Geophysics 437:
Application of Methods in Environmental and Exploration Geophysics
Fall 2008
Instructor: V. Kravchinsky
TA: Dennis Rippe
Assignment 3, Weight
20%, due Tuesday, November 4 (5:00pm)
Data Analysis: Filtering the
anomalies and modeling the sources
a)
Continue with your corrected (but not interpolated) Bouguer gravity anomaly
data after planar detrending (your assignment 2 or can be downloaded from here (columns are DE (relative to the
base station 2 easting in km), DN (relative northing in km), detrended Bouguer
anomaly (mgal))). Interpolate the data onto a plain of constant spacing and
with the number of points being a power of 2. This helps with the Fast Fourier
Transform (FFT). Write a program to FFT the interpolated gravity data. Using fftshift(…) in Matlab create a plot of
the amplitude spectrum. Scale the horizontal axis using what you know about the
Nyquist frequency or Nyquist wavenumber. Comment on what the results show.
Describe the mathematical approach used to derive the upward/downward
continuation for gravity (see lecture notes, Gunn’s paper and Bhattacharyya’s paper). Please start
with an explanation of the gravitational potential derivation.
b)
Apply detrending of order 2 or 3 for magnetics instead of planar detrending
used in the previous assignment (see lecture notes how to apply higher polynomial detrending). Interpolate your corrected
(including detrending) magnetic data onto a uniform 2-dimensional grid with
length and width of powers of 2. This task is analogous to part (a). Create an
image of the amplitude spectrum. Scale the horizontal axes as in (a).
c)
For the gravity data apply the following 2-D filters and produce plots
(illustrate every filter along with filtered data maps). For 1), 2) and 3)
below choose the filter size that gives easily interpretable results. Briefly
discuss your result for every filter.
1)
Low pass filter (remove high wavenumbers)
2) High pass filter (remove low wavenumbers)
3) Band pass filter (remove very high and very low wavenumbers)
4) Upward continuation; show two different heights (try different heights, for
example, 100m, 1km)
5) Downward continuation; demonstrate with two different heights (for example,
start with 50m, 200m)
d) First of all you need
to specify smaller area you are going to work with in the magnetic section. The
recommended area where two dykes are better registered is limited by
coordinates of the current values for the longitude and latitude long_min=443000; long_max=444200;
lat_min=5452100; lat_max=5453300. To cut off the specified area in the magnetic
dataset you may use the function data_subset prepared by D. Rippe (click here to download).
For
the magnetic data, apply the following 2-D filters and produce images. For 1),
2) and 3) below choose filters that give easily interpretable results. Briefly
discuss your result for every filter.
1)
Low pass filter (remove high wavenumbers)
2) High pass filter (remove low wavenumbers)
3) Band pass filter (remove high and low wavenumbers)
4) Upward continuation (demonstrate with two different heights)
5) Downward continuation (demonstrate with two different heights)
6) Reduction to the Pole (RTP) filter (see Baranov’s
paper and Silva’s paper). For this filter you need
to estimate remnant magnetization direction for two cases: normal and reverse
polarity remnant magnetization. To estimate the induced magnetization direction
go to the web-page: http://www.ngdc.noaa.gov/seg/geomag/jsp/IGRFWMM.jsp.
Here is the dataset of the North American poles from the paper of Besse and
Courtillot (2002): B&C02.pdf. Here is
the link to the Geomagnetic Polarity Time Scale: GPTS.jpg.
On the radiogenic age of the
e) Prepare your filtered
dataset for the next assignment (see lecture notes). Conclude on your results.
Which filter(s) did perform better to evaluate the subsurface structures in
your opinion? Give a short geological interpretation of your gravity data and
suggest where to drill a borehole to target a potential aquifer in the area of
the survey and why. Briefly discuss your magnetic result: where to drill for
reconnaissance purposes of the future diamond exploration and why.
Materials to hand in:
1) Hard copy of report, including figures (about 10±2
pages). Combine figures to make your report shorter.
2) Send your scripts and input files by email to me or TA, send your report.
Alternative Geomagnetic Field Calculator: http://williams.best.vwh.net/magvar.htm
Here from you may download an example of the FFT prepared for
you by Dennis:
fft_example.m
Note
that all anomalies obtained by different students are slightly different. It
may depend on differences in regional trend orientations and does not necessary
mean that your estimation of the Bouguer gravity or magnetics was wrong in your
report.
