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GRAVITY COMPUTER LAB
___________________________________________________________________
Forward and Inverse Modeling of Gravity Data:
Locating buried glacial channels and evaluating the results of
published
analysis___________________________________________________________________
During this lab your task will be to evaluate the accuracy of
the model developed by Stewart
along profile XX(page 29, Figure 7) in the paper "Gravity Survey
of a Deep Buried Valley".Below, a series of steps are presented to
give you some additional practice with GM-SYS and its
usage.
1) Go to the Common Drive and copy the folderStewart to your
G:\Drive.2) Start GM-SYS and open the file Stewart.sur in the
Stewart folder.
The following model and data windows will appear:
Open word to storeyour screencaptures.
Use flash drive as
secondary backup.
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Stewarts residual gravity data and depth-model or cross section
are plotted below for reference.
3) Use the examine function (eyeball on the action toolbar) to
check the model parameters.The density of the till is ___________
gm/cm3The density of the bedrock is __________ gm/cm3
The density contrast (bedrock to till) is ___________ gm/cm3What
should the density contrast be? __________gm/cm3
Change the density of the bedrock so that the correct density
contrast will be presentbetween the bedrock and overlying till.
4) Open up a word file and copy this view window (Alt- Prt
Scrand then in a word textbox Ctrl V) to your word report file. You
may want to review the earlier handout onthese screen copy and
paste procedures; i.e. reset the density to 2.6 gm/cm3.
At this point, note that there are significant differences
between the calculated gravity (the solid line
in the upper pane) and the observed gravity (dots at each
observation point). The calculated gravityfor Stewarts model does
not agree with the observations taken from his residual gravity map
along
the profile XX.
?
X
A.
B.
Gravity residuals taken from Stewart's Figure 5, page 27 along
profile XX'.
Depth model is simplified from that presented by Stewart (Figure
5, page 27).
X X'
-1.0
0.0
1.0
2.0
Milligals
0 5000 10000 15000 20000
Distance along the profile (feet)
X'
0 5000 10000 15000 20000
Distance along profile (feet)
0
200
400
600Depth(feet)
Drop the starting figure into word thefirs t figure in your lab
report ! You can
discard unneeded figures later.
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Before doing anything ask yourself how the subsurface
representation of this cross sectioncould be changed to better fit
the observed gravity. In the figure below, Ive labeled a couple
areas
(A andB) where significant disagreement occurs.
How might the configuration of the bedrock/till horizon be
changed to correct for these differences?
5) Use the move point option and manually adjust the locations
of points defining the till/bedrockinterface. Note how the gravity
anomaly varies. Attempt to eliminate the differences
betweenobserved and calculated anomaly.
Note that will holding down on the point and moving it around,
your anomaly window willautomatically be updated, and the error
(difference between the calculated and observed gravity
anomaly) will appear as a red line (see below).
A
B
B A
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In the figure below, Ive eliminated the differences at B.
To eliminate the differences associated with anomaly A, lets use
a different method inversion.
This is the sort of thing you did a lot with in our terrain
conductivity and resistivity modelingexercises. The inverse options
leave it to the computer to make
adjustments in the layer configuration to achieve a better fit
betweenthe calculated and observed gravity values.
6) To undertake the inverse operation first click on
theINVbutton onyourAction Toolbar (right).
This will bring up the inversionparameters window (right).
B A
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7) Click on the X button in the inversion parameters window and
select XZ. Doing this willallow both the X and Z values for
selected coordinates to be adjusted by the computer.
Check the AutoDCcheck box. This will allow the computer to make
bulk-up and down
shifts of the entire curve to help improve the fit.
Click on Constraints and set the dX and dZ values to 50 feet.
This will restrict the distanceover which individual coordinate
points will be allowed to move.
Lastlyclick on the layer points that you want to free for the
inversion. Those points will be
highlighted by a cyan colored +.
It is recommended that you zoom in on the surface points between
13000 and 15000 feetalong the profile. This will ensure that you
actually pick the layer coordinates and not the
topographic surface coordinates.
After points have been selected, your model should look like
that shown below
Now Click GO.
The first inversion step will be displayed and you will have the
option to accept, cancel or
go an additional step (see figure top of next page).
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We need to go a little further so Click on Next Step.If this
seems to throw the whole model off - just click undo. You can undo
or back up as
many times as youd like.
