Geoph437
Assignment #1: Gravity reductions and density determination exercise (Tuesday, September 23, 2008 due 5 pm)
In this exercise, you will use a small gravity data set to get an estimate of
the density of the shallow crust beneath our field area. The data were
collected by ascending a sloping valley, located south-east of
Instructions:
Download the gravity data from the profile 3 of the 2005 dataset: hillgrav2005.xls.
Background material:
Read chapter 2 of
Read chapter 6 of Kearey et al., An Introduction to
Geophysical Exploration, 2002.
Exercise:
1) Write an introduction to the report. State the dates and location of the field school survey. Preferable format of your report would be double spaced. Try to keep it to not more than 10±2 pages with figures (combine figures, make subfigures).Include figure captions under every figure, references and acknowledgment. Appendix with your Matlab codes is additional pages. Your appendix with matlab code should contain as many as possible clear comments of what you were doing. The report should include brief explanation of corrections and numerical methods you are applying. Include detailed explanation on one of the applied techniques of your choice: Nettleton’s method, Parasnis’ method, deriving the liner regression or using the standard deviation.
2) The Free Air Anomaly
(a) Apply the instrumental drift correction (in Matlab). Plot the graph of observed gravity and instrumental drift corrected gravity vs. time (can be a subfigure of the Figure 1).
(b) Derive the latitude correction starting with the formula for normal gravity. Compute the latitude correction for the data set, plot the latitude correction vs. northering along profile as a subfigure. Comment on significance or insignificance of this correction.
(c) Starting with the formula for the gravitational acceleration of the Earth, find the rate of change of gravity with respect to elevation at the earth's surface. This gives you the Free Air Correction. Explain the significance of the sign of the Free Air Correction.
(d) Plot the relative elevation from the base station as a function of relative northerning. Obtain and plotthe Free Air Anomaly for the available gravity data as a function of distance (northering) along the observation path. Comment on shape similarity between these two subplots.
3) Density of the Subsurface
(a) Use Nettleton's method to obtain an average density of the subsurface. Illustrate the method (subfigure). Apply calculation of the standard deviation to find the best value of the density.
(b) Use Parasnis' method to obtain another average density of the subsurface. Illustrate the method (subfigure).Find the best fit line for the slope.
(c) Do your results from (a) and (b) make sense considering the density of typical crustal materials? You can use Table 2.2, page 16 in Telford et al. to get a comparison of your densities to crustal rocks. Compare your density results obtained with both methods.
4) Bouguer Anomaly
(a) Using your densities from 3a and 3b calculate two Bouguer anomalies. Plot them as a function of distance along the observation path. Comment on similarity/difference.
(b) What is the relative magnitude of the Free Air and Bouguer anomalies? Is this what you would expect for the area of the gravity survey?
General notes:
On structure of your report please see example from the GRL journal: GRL-paper-2004.pdf.
Materials to hand in:
1) Hard copy of report, including figures (approximately 10±2 pages plus Matlab code
appendix). If you have no color ink printer you may print all figures white and
black but send me the MS-DOC file with color figures.
2) Send your Matlab code and input files by email
(preferable) or submit a floppy or zip or CD disk. When sending the report and matlab files by email please compress them with ZIP or TAR
or another common compressor.
UTM coordinates converter: http://www.ngs.noaa.gov/TOOLS/utm.html