## Dry Tilt (Grades 9-12)

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.
Click
here for the
handouts for Activity 13.

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.