Thenclick Accept (you can x out of the inversion setup
window).Your model should look similar to that shown below.
You can use the move point option to fine tune your model or
test out other ideas.
Inverted points will remain highlighted until you select another
function from the toolbar.
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8) Finally, display the error between the calculated and
observed gravity by clicking onDisplay and then checking off the
Grav, Err item in the list.
9) Make another copy of your screen and place it in your word
lab report file.
If desired, you can click on the examine button and assign
different color and texture schemes toenhance the appearance of
your model for presentation.
10) Now lets explore the relationship of these anomalies to the
predictions based onStewarts equation t = 130g.
Place your mouse arrow on the gravity value observed over the
deepest valley along the profile
marked by the V in the figure above.
The gravity anomaly gv at this point is ____________milligalsThe
predicted value of t = 130 gv is ____________ feet.
Bring your mouse arrow down into the model window and rest it on
the valley floor. Read the depthof the valley floor off the
coordinate values listed in the lower right of your GM-SYS
window.
The depth to the valley floor is ____________ feet.
How well does Stewarts formula work?
Why do you think we have a disagreement?10) Use the examine
function and change the density of the till to 0.6gm/cm3 and
the
density of the bedrock to 0 gm/cm3.
Calculation Error
V
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Why did we do that?
___________________________________________________________________________________________________________________________
____________________________________________________________________________________________________________________________________________
We now have a model that fits the assumptions made by
Stewart.
To illustrate this effect of this change right click on the
gravity window andclick on set DC
shift. Then click on absolute andOK. The value in the absolute
shift box should be 0.
Note that this will shift all the calculated values into the
negative (see below).
Now repeat the comparison at point V
The gravity anomaly gv at this point is ____________milligalsThe
predicted value of t = 130 gv is ____________ feet.
The depth to the valley floor is ____________ feet.Did the
method work a little better?
Why do you think there is still an error in the depth
estimate?11) Our last task for the day will be to examine the
potential effects associated with a
limited rather than infinite extent of the model layers. Set the
DC Shift back to Automatic.What we mean by infinite extent refers
to the extent of the layers in and out of the plane of
our model as well as along the direction of the cross section.
By default, the layers areassumed to extend out to plus and minus
infinity in and out of the plane of the section.
V
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As opposed to taking the default, we can limit the extents in
and out of the plane of thesection and examine the effect.
To do this use the examine function and click on the Glacial
Till layer in your model. Then
check the 2 3/4 D box. When you do this, note that an additional
two tabs appear across the
top of the Block Parameters window: a Y+ Block and Y- Block (see
below).
Click on the Y+ tab and change units to feet, set density at 0
and set the length to 1000 as
shown below. The density in this case (0) refers to the density
of the material out beyond thelimits of the till i.e. that of the
bedrock.
Note that Ive also set the color and pattern to indicate that
the bedrock comes up to thesurface and bounds the valley out of the
plane of the section
For the Y- Block assign a negative value to the length.
Basically the negative sign tells the
computer that the block extends into the screen. If you leave
the units in kilometers set theextent to -0.3048km.
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Note the difference that occurred. In the figure below Ive drawn
down the plan view pane
and have set the depth to 100 feet (right click to change the
plan view depth). In the viewbelow we are looking at a slice
through the earth at a depth of 100 feet depth. The plan view
cuts through bedrock highs in two locations. Change the plan
view depth to experiment withthis view.
Now lets bring the sides of the valley in even more. Narrow the
valley to about 650 feet intotal width. This would be 0.1 kilometer
for the Y+ block and 0.1 kilometer for the Y-
block.
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Our survey now runs down the length of this narrow valley.
Reset DC Shift to Auto and adjust the gravity scale range.At
point V, consider the following:
What is the maximum negative value of the gravity anomaly when
calculated for a valley that
extends significant distances in and out of the plane of the
section (effectively to plus and minusinfinity)?
______________ milligals
What is the anomaly at V when the valley width is reduced to
2000 feet (i.e. 1000 feet on eitherside of the survey line)?
______________ milligals
What is the anomaly at V when the valley width is reduced to
approximately 650 feet (i.e.0.1km on either side of the survey
line)?
