Dry tilt station. Photo courtesy of U.S. Geological Survey.

In the early 1980s, a second method was developed to measure tilt. This method, called dry tilt because no water is involved, offers several advantages over tiltmeters. Unlike water-tube tiltmeters, which require temperature-stable vaults, dry tilt can be determined at the surface under most atmospheric conditions. Dry tilt measurements can be made efficiently. Two people can make the measurements for one station in one hour. The instruments and methodology for dry tilt are relatively easy. Dry tilt is now used at over 20 stations on Kilauea and more than 100 stations on the Island of Hawaii.

This activity introduces the mathematics used to calculate a tilt vector from dry tilt data. After calculating the tilt vector, students must plot the vector and interpret its significance.

Detailed instructions for installing a dry tilt station are given in Yamashita (1981). An ideal dry tilt station is an equilateral triangle, with one vertex in the south quadrant (activity 13). Each side of the triangle is 40 m. The vertices are labeled X, Y, and Z. The instrument is placed at the center of the triangle. Survey rods are placed at each vertex. (Rod locations are marked by benchmarks). A set of readings are made between the instrument and each rod. A sample data set is presented in activity 13.

Prior to calculating the tilt vector, the change in tilt along each leg of the triangle must be compared to the previous set of measurements. Two sets of readings are provided. The net change is the difference between the readings. Students must record this change in the space provided. For example,

```	ADJUSTED READING		PREVIOUS READING
1/17/79  			7/17/78			Change (cm)
Y-X	-130.650			-130.645		-.005
X-Z	+ 33.300			+ 33.310		-.010
Z-Y	+ 97.350			+ 97.335		+.015.
```
The formula for determining the tilt vector and magnitude was determined by Eaton (1959). The formula is:

The parameters used in the equation are shown in activity 13. Using the values provided, the formula reduces to: (NEED TAU (N) = (-0.077(Y-X) - 0.279(X-Z)) - 1000 (NEED TAU (E) = (0.277(Y-X) - 0.072(X-Z)) - 1000 Inserting the changes yields:

(NEED TAU (N) = (-0.077(-0.005) - 0.279(-0.10)) - 1000 = +3.18

(NEED TAU (E) = (0.277(-0.005) - 0.072(-0.10)) - 1000 = -2.11

The formulas for determining the azimuth of the tilt and the magnitude are Magnitude in microradians =

Azimuth in degrees =

If (NEED TAU (N) is positive, the vector is in the north half and down.

If (NEED TAU (N) is negative, the vector is in the south half and down.

If (NEED TAU (N) is positive, the vector is in the east half and down.

If (NEED TAU (N) is negative, the vector is in the west half and down.

For the data provided, the magnitude of the tilt vector is 3.80 microradians in the direction 33.5 degrees west of north. The location of the tilt station is shown in Activity 13. The vector points away from the summit region, suggesting inflation of the volcano. Additional measurements would confirm that the summit has inflated and help to locate the center of uplift.

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