1. Use Excel, or a programming tool of your choice, to calculate the gravity anomaly over a buried sphere as in the figure to the right. Let the height of the cliff be 500 meters, the radius of the sphere be 500 meters, the depth to the center of the sphere 1000 meters below the lower ground level, and the density contrast be 500 kg/m³. Calculate a large enough number of points to get a smooth profile. Think about it, play with it (different depths, different density contrasts).

2. Processing and Interpreting Observed Gravity: Below, and in the linked spreadsheet, are some gravity observations from ~114.108^oW in the Missoula Valley. The short explanation of the problem set is: interpret the residual gravity. A longer explanation is:

• Fill in the blanks in the table at the bottom of the page (here's the spreadsheet. I recommend adding a few columns, especially while calculating the latitude correction, to reduce errors with parentheses; columns are cheap.)

  For your theoretical gravity correction use: gth = 9.7803267714*((1 + 0.00193185138639*SIN²(Lat))/(sqrt(1- 0.00669437999013*SIN²(Lat))))* (m/s²)
  This is for the recent, 1984, Geodetic Reference System adopted by the International Association of Geodicists and corresponds to the WGS84 datum from Blakely, 1995, Potential Theory in Gravity and Magnetic Applications, Cambridge Univ. Press, 441 p.

  For free air corrections use 0.3086 mgals/m (add this for observations above MSL).

  For Bouguer slab corrections (@2670 kg/m³) use 0.11195 mgals/m (subtract for observations above MSL).

  Note that I provided the terrain corrections to use for the complete Bouguer anomaly.

• Make nice graphs of the free air anomaly, simple Bouguer anomaly, and complete Bouguer anomaly versus a south-north (looking west) axis in kilometers (use 6,371 km as Earth's radius) - stare at them until they make sense.
  
• The northern and southern most observations are from the contact between Precambrian Belt rocks and Tertiary valley fill across which there is a density contrast of about 700 kg/m³. Use this information to calculate a linear trend for regional gravity and subtract that to produce a residual gravity due solely to the basin fill (what should that value be at the basin's edge?). Make a nice graph (south-north, looking west) of the residual.
  
• Import the data into GravCadW and make a nice model (use density contrast = 700 kg/m³) of the subsurface shape of the Belt-Tertiary contact.The data for GravCadW must be in a two-column (x, g), space-delimited, ASCII file which you can produce with Excel by using Save As ... and saving as .txt or .prn or pasting into Notepad, surfer's Worksheet, etc. There's an example in the image to the right; if this makes no sense to you, see me. Either print out your final GravCadW model or past it into a Word/Excel page and turn it in with the other graphs. One known bug that gets people is GravCadW's printing routine will crash if you have two points at exactly the same x-position.
  
• Fiddle with your model's shape and various density contrasts enough so that you can answer these questions:

  1. Which gravity observations provide the best constraint on the shape of the deep part of the basin?
  2. How do those observations limit the density contrast? (the observations have little associated uncertainty).
  3. How much leeway do you have on changing the dip of the contact at the north edge of the basin?
  4. Suppose a drillhole in the center of the profile hit Precambrian Belt rock, how would that constrain your density contrast?
  

  Observed gravity from the central Missoula Valley - treat as 2D profile at 114.108 degrees west.
  Site Name	HAG (m)	Lat (Deg)	Long(deg)	Observed g	Theoretical g	FAC	BC	TC	FAA	Simple BA	Complete BA	Residual g
  CE1	1066.61	46.98531	114.10348	980425.51009				2.81
  CE103	1032.36	46.98582	114.11614	980433.44244				3.46
  CE106	1053.05	46.98752	114.10892	980431.25013				4.17
  CE116	986.83	46.93696	114.10705	980430.91206				2.80
  CE127	999.82	46.96469	114.11748	980430.45967				3.35
  CE140	981.15	46.87272	114.10450	980432.86155				3.27
  CE141	993.32	46.83157	114.10936	980427.47945				3.04
  CE143	1022.47	46.95102	114.10275	980424.22473				1.55
  CE156	1014.02	46.95807	114.11630	980426.35340				1.57
  CE93	989.06	46.96124	114.11749	980431.79874				1.70
  CT10	1060.82	46.98289	114.10381	980424.56217				2.57
  CT11	1058.63	46.98388	114.10233	980425.94219				2.73
  CT2	1129.23	46.97522	114.10585	980407.09251				1.71
  CT4	1142.97	46.97771	114.10531	980404.94290				2.12
  CT6	1115.89	46.98038	114.10462	980412.00701				2.93
  CT7	1094.76	46.98121	114.10601	980416.71085				2.69