii. Map supplement from National geographic

          magazine, November, 1983, Washington: National

          Geographic Society.

Plummer, C. C. & McGeary, D. (1996). Physical geology (7th ed.).

          Dubuque, IA: Wm. C. Brown.    

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