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## EART20170 Computing, Data Analysis

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Title: EART20170 Computing, Data Analysis

1
EART20170 Computing, Data Analysis
Communication skills
Lecturer Dr Paul Connolly (F18 Sackville
Building) p.connolly_at_manchester.ac.uk
2. Computing (Excel statistics/modelling) 2
lectures assessed practical work Course notes
etc http//cloudbase.phy.umist.ac.uk/people/conno
lly LAST LECTURE!
methods in Geology. George, Allen Unwin
2
Plan
• This lecture plus two more drop-in sessions in
computer labs
• Assessment handed out today and need to hand in
by 1600, Tuesday December 12th.

3
Lecture 5
• Monte Carlo method of error propagation.
• Using Goal seek to root-find
• Using solver for optimisation
• Basic macros.
• Mega Tsunami

4
Statistical approach to error propagation
• Computers enable the use of a very simple
statistical method to propagate errors.
• Monte Carlo methods provides approximate
solutions to a variety of mathematical problems
by performing statistical sampling experiments.
• The statistical approach is particularly useful
for propagating errors in complex functions.

5
Monte Carlo methods
• Monte Carlo simulations or methods are named
after Monte Carlo, Monaco, where the primary
attractions are casinos containing games of
chance exhibiting random behaviour.
• The random behaviour in games of chance is
similar to how Monte Carlo simulation selects
variable values at random to simulate a model.
• For each uncertain variable (one that has a
range of possible values), you define the
possible values with a probability distribution
(e.g. the Excel function norminv(rand(),mean,stdev
)).

6
Monte Carlo in Error Propagation
• Lets use a previous example of measuring bed
thickness. We have two populations of
measurements x 12.1 0.3 and y 4.2 0.2.
• By repeatedly taking samples at random (e.g. by
the nested Excel function norminv(rand(),mean,st
dev)) from x and y, and adding the values, we
should obtain a third population with a mean of
16.3cm and a standard deviation approximately
equal to that obtain from the analytical solution
( 0.4 cm).
• The statistical approach is particularly useful
for propagating errors in complex functions

7
A more complicated formula
This is one used in geochronology (dont worry
The error propagation formula is given by
where T 1/l
8
A more complicated formula
Using the following data R 49.704 0.381 t
1.072 0.011 billion years l 5.543 ? 10-10
years-1
Then using the equations J 0.016329
0.000255
OK so what about the Monte Carlo?
With a table of R and t calculated from the
norminv function (10000 values are typically used
for good statistics) we calculate J and can
therefore calculate the average and stdev.
9
Using Goal seek to root-find
• What if I want to find the inverse of a function?

?
• Sometimes I can find the inverse analytically,
e.g.
• But not always (and if maths isnt your forte).

10
Using Goal seek to root-find
• What height of fall will result in a height of
single tsunami 30 m?
• This is sometimes difficult (or impossible!).
• Instead use iteration gt Goal seek.

11
Using Goal seek to root-find
• Here are some arbitrary values
• Go to tools-gtgoal seek

12
Using Goal seek to root-find
• Enter the cell you want to change and the value
(i.e. the actual energy) and the variable that
will be changed press OK
• The cells change until the goal is found. Press
OK at the next prompt

Your value for HD is now displayed in the correct
cell. And you didnt have to do any maths!
13
Using solver for optimisation
• Goal seek only works for functions of one
variable.
• Goal seek is good for route finding, but what if
I want to find other properties such as minimum,
maximum values?
• E.g. Mining a gold seam. How can I break even?
Whats the max profit I can make? Whats the min
number of days I can mine before making a profit?

14
Using solver for optimisation
• Example say that it costs 100 per day to hire
• And you manage to extract 4 tonne per day of gold
from rock.
• But as the number of days increase it becomes
more difficult to extract the gold from the shaft
as extra equipment has to be rented usually
have some a-priori knowledge (0.2xday2).
• The market value for gold is 321 for 31.1g.

15
Using solver for optimisation
• You wish to know
• How many days you should work before breaking
even?
• What is the maximum net profit you can make
• How long can you work before your net rate of pay
drops below 40 per day

16
Using solver for optimisation
17
First How many days to break even?
• Go to Tools-gtsolver
• On the pop-up menu, set the target cell to the
Net cell reference and the changing cell to the
Days cell reference. Also check the Value of
tab and set this value to 0 (i.e. break even)

18
First How many days to break even?
• You should also set the constraint that the
number of Days is greater than or equal to zero!
Click on add and in the next box put in that
Days should be greater than 0 OK.
• On the first popup window press solve
• The cell values change and another popup asks if
you want to keep the solution OK.

19
First How many days to break even?
• You see that it after 243 days the venture will
start to become non profitable. Your total costs
were 36139 all of which you got back from the
gold seam.

20
Second What is the max net profit?
• Go to Tools-gtsolver
• On the pop-up menu, set the target cell to the
Net cell reference and the changing cell to the
Days cell reference. Also check the max tab.

21
Second What is the max net profit?
• You should also set the constraint that the
number of Days is greater than or equal to zero!
Click on add and in the next box put in that
Days should be greater than 0 OK.
• On the first popup window press solve
• The cell values change and another popup asks if
you want to keep the solution OK.

