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Practical – Week 4
Anatomy of a Mountain Belt
Aim : To calculate the stratigraphy and gravity anomaly of a foreland basin that forms
by flexure of the lithosphere in front of a thrust/fold load.
We showed in class that the gravity anomaly and the depth to basement at many
foreland basins can be explained by a simple model in which thrust/fold loads flex the
lithosphere as they migrate across it. A commonly used model is a semi-infinite or broken
plate model.
The flexure of a broken plate (e.g. Watts, 2001) is given by:
y
Pb 
e xCosx
(m  inf ill )g
(1)
where:
Pb = applied line load / unit width of the plate (Note : downward acting loads are
negative - upward acting loads positive). The load is assumed to be applied at the plate
break, i.e. x = 0.
y = flexure(negative downwards, positive upwards)
m = density of material beneath the plate
infill = density of material above the plate
g = average gravity
x = horizontal distance
= flexural parameter which is given by:
(  m   inf ill )g 1/ 4
  



4D
(2)
D = flexural rigidity of the plate given by :


D
ETe3
12(1 v 2 )
where:
E = Youngs Modulus
v = Poisson'sRatio
Te = Elastic thickness of the lithosphere
(3)
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PART 1:
Use Excel to calculate the flexure of the lithosphere due to the load Pb,
assuming it to act on the end of a semi-infinite (i.e. broken) plate. Calculate the
flexure for values of the elastic thickness, Te, of 75, 100 and 125 km assuming the
following parameters :
m = 3330 kg m-3
infill = 2400 kg m-3 (i.e. the flexure is infilled by sediment)
g = 9.81 m s-2
Pb = 6.0 × 1012 N m-1
v = 0.25
E = 100 GPa
Display your results on a graph.
Hint :
1. Enter the values of elastic thickness in column A. Suggestion : begin in a
row to allow for headings. Then, use Equations (3) and (2) to calculate D (the flexural
rigidity) andthe flexural parameter) placing the results in columns B and C
respectively.
2. Select a set of x values at which you want to evaluate the flexure and place
them in column B. Suggestion : begin in column A and make a list of the number of x
values, say from 0 to 15. Then, choose an x step and calculate the distance of each x
value in km. A maximum distance of 600 km should be sufficient, but allow enough
rows to add more values later.
3. Use Equation (1) to calculate the flexure for Te of 75, 100 and 125 km and
place the results in columns C, D and E respectively.
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4. Plot the results on a graph showing the flexure curves as a function of
distance. Click on the chart and legend and use ‘Chart’ and then ‘Chart Options’ and
‘Source Data’ to label your graph.
5. Note the distance to the first point of zero flexure (i.e. the node) and plot a
graph showing the relationship between the distance to the node and Te.
PART 2 :
Use Excel to calculate the stratigraphy of a foreland basin that forms by
progressive flexural loading.
Assume :
1. The basin is formed by 3 incremental loads, each of which has a value 1/3
of Pb .
2. The first load is emplaced on relatively weak lithosphere (i.e. one with Te =
75 km), the second on intermediate strength lithosphere (i.e. one with Te =
100 km) and, the third and final load on relatively strong lithosphere (i.e.
one with Te = 125 km).
3. All flexural bulges - except the one associated with the final load - are
eroded to sea-level. Ignore any uplift that might result from the erosion.
Hint :
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Begin with the youngest load (i.e the one that has been emplaced
on lithosphere with Te = 125 km).
Calculate the sediment-filled flexure due to a load 1/3 of Pb
Next, consider the intermediate load (i.e the one that has been
emplaced on lithosphere with Te = 100 km).
Calculate the sediment-filled flexure due to a load 1/3 of Pb.
Erode the bulges
Calculate the depth of the sediment-filled flexure, noting that it
underlies the sediment-filled flexure of the youngest load.
End with the oldest load (i.e the one that has been emplaced on
lithosphere with Te = 75 km).
Calculate the sediment-filled flexure due to a load 1/3 of Pb
Erode the bulges
Calculate the depth of the sediment-filled flexure, noting that it
underlies the sediment-filled flexure of both the youngest and
intermediate loads.
Display the stratigraphy and label main features.
PART 3 :
Use Excel to calculate the gravity anomaly of a foreland basin that forms by
flexural loading.
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Assume:
1. The density of the sediments, s, crust, c, and mantle, m, are uniform and
2600, 2800 and 3330 kg m-3 respectively.
2. The gravity anomaly can be computed using the Bouguer slab formula.
Note: The gravity effect of the sediment/crust interface (for example) using the
Bouguer slab formula is :
2G(s  c )y
where G = Universal Gravitational Constant = 6.67 × 10-11 N m2 kg-2, 1 N = kg m s-2
, 1 m s-2 = 105 mGal, y = depth to base of the sediments in m, s = density of
sediments = 2600 kg m-3, 
and c = density of crust = 2800 kg m-3.
PART 4:
The final part of the practical is to use the flexure model to estimate Te of the
continental lithosphere that underlies the Ganges foreland basin in northern India.
This basin, which formed by flexure of the Indian lithosphere due to southward
directed thrust/fold loads in the Himalaya, has been extensively studied. As a result,
there is now a reasonable coverage of stratigraphic (Burbank, 1992) and gravity
anomaly (e.g. Karner & Watts, 1983; Lyon-Caen & Molnar, 1983) data over the
basin.
We will examine Profile A which crosses the Main Boundary Thrust (MBT)
at (approximately) longitude 80 o E.
A
You can download the topography, Bouguer gravity anomaly, and the depth to
the base of the foreland sequence along Profile A by going to the course web page at:
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http://www.earth.ox.ac.uk/~tony/watts/teaching/anatomy/07H.html
and clicking on ‘Resources’. Note: the data is in 2 columns. The first column is the
distance, x, in km from the MBT. (Negative distance to the north, positive to the
south). The second column is (depending on the file) the topography in m, the depth
to the base of the foreland sequence in m, and the Bouguer gravity anomaly in mGal.
Use Excel to plot the depth to the base of the foreland sequence and the
gravity anomaly. You may find it easier to import the observed data and do the plots
on two separate work sheets.
Assuming that the load of the Himalayas can be represented as a line load on
the edge of a broken plate, calculate the flexure and gravity anomaly at (e.g. in steps
of 10 km) for 75 < Te < 125 km.
Note: calculate the flexure and gravity anomaly at the same x values as the
observed depth to the base of the foreland sequence and gravity anomaly data. This is
so you can plot the standard deviation or Root Mean Square (RMS) of the difference
between observed and calculated data and estimate the best fit value for Te. The RMS
is given by:
0.5
 n

