Real-Life Math
Volcanologists use math everywhere, says volcanologist Ben Edwards.
"It's in everything we do."
Volcanologists collect rock samples, then
use math to analyze the results to learn more about how the volcano erupted.
They take photos and measurements of volcanoes to observe changes. They use
statistical analysis to determine what happened when a volcano erupted.
By
studying what happened in the past, they can better determine what might happen
during future volcanic eruptions. They can also apply their findings to look
for valuable ores.
Edwards has done extensive research
on a volcano in northwestern British Columbia, just north of the Iskut River,
called Hoodoo Mountain.
He studied the evolution of the mountain and
worked on improving scientific modeling techniques for predicting the consequences
of magmatic assimilation (when magma from the Earth's core mixes with the
crust).
Part of the research Edwards does involves measuring the size
of rocks at a volcano. He then analyzes that data to determine what type of
volcanic (or non-volcanic) event brought the rock to the site.
"There
are many types of rock deposits found at young volcanoes," says Edwards. "Three
of the most common types of deposit are pyroclastic flow deposits, airfall
deposits and avalanche deposits."
- Pyroclastic flow deposits form when the gas and rock column from an erupting
volcano gets too heavy and part of the column collapses.
- Airfall deposits are formed from rock fragments and pumice (solidified
lava that is full of airpockets called vesicles) that are shot out of the
mouth (vent) of the volcano and then fall to the ground.
- Avalanche deposits can be caused by earthquakes associated with volcanic
eruptions, or they can form from earthquakes not associated with volcanic
eruptions. Since volcanoes are typically very steep, avalanches commonly occur
on the slopes. Thus, avalanche deposits are commonly found at volcanoes.
Each type of deposit can be characterized by the sizes of rock in
it. A volcanologist can tell what type of deposit occurred by looking at a
graph showing the size of rocks in a sample.
- An airfall deposit is characterized by having a well-sorted deposit. Most
of the rock, if not nearly all of it, is about the same size.
- A pyroclastic deposit has fairly well-sorted rock, but not nearly as well
sorted as an airfall deposit.
- An avalanche deposit has rocks of all sizes.
Three 10-kg buckets of rock are collected from different locations
on Mount Meager volcano. Each bucket (labeled A, B, and C) contains rocks
collected from a different type of deposit. You've brought the buckets back
to the lab and now it's time to analyze the contents.
The contents
of each bucket is sorted separately. You use a series of sieves that allow
you to divide the rocks into size groups. Then you weigh the rocks in each
size range. You repeat the process for each bucket. This is your data:
Sample
A has the following ranges of rock sizes:
1) anything under
0.1 cm = 0.5 kg
2) 0.1 to 0.5 cm = 0.2 kg
3) 0.5 to
1 cm = 8.3 kg
4) 1 to 10 cm = 0.5 kg
5) 10 cm = 0.5
kg
Sample B has the following distribution of rock sizes:
1) <0.1
cm = 1.4 kg
2) 0.1 to 0.5 cm = 1.1 kg
3) 0.5 to 1
cm = 5.4 kg
4) 1 to 10 cm = 1.8 kg
5) 10 cm = 0.3
kg
Sample C has the following distribution of rock sizes:
1) <0.1
cm = 0.8 kg
2) 0.1 to 0.5 cm = 2.3 kg
3) 0.5 to 1
cm = 2.1 kg
4) 1 to 10 cm = 2.9 kg
5) 10 cm = 1.7
kg
Make a plot of particle size (X axis) versus cumulative mass of
the sample (Y axis).
Now interpret those plots. Does your plot indicate
that the sample was collected from an airfall deposit from a volcanic eruption?
Or was it a sample taken from a pyroclastic flow site? Or did the rocks arrive
at the sample site in an avalanche?
Make an analysis of each plot.
Determine what kind of deposit was the source for each sample.