GPH 492/692 - Gravity Inversion Lab

John Louie, March 22, 2009

Assignment

  1. The table below shows gravity data collected in the field, in central Chicago Valley, eastern California, by the 1992 class:
    Station Time, UTC Dist, m  g, mGal   Terrain Cor  Elev., m
     BASE    17.8              3298.018        0
       168   17.98    400650   3297.19         0      1085.4
       169   18.15    400300   3297.706        0      1100.6
       170   18.3     400150   3298.079        0      1112.8
       171   18.5     400000   3298.008        0      1131.1
       173   18.8     399450   3294.797        0      1182.9
       172   19       399700   3296.622        0      1146.3
     BASE    19.5              3298.038        0
       174   19.75    399150   3293.508        0      1198.2
       140   19.85    399000   3292.532        0      1201.8
       175   20.1     399000   3291.514    0.093      1204.3
       176   20.6     399900   3290.011    0.019      1225.6
       177   20.75    399750   3288.129    0.012      1256.1
     BASE    21.3              3298.12         0
    
    You can also download the grav2d.zip ZIP archive, and unpack it to get the examp.xls Excel spreadsheet with these data. The quickgrav.xls spreadsheet with fake data similar to our 2009 Bango Rd. profile contains useful Excel formulae. Also, remember that the formula for the total free-air plus Bouguer-slab elevation correction is:
    dg = h (0.3083 - 0.04192 rho)
    where dg is in mGal, h is in meters, and rho is in g/cc.

    Using the information above compute the simple Bouguer anomaly at each of the numbered measurement stations (not the base station). The ``simple Bouguer anomaly'' includes the drift correction and the two elevation corrections but only the inner-ring terrain correction. The terrain corrections given above are in mGal and are field-estimated B and C ring corrections. (After complete terrain correction the anomaly value is called the ``complete Bouguer.'') Use a datum elevation equal to the elevation of the lowest station, and use 2.67 g/cc for the Bouguer correction.

  2. From the results of your computation above, identify the stations where the simple Bouguer anomaly value is highest (most positive), and lowest (most negative). Report the difference in anomaly between these stations (between different survey points, not between the corrected and uncorrected data). Then assume that this difference is the result of being located on a basin having an average density contrast of -0.5 g/cc against the surrounding bedrock. Basin sediment thickness is zero at the station with the highest anomaly value. Use the Bouguer slab equation to get a quick estimate of the maximum basin thickness this survey shows.

  3. Download the grav2d.zip ZIP archive, and unpack it to a new folder on your computer or to your memory stick on a UNR lab computer. After extracting or unpacking the archive file, you should be able to see a folder named ``grav2d'' containing 3 .xls Excel example files, 3 .txt text files input gravity files, 2 .class Java executables, and 1 .java Java source-code file. On Windows NT, 2000, and XP, Mac OS X, or UNIX, you need to open up a Command Prompt, Terminal, or shell command-line input window to type the commands needed to run the grav2d application. It has no user interface. The first command takes you to the place where you just made your new ``grav2d'' folder, and the second one is an example of how to run the Talwani inversion:
    cd grav2d
    java -cp . grav2d 1.0 reno1.txt reno1.grav
    
    The grav2d run takes the input text file ``reno1.txt'' and inverts for basin depths using a tolerance of 1.0 mGal. The output is placed in a text file called ``reno1.grav''. (You will need to change the file names for different runs below.)

    The open-source Java code is grav2d.java. The parts that do all the computation only amount to about 40 lines. All the other stuff is i/o and error checks.

  4. Take the the reno1.txt data file in your ``grav2d'' folder and run it through the grav2d program with a tolerance of 2 mGal. The density contrast is -0.5 g/cc (found at the top of the input file). The profile starts in Mogul and extends to the east side of the Truckee Meadows at the sewer plant. Since the reno1.grav output text file contains the result of every iteration, you will find the final inverted model at the end of the file. For each inversion, you will find it helpful to import just the final result into a spreadsheet such as the reno-talwani.xls sheet proivided, and make two plots, on the same x-axis and with one placed above the other: 1) depth (basin thickness, really) plotted against distance (which is in km), with depth increasing down, of course; and 2) both Ganom and Gcalc plotted against distance. Remember that each depth value is for the bottom of a rectangular prism bounded by X1 and X2 in distance relative to the first station. I also like to plot unconnected points at the Ganom field data and a continuous line with no points for the Gcalc synthetic data.
    1. You do not have to turn in the plot, but describe the basin geometry, maximum depths, and roughly the average and maximum mismatch between data and synthetic gravity.
    2. If the average mismatch were due to elevation error, how much elevation error would be needed? Could you be trying to fit elevation errors instead of real gravity anomalies?
    3. Where is the mismatch error between Ganom and Gcalc the greatest?
    4. From the minimum anomaly, make a Bouguer slab estimate of basin depth using the same drho=-0.5 g/cc. How does this compare with the inverted depth? Explain the reason for the difference.

  5. Try running the reno1.txt data through grav2d using tolerances of 0.5 and 0.1. What happens as you try to get a more exact fit to the data? Even if convergence isn't reached, you can still examine and/or plot the final iteration's result. Where in the profile does altering the tolerance have the most effect?

  6. Examine the reno2.txt data file in your ``grav2d'' folder. Note that it is exactly the same as the reno1.txt file, except for an error in one reading.
    1. Run it through grav2d with a tolerance of 2 mGal, and also 0.5 mGal. How does the error affect the result?
    2. Compare the effect of the 2 mGal error on the inversion, against the depth error that would result from a simple Bouguer slab calculation. Which modeling method is more resistant to errors?
    3. To get a 2 mGal data error, how much elevation error would you need?

  7. What you used above was smoothed data. Now take the real reno-river.txt data file in your ``grav2d'' folder (surveyed by Rob Abbott and Christine Mann in 1997) and run it through grav2d at a range of tolerances. I suggest 5, 2, and 0.5 mGal.
    1. Describe the profile of the Reno basin along the Truckee river.
    2. Describe the uncertainties in this depth profile. How does your confidence in the inverted depths vary along the profile?
    3. Discuss the contribution of lack of knowledge of densities to your uncertainties.