Measuring Tilt (Grades 9-12)

Geologists use various instruments to monitor changes in active volcanoes. One important instrument that monitors change is a tiltmeter. A tiltmeter reports changes in the slope of the volcano. This activity requires students to use simple trigonometry to calculate the tilt (slope) at three locations. The angles are very small, but do differ with location. Based on their calculations, students must decide the optimum location for a single tiltmeter. Activity 6 provides a contour map of the uplift that occurred in September and October 1967 (Kinoshita and others, 1974). Shortly after the uplift, an eruption began and continued for 251 days. The contours are in millimeters. A map scale is provided in the legend.

Click here for Activity 7.

The students must answer the following questions:

Calculate the tilt angle between the 0-30 and 60-90 mm contours. Hint: a=30-0=30 mm and 90-60=30 mm, b=distance between contours=3.6 km and 1.4 km, respectively.
To calculate the tilt angle, the numbers must be in the same units. To convert km to mm:
```
3.6 km x 1000 m x 1000 mm = 3,600,000 mm.
	 ------   -------
	  1 km      1 m
```
Repeat for 1.4 km. Plugging the numbers into the equation yields:
```
tan A =           30 mm            and A = 1.5 x 10-7 degrees and 
		------------
                3,600,000 mm

tan A =            30 mm           and A = 3.7 x 10-7 degrees.
		------------
                1,400,000 mm
```
Notice that the tilt between the 60-90 mm contours is more than twice the tilt between the 0-30 mm contours.
Estimate the tilt angle near the center of the uplift. Assume maximum uplift is 115 mm at the center of the 105 mm contour.
a=115-105=10 mm. b is determined using the map scale and is equal to 1.5 km (1,500,000 mm). Plugging the numbers into the equation yields: tan A = 10 mm and A = 1.1 x 10-7 degrees. ------------ 1,500,000 mm
Do you think a geologist standing on the summit of the volcano would detect the change in tilt?
No. The angles are too small and require very sensitive instruments to measure.
Which location has the greatest tilt angle?
The location on the flank of the volcano has the greatest tilt angle.
Is the maximum tilt the same, two times greater, five times greater, or ten times greater than the tilt at the other two locations? (circle one)
The maximum tilt is about two times greater than the other measurements.
To maximize the utility of a tiltmeter, should it be placed at the center, flank, or edge of an area of uplift? (circle one)
Since the greatest changes occur on the flanks of the uplift, this is the best location for a tiltmeter. The small changes in tilt at the top and edges of the uplift would be harder to detect.


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