_
1
RMS  
(x s  x s ) 2 
n 

 s1

_
where n = number of differences, xs = difference at the sth point, x s = mean
difference. The RMS can be calculated using the Excel function STDEV.

Plot graphs of the RMS difference against Te for both the flexure and gravity
 data. How well
anomaly and estimate the Te that best explains the observed
determined are your estimates ? Do the flexure and gravity anomaly give the same
results. If not why not ?
Hint: The gravity anomaly calculation is based on the Bouguer slab formula
and so may over-estimate the effect of the sediment/crust and, particularly, the
crust/mantle interface. Test this by reducing the mantle density.
The crustal thickness beneath the Ganges foreland is ~ 40 km. What do your
results from flexure modelling indicate to you about the long-term strength of the
Indian continental lithosphere ?
References Cited
Burbank, D.W., 1992, Causes of recent Himalayan uplift deduced from deposited patterns in
the Ganges basin, Nature, 357 , 680-683.
Karner, G.D., and A.B. Watts, 1983, Gravity anomalies and flexure of the lithosphere at
mountain ranges, J. Geophys. Res., 88 , 10,449-10,477.
Lyon-Caen, H., and P. Molnar, 1983, Constraints on the structure of the Himalaya from an
analysis of gravity anomalies and a flexural model of the lithosphere, J. Geophys.
Res., 88 , 8171-8191.
Watts, A.B., 2001, Isostasy and flexure of the lithosphere, 458 pp., Cambridge University
Press, Cambridge.