Free-Air Gravity Exercise

The object of this exercise is to

• familiarize you with the Worden gravimeter and its use
• learn about aspects of gravity data acquisition, including instrument drift
• explore the importance of the free-air and Bouguer corrections.

Treat the meter with the respect any venerable, old (it is older than you are), delicate instrument deserves.  Do not pick up the "milk can" by the handle on top; it could break.  Never tilt the meter more than a few degrees. This means always having help from another person when attempting to put the milk can on your back with the straps. If you wear a hat with a bill (baseball cap), turn the brim around so it won't hit the meter.

Procedure

You will take several gravity readings at the top and bottom of the Energy Center to see what effect elevation has on the readings.  Note the meter constant on the tag on the side of the meter. Dial readings are multiplied by this constant to convert to relative milligals.  The number in the little window on the dial is hundred of dial divisions.

• First floor, outside of elevator (always use the same, relocatable spot). This is your base station, to which you return to determine instrument drift.
  • Level the meter carefully.  If you were outside, you would set the meter on the tripod dish and, holding the meter near its base, slide it around until it is approximately level by observing the bubble levels.
  • Take three readings:
    • Get the beam to the left of the center, then bring it to the center from the left. If the beam drifts past to the right of center, take it to the left of center and start over. The reason for always bringing the beam from the left is to minimize the effect of backlash (slop) in the gears
    • Recheck the bubble levels.
    • Move the beam to left of center.
    • Repeat.
  • Record the three readings, the time, location, relevant observations ("beam was shaking" for example).
• Take elevator to 15th floor, go up the south stairwell to roof-top door - do not go out on roof; take readings on landing (always use the same, relocatable spot) just as you did in the basement.  Don't forget to record the time.
• Go back to basement, back to roof, and back to basement, for a total of two occupations of the roof and three at the basement

Reading the Dial

In the figure below, the dial reads 1274.6 dial divisions.  The number in the window gives hundreds of dial divisions. Next you read the position of the tick mark on the vernier scale with the 0 below it. In the figure, this tick mark falls between 74 and 75 on the inner dial.  To get the tenths, find the tick mark on the vernier dial which comes closest to being exactly lined up with a tick mark on the inner dial.  In the figure,  tick mark number 6 on the vernier is exactly across from the 80 tick mark on the inner dial, giving a value of 6 tenths.

Report

I will grade reports as much on neatness and organization as on completeness and correctness.  Report should include

• a table of data (as an Excel spreadsheet, for example) including location, time, three readings, average and standard deviation of the three (after discarding outliers) readings taken at each station
• a graph of base station readings (y-axis, vertical) versus time (x-axis, horizontal)
• a graph of roof station readings versus time
• your best, most clever estimate of the difference in gravity between the basement and roof, taking into account that you have multiple readings at both places
• answers to the following questions:

Questions:

1. Is the drift the same for both locations (top and bottom of Energy Center)?
2. Compute the gravity gradient (mgals/meter). The elevation difference between the basement floor and the roof is 208'8" (from physical plant plans). How does that compare to the free-air effect of 0.3086 mgal/meter?
3. You might assume the difference is due to the gravitational pull of the material in the building itself.  What "Bouguer density" would the building have to have to explain the gradient you observed? The Bouguer correction, in milligals per meter, is 0.04193*density in grams per cubic centimeter.
4. Does this density make sense?
5. Is the Bouguer approximation (the material holding you up is an infinite slab) a good one to use here?