______________ milligals
V
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Follow the standard reporting format. Include the following or
similar subdivisions:
Lab Report
Abstract: a brief description of what you did and the results
you obtained (~200 words).Background: Provide some background on
the data were analyzing. All of this would come from
Stewarts paper. Explain his approach and answer question 1 below
in this section to illustrate his
approach.Results: Describe how you tested the model proposed by
Stewart along XX. Include answers toquestions 1 through 4 below in
this discussion.
Conclusions: Summarize the highlights of results obtained in the
forgoing modeling process.
In your lab report incorporate answers to the following
questions and refer to them by numberfor identification.
1. The residual gravity (gravity anomaly) plotted in Figure 5 of
Stewart's paper (also seeillustrations in this lab exercise) has
both positive and negative values. Assume that an anomaly
extends from +2 milligals to -2 milligals. Use the plate
approximation (i.e. Stewarts formula) andestimate the depth to
bedrock? What do you need to do to get a useful result? Residuals
of any kind
usually fluctuate about zero mean value. How does Stewart shift
these values so he can use hisformula t=130g?
2. At the beginning of the lab you made a copy of GMSYS window
showing some
disagreement between the observations (dots) and calculations
(solid line) across Stewart's model(section XX' Figure 7). As we
did in class and in the lab manual, note a couple areas where
the
difference between the computed g associated with the model
varies considerably from theobservations. Label these areas in your
lab report figure for reference. In your lab report discussion
offer an explanation for the cause(s) of these
differences?Assume that the differences are of
geological origin and not related to errors in the data.
3. With a combination of inversion and manual adjustments of
points defining thetill/bedrock interface, you were able to
eliminate the significant differences between observed and
calculated gravity. Your model is incorrect though since the
valleys do not extend to infinity in andout of the cross section.
Use the 2 modeling option to reduce the extents of the valleys in
and out
of the section to 800 feet. Make the changes to the Y+ and Y-
blocks and then apply. Take a screencapture to illustrate the
reduction in g associated with the glacial valleys. Make a screen
capture of
this display showing the new calculation line and the dashed
gray values associated with the infinitevalleys. In clued this
figure in your report and discuss your results.
4. Use Stewart's formula t = 130g and estimate the depth to
bedrock at the x location of 7920feet along the profile. Does it
provide a reliable estimate of bedrock depth in this area? Explain
in
your discussion.5. Lastly, describe the model you obtained and
comment on how it varies from the starting
model taken from Stewart.
These questions provide discussion points in your lab report.
Use figures you've generated inGMSYS to illustrate your point. All
figures should be numbered, labeled and captioned.
Assignment is due _____________ . Assignments are due on the
date noted in
class. Write down these due dates in the above blank space. A
letter grade will
be deducted from labs not handed in on the requested date.
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Reference list of Residual Gravity across Stewart's Profile
XX'The following data taken from the residual gravity map shown in
Figure 5 of Stewart's paper.
Profile XX' was artificially sampled at 500 foot intervals.
Station
#
Distance
(feet)
Observed
Anomaly
(milligals)1 0 -0.70
2 500 -0.70
3 1000 -0.70
4 1500 -0.63
5 2000 -0.55
6 2500 -0.20
7 3000 0.40
8 3500 1.00
9 4000 1.62
10 4500 1.77
11 5000 1.62
12 5500 1.41
13 6000 1.22
14 6500 1.00
15 7000 0.80
16 7500 0.30
17 8000 -0.38
18 8500 -0.80
19 9000 -1.10
20 9500 -1.20
21 10000 -1.00
22 10500 -0.50
23 11000 0.0024 11500 0.10
25 12000 -0.20
26 12500 -0.40
27 13000 -0.50
28 13500 -0.30
29 14000 0.20
30 14500 0.90
31 15000 1.57
32 15500 2.20
33 16000 2.20
34 16500 1.3035 17000 0.50
36 17500 -0.20
37 18000 -0.50
38 18500 -0.70
Reference coordinate listVERTEX # X-LOC Z-LOC
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1 -200000 02 -200000 400
3 0 4204 1500 450
5 2500 450
6 4200 1857 5300 1758 7500 250
9 8500 40010 9000 630
11 9700 63012 11000 280
13 12000 28014 12800 400
15 13300 40016 15400 0
17 16300 018 17000 100
19 18500 30020 20000 350
21 200000 35022 200000 0