22
Second What is the max net profit?
• You see that it takes 121.6 days to get the
maximum net profit of 2960. Your total costs
were 15113 and your average rate of pay was 24
per day.

23
Third At least 40 per day?
• Go to Tools-gtsolver
• On the pop-up menu, set the target cell to the
Rate cell reference and the changing cell to
the Days cell reference. Also check the Value
of tab and set this value to 40 (i.e. 40/day)

24
Third At least 40 per day?
• You should also set the constraint that the
number of Days is greater than or equal to zero!
Click on add and in the next box put in that
Days should be greater than 0 OK.
• On the first popup window press solve
• The cell values change and another popup asks if
you want to keep the solution OK.

25
Third At least 40 per day?
• You see that after 43 days your average net rate
of pay will drop below 40. Your total costs were
4687 and your net pay was 1730.

26
Basic macros
• The goal seek and solver tools are very powerful,
but they can be time consuming if you want to
work on vast data sets.
• You can save a macro to a worksheet and use it
again and again without having to always remember
the exact sequence.
• We will look at recording and using a macro for
using the goal seek tool.

27
Basic macros
• Go to tools-gtMacro-gtrecord new macro
• You can name the macro and give it a shortcut key

28
Basic macros
• The macro recorder is now visible with a stop
symbol. All your actions will now be recorded.
• Again use goal seek in the same way as before

29
Basic macros
• Enter your values as before.
• The solution is found
• Now press the stop button to cease recording

30
Basic macros
• You can now run your macro by going to
tools-gtmacros-gtmacros
• Selecting the macro you recorded and pressing
run. You could have also used a shortcut

31
A subtlety
• When using goal seek it is nearly always more
convenient to solve for a zero.
• This is because goal seek doesnt allow the
value to be input by a cell reference.

32
A subtlety
• In this case you put zero in the To value box
in goal seek

Put zero here
33
Mega tsunami
34
Volcano collapse
• All volcanoes are inherently unstable and edifice
growth will ultimately lead to some degree of
collapse.
• Major collapse of the old volcanic edifice,
Soufriere Hills volcano early on 26 December 1977

35
Caldera collapse
• The movement associated with collapse can be
either vertical (caldera) or horizontal (lateral
collapse).

36
Mount St Helens 1980
The landslide moved northward at speeds of 110 to
155 mph and advanced . Part of the avalanche
surged into and across Spirit Lake, but most of
it flowed westward along the North Fork of the
Toutle River for 13 miles filling the valley to
an average depth of 150 ft.
http//pubs.usgs.gov/publications/msh/debris.html
37
Hazard Potential
• Lateral collapse of oceanic island volcanoes are
amongst the most spectacular natural events on
Earth.
• There is a potential for submarine landslides to
generate tsunami and mega-tsunami.
• Mega-tsunami have never been witnessed
historically and geological evidence for their
existence is controversial.
• With 1 of the worlds population (60,000,000
people) living in regions susceptible to giant
waves around the coastlines of the worlds
oceans, they pose a very serious threat.

38
Mega-tsunami
• Mega-tsunami are long wavelength (typically
300-400 km) wave trains that travel thousands of
kilometres, across ocean basins at velocities in
excess of 500 km hr-1.
• As they pass into shallower water towards land
their wavelength is compressed and height
amplifies, typically 10- to 20-fold, generating
waves up to hundreds of metres high that may
incur many kilometres inland.

39
Hawaiian lateral collapses
• The Hawaiian islands are surrounded by more than
68 slumps and avalanches gt20 km long.
• There are gt20 giant collapses of up 5000 km3
(approx. 2000 times larger than Mt St Helens)

From http/www.mala.bc.ca/earles/kilauea-feb02.h
tm
40
From Ward, 2002
41
Prehistoric Hawaiian Collapse
USGS http//vulcan.wr.usgs.gov/Volcanoes/Hawaii/Ma
ps/map_location_hawaii.html
42
Lanai tsunami impact
HAWAII
Source of
PACIFIC OCEAN
tsunami
NEW GUINEA
Wave
impact
FIJI
AUSTRALIA
Wave
Sydney
impact
Wave
impact
NEW ZEALAND
TASMANIA
From Davidson, 1992
43
New South Wales Tsunami Deposits
The tsunami carved these scour pools within a few
minutes as it overtopped a 20-25 m high headland
Blocks stacked against against 30 m high cliffs.
Note the person circled for scale. Some of the
blocks are as large as rooms in a house.
Source E.A. Bryant http//www.uow.edu.au/science/
geosciences/research/tsun.htm
44
Tsunami wave model
Potential energy released by the collapse
Archimedes force
D0
Ds
V volume of collapse block (m3) pw density of
seawater (1030 kg m3) pr density of rock (2800
kg m3) g acceleration due to gravity (9.8
m/s/s) D0 initial depth of sliding block (m) Ds
final depth of sliding block (m)
45
The wave energy, Et
HD H, the wave height near shore (Depth 0)
L length of wave perpendicular to the
propagation direction