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Lab notes 

Lab 5
How is the high topography of the Himalaya and Tibetan Plateau supported at depth?
This lab/assessment provides an opportunity to use the knowledge, techniques and forward modelling approach we have covered in the previous lab sessions, reading and during lectures on a real world example. In this case the aim of the lab session is to use the semiinfinite slab approximation model to help interpret measured gravity data extracted from three parallel transects across the HimlayaTibet mountain front.
The key question we need to address here is; How is the topography of the HimalayaTibet mountain range supported at depth?
The key to tackling the modelling part of this lab/assessment is to recognise that it is essentially an extension/adaption of what we did in Lab 4, but in this case we have real data, not synthetic data.
Plotly plot test
Task 1
Examine and compare the gravity data for the three transects across the Himalya mountain front. For all tasks in the assessment you must use the personalised version of the data that were provided to you. These data were extracted from the WGM2012 data set which a high resolution global dataset of Earth's gravity anomalies (Bouguer, isostatic and surface freeair), computed at global scale in spherical geometry. See the BGI website for further details; http://bgi.omp.obsmip.fr/dataproducts/Gridsandmodels/wgm2012
The raw gravity data have been processed following the standard procedures you used in previous labs to calculate the Free Air and Bouguer anomalies. For each transect the mean gravity anomalies (and the calculated standard deviation) were extracted from 20km wide (measured at right angles to the transect line) and 5km long (measured along line of transect) windows along the line of the transect. This yields estimates of the gravity anomalies and the standard deviation at 5km intervals along each profile.
Inspect the gravity anomaly profiles for each line by plotting graphs of the anomaly values and the topography (adjust the scale of the topography, or use a secondary yaxis option in Excel for the elevation values, as required so you can plot the curves on one graph) on the yaxis versus centre distance on the xaxis. Compare the shape and magnitude of the anomalies with respect to the topography (i.e. elevation) for each transect.
Compare the observed anomalies for the HimalayaTibet mountain range to those analysed in the previous lab session for a mountain in Airy isostatic equilibrium.
You will see on inspection of the data files that the raw gravity data has already been processed, and the Free Air and Bouguer gravity anomaly values are provided along with an estimate of the standard deviation for these estimates.
The first part of any analysis is clearly to inspect and understand the data you have available. So in this case it would be a good idea to draw graphs of the Free Air and Bouguer anomalies along each of the three transects (line 1, line 2 and line 3) as well as the topography along these transects (see topography profiles example below).
That is, plot the gravity anomalies on the yaxis versus central distance along the xaxis (as shown below for the elevations)...I find it easiest to compare/evaluate these data by plotting the gravity and elevation values on the SAME graph...so it is easy to see how each varies relative to the other. Makes seeing patterns much easier.
Task 2
Use an Airy isostatic model and a simplified crustal structure such as illustrated in the sketch below to calculate the thickness of the crustal root (hm) and the total crustal thickness (hM ) under the Tibetan Plateau assuming the surface topography is completely supported by the crustal root, i.e. it is in Airy isostatic equilibrium (ρc = 2.67, ρm =3.1, ρa = 0 all in g.cm3).
You will need to estimate an appropriate height for the topography (h1=ha in the diagram here) from the actual data (look at your graphs of topography from Task 1...BUT, remember to use the ACTUAL values, not the scaled values.
You will also need to calculate the thickness of the crustal root, hm (h2=hm in the diagram here) assuming Airytype local isostatic compensation. So setup and solve the simultaneous equations for equal height and equal pressure to obtain an expression for hm. Follow the same procedure as used in Lab 4 to do this.
Task 3
Use the semiinfinite slab approximation (see pages 250, 257 and 258, Chapter 8, Lillie) to model the Free Air gravity anomaly and the Bouguer gravity anomaly across the HimalayaTibet mountain front assuming a simple Airy isostatic model. It will be useful and convenient to set up your model so that the xdistance intervals match those in the observed datasets (i.e. from c. 300 to 400 km). If you copy the column of xdistances from the observed data you could use these directly to set yu model up, or simply replace the xdistances in an existing model spreadsheet (e.g. from Lab 4) with the new values for your observed data.
Test your model predictions of the BA and FAA by comparing the model anomalies with the observed anomalies along each of the three transects, lines 1, 2 and 3. You could do this by testing your model against each transect separately.
Given that our model design/geometry is very simple, you might consider whether an "average model", i.e. a model that attempts to fit the mean of the observations calculated across all three lines is appropriate. That is calculate the mean Free Air anomaly and the mean Bouguer anomaly (based on the three transect values available) and fit a single model to these mean values. Averaging the observations made along the three transects will "smooth" some of the variation arising from spatial differences in density, topography etc.
Ensure that you calculate the Root Mean Square Deviation (RMSD), i.e. the average misfit between your model predictions and the observations, for each model you test and compare this with the mean standard deviation on the observations for the transect.
Also, make sure you plot a set of suitable graphs to illustrate the observed anomaly data, topography and your model results for each transect/line, ensuring that a plot of the residuals is also included to aid the evaluation and assessment of the model.
This task/section essentially requires the same approach we took in Lab 4, so review your spreadsheet/model/notes for Lab 4 to refresh your memory on how to setup the semiinfinite slab model if you need to.
Task 4
 Compile, summarise and report the data and your modelling results from the tasks 1 to 3 (include a simple sketch for your model design (from Task 1), and you must show your workings for the calculation of hm and hM in Task 1) into a report. Explicitly discuss, and quantify using the appropriate statistics, how well your model fitted the observed gravity data. [40% of CA grade]
 Read the papers discussing the gravity and structure of the HimalayaTibetan Plateau and those on lithospheric strength and effective elastic thickness listed on Moodle (under Lab 5 section) and at LEAST two other relevant papers (use Google Scholar and the web, or even the library, to source other relevant papers).
 Discuss your model results and your interpretation of these in terms of George Box’s famous statement (Box, 1976) that “All models are wrong, but some are useful.” Focus on whether, and if so, how, your model has advanced understanding of the likely mode of isostatic compensation of the Tibet PlateauHimalaya. Make sure you include analysis and commentary on the problem of defining and measuring the strength of the continental lithosphere, and its role in regional isostasy [60% of CA grade]
 Your overall report must be less than 2500 words.
Box, George E.P. (1976) Science and Statistics, Journal of the American Statistical Association, Vol. 71, No. 356, pp. 791799.
Please note that the deadline for submission of the assessment report is 1000 Monday 26th Nov 2018.