Forward and Inverse Modeling of Gravity Data: Locating buried glacial channels and evaluating the results of published analysis

Transcription

1 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 folder Stewart 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 store your screen captures. Use flash drive as a secondary backup. 76

2 Stewart s residual gravity data and depth-model or cross section are plotted below for reference. X X' A. Milligals Distance along the profile (feet) Gravity residuals taken from Stewart's Figure 5, page 27 along profile XX'. Depth (feet) X? X' B Distance along profile (feet) Depth model is simplified from that presented by Stewart (Figure 5, page 27). 3) Use the examine function (eyeball on the action toolbar) to check the model parameters. The density of the till is gm/cm3 The density of the bedrock is gm/cm3 The density contrast (bedrock to till) is gm/cm3 What should the density contrast be? gm/cm3 Change the density of the bedrock so that the correct density contrast will be present between the bedrock and overlying till. 4) Open up a word file and copy this view window (Alt- Prt Scr and then in a word text box Ctrl V) to your word report file. You may want to review the earlier handout on these 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 gravity for Stewart s model does not agree with the observations taken from his residual gravity map along the profile XX. Drop the starting figure into word the first figure in your lab report! You can discard unneeded figures later. 77

3 Before doing anything ask yourself how the subsurface representation of this cross section could be changed to better fit the observed gravity. In the figure below, I ve labeled a couple areas (A and B) where significant disagreement occurs. B A B A 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/bedrock interface. Note how the gravity anomaly varies. Attempt to eliminate the differences between observed and calculated anomaly. Note that will holding down on the point and moving it around, your anomaly window will automatically be updated, and the error (difference between the calculated and observed gravity anomaly) will appear as a red line (see below). 78

4 In the figure below, I ve eliminated the differences at B. B A To eliminate the differences associated with anomaly A, let s use a different method inversion. This is the sort of thing you did a lot with in our terrain conductivity and resistivity modeling exercises. The inverse options leave it to the computer to make adjustments in the layer configuration to achieve a better fit between the calculated and observed gravity values. 6) To undertake the inverse operation first click on the INV button on your Action Toolbar (right). This will bring up the inversion parameters window (right). 79

5 7) Click on the X button in the inversion parameters window and select XZ. Doing this will allow both the X and Z values for selected coordinates to be adjusted by the computer. Check the AutoDC check 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 distance over which individual coordinate points will be allowed to move. Lastly click 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 and feet along 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). 80

6 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 you d like. Then click 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. 81

7 8) Finally, display the error between the calculated and observed gravity by clicking on Display 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 to enhance the appearance of your model for presentation. Calculation Error V 10) Now let s explore the relationship of these anomalies to the predictions based on Stewart s 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 g v at this point is milligals The predicted value of t = 130 g v is feet. Bring your mouse arrow down into the model window and rest it on the valley floor. Read the depth of 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 Stewart s 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. 82

8 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 and click on set DC shift. Then click on absolute and OK. The value in the absolute shift box should be 0. Note that this will shift all the calculated values into the negative (see below). V Now repeat the comparison at point V The gravity anomaly g v at this point is milligals The predicted value of t = 130 g v 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 are assumed to extend out to plus and minus infinity in and out of the plane of the section. 83

9 As opposed to taking the default, we can limit the extents in and out of the plane of the section 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 the limits of the till i.e. that of the bedrock. Note that I ve also set the color and pattern to indicate that the bedrock comes up to the surface 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 the extent to km. 84

10 Note the difference that occurred. In the figure below I ve drawn down the plan view pane and have set the depth to 100 feet (right click to change the plan view depth). In the view below 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 with this view. Now let s bring the sides of the valley in even more. Narrow the valley to about 650 feet in total width. This would be 0.1 kilometer for the Y+ block and 0.1 kilometer for the Y- block. 85

11 Our survey now runs down the length of this narrow valley. V 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 minus infinity)? milligals What is the anomaly at V when the valley width is reduced to 2000 feet (i.e feet on either side 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 86

12 Lab Report Follow the standard reporting format. Include the following or similar subdivisions: Abstract: a brief description of what you did and the results you obtained (~200 words). Background: Provide some background on the data we re analyzing. All of this would come from Stewart s 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 to questions 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 number for identification. 1. The residual gravity (gravity anomaly) plotted in Figure 5 of Stewart's paper (also see illustrations 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. Stewart s formula) and estimate 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 his formula 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 the observations. 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 the till/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 and out of the cross section. Use the 2 ¾ 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 screen capture 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 infinite valleys. 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 7920 feet 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 in GMSYS 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. 87

13 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) Reference coordinate list VERTEX # X-LOC Z-LOC 88

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