Description:
ABOUT LAVA DOME GROWTH AT MT. ST. HELENS VOLCANO
Mt. St. Helens, a stratovolcano in the Cascade Range of Washington State, erupted violently on 18 May 1980. The giant landslides and subsequent eruption created a large, horseshoe shaped crater. A dome shaped "bunion" of dacite (a pale volcanic rock) began to form in the crater shortly after the initial eruption. The lava dome grew for the next few years, in short episodes often accompanied by small eruptions. It was expected that the dome would eventually fill the entire crater and rejuvenate Mt. St. Helens but dome growth stopped in the mid 1980's and the volcano has been very quiet since.
An approximate volume of the dome in cubic meters was calculated using measurements of the dome's length, width and height, assuming a rectangular paralleopiped. This geometry overestimates the actual dome volume but maintains a self consistent approach (the shape of the dome has also changed with time).
The rate of lava dome growth has decreased with time, as discussed above. This type of growth can be modeled with a power law with the exponent less than unity. The student will encounter a problem immediately with the first data point and will have to devise a reasonable solution. The power law "decay" of growth rate might reflect incremental tapping of a finite magma reservoir or incremental decrease in material available for melting at depth.
The best fit power law regression to the data gives a reasonable correlation coefficient, however the shape of the best fit regression looks nothing like the actual data, "missing" every data point except two. Students should try their own power law models, using various combinations of the initial value and exponent, to generate a curve whose shape and position corresponds more closely to the data. The students can then be challenged to explain why their better looking curves represent a poorer fit; what are the sums of the squares of the deviations in both cases, and what is the source of the "problem"?
