Applied Geophysics
Gravity Homework Problems

Assigned:30 January
Due:6 February

  1. Show how you can determine the density of a rock given only the following two bits of information: the mass of the rock measured in air (or a vacuum) and the mass of the rock measured while it is submerged in water.

  2. According to the International Gravity formula, what is the expected gravitational acceleration at West Hall? What is the rate of change of gravity with distance north at this point?

  3. If you were planning a gravity survey of the RPI campus, and you wanted to be sure your readings were accurate to 0.1 mgal, determine to what accuracy you would need to know the location and elevation of any gravity station.

  4. In addition to elevation, for the survey mentioned in the previous problem we need to have some idea of density of rocks near the surface in order to make a correct Simple Bouguer Correction. If we are 10 meters above our reference level, and we want to correct our reading to this level, how well must we know this density in order for our data to be accurate to 0.1 mgal?

  5. The following gravity data were collected near Glens Falls. Using the information in the table, calculate the Simple Bouguer Anomaly at stations S02 and S03 relative to the base. Ignore tidal corrections, and assume a density of 2.0 gr/cm3.

    StationUTM NorthUTM EastElevation
    (ft)    		Reading
    (Mgals)
    BASE4792.03858603.83929379.29153.486
    S024792.05811603.86188379.35153.251
    S034792.07764603.88538379.47152.955

  6. How much of a signal would your body produce if you stood directly over the gravity meter? Assume that your density is about 1.1 gr/cm3. For purposes of calculation you can approximate your shape by a cylinder (no offense intended). How wide would you have to be to produce a signal of 0.01 mgal?

  7. Prisoner Tall attempts to escape from prison by digging a cylindrical tunnel 2 meters in diameter under the prison wall. The top of the tunnel is 1 meter below the surface. Policeman Small wants to detect this tunnel using a gravity meter, and hires you as a consultant. How accurate must your readings be in order to detect the tunnel (in the sense that you will need to be at least as accurate as the maximum value of the signal produced by the tunnel)? Assume that the rocks through which the tunnel was dug have a uniform density of 2.67 gr/cm3.