EART20170 Computing,
Data Analysis &
Communication skills
Lecturer: Dr Paul Connolly (F18 – Sackville Building)
p.connolly@manchester.ac.uk
2. Computing (Excel statistics/modelling)
2 lectures
assessed practical work
Course notes etc:
http://cloudbase.phy.umist.ac.uk/people/connolly
LAST LECTURE!
Recommended reading: Cheeney. (1983)
Statistical methods in Geology. George, Allen &
Unwin
Plan
 This lecture plus two more drop-
in sessions in computer labs
 Assessment handed out today
and need to hand in by 16:00,
Tuesday December 12th.
Lecture 5
 Monte Carlo method of error
propagation.
 Using `Goal seek’ to root-find
 Using `solver’ for optimisation
 Basic macros.
 Mega Tsunami
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.
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)).
Monte Carlo in Error
Propagation
 Let’s 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,stdev))
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
A more complicated
formula:
This is one used in geochronology (don’t
worry about the details):
exp(  t)  1
J 
R
The error propagation formula is given by:
J  J 
2
R
2
2
1 
t 
2
    1 
  t
T  RJ
where T = 1/
A more complicated
formula:
Using the following data:
R = 49.704 ± 0.381
t = 1.072 ± 0.011 billion years
 = 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.
Using `Goal seek’ to rootfind
 What if I want to find the inverse of a
function?
A typical function
25
20
f(x)
15
10
5
0
?
-5
0
1
2
3
4
5
6
x
 Sometimes I can find the inverse
analytically, e.g.
y  x 2  10
x  y  10
 But not always (and if maths isn’t
your forte).
Using `Goal seek’ to rootfind
 What height of fall will result in a
height of single tsunami 30 m?
8 g w
HD3 L
3 3
HD  wave height near shore
Et 
L  Lengthof wave perpendicular to propagation direction 2r
HD  3
3 3E t
8 g w L
HD  wave height near shore
L  Lengt h of wave perpendicular t o propagat ion direct ion  2r
 This is sometimes difficult (or
impossible!).
 Instead use iteration => Goal seek.
Using `Goal seek’ to rootfind
 Here are some arbitrary values
 Go to tools->goal seek
Using `Goal seek’ to rootfind
 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
didn’t have to do any
maths!
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?
Using `solver’ for
optimisation
 Example: say that it costs £100
per day to hire your basic digging
equipment.
 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 apriori knowledge (0.2xday^2).
 The market value for gold is £321
for 31.1g.
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
Using `solver’ for
optimisation
First: How many days to
break even?
 Go to Tools->solver
 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)
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.
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.
Second: What is the max
net profit?
 Go to Tools->solver
 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.
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.
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.
Third: At least £40 per
day?
 Go to Tools->solver
 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)
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.
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.
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.
Basic macros
 Go to tools->Macro->record new
macro
 You can name the macro and
give it a shortcut key
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
Basic macros
 Enter your values as before.
 The solution is found
 Now press the `stop’ button to cease recording
Basic macros
 You can now run your macro by going
to tools->macros->macros
 Selecting the macro you recorded and
pressing run. You could have also used a
shortcut
A subtlety
 When using goal seek it is nearly
always more convenient to solve
for a zero.
 This is because `goal seek’
doesn’t allow the value to be
input by a cell reference.
A subtlety
 In this case you put zero in the
`To value’ box in goal seek
Put zero
here
Mega tsunami
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
Caldera collapse
 The movement associated with
collapse can be either vertical
(caldera) or horizontal (lateral
collapse).
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
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 world’s population
(~60,000,000 people) living in regions
susceptible to giant waves around the
coastlines of the world’s oceans, they
pose a very serious threat.
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.
USGS
http://vulcan.wr.usgs.gov/Volcanoes/Hawaii/Maps/map_location_hawaii.html
Hawaiian lateral collapses
 The Hawaiian islands
are surrounded by
more than 68 slumps
and avalanches >20
km long.
 There are >20 giant
collapses of up 5000
km3 (approx. 2000
times larger than Mt
St Helens)
From: http:/www.mala.bc.ca/~earles/kilauea-feb02.htm
From: Ward, 2002
Prehistoric Hawaiian
Collapse
Lateral collapse
Molokai
N
Lanai
10 km
USGS http://vulcan.wr.usgs.gov/Volcanoes/Hawaii/Maps/map_location_hawaii.html
Lanai tsunami impact
PACIFIC OCEAN
Source of
tsunami
NEW GUINEA
Wave
impact
FIJI
AUSTRALIA
Sydney
Wave
impact
TASMANIA
From Davidson, 1992
Wave
impact
NEW ZEALAND
HAWAII
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
Tsunami wave model
Potential energy released by the collapse:
E p  V  ( r  w )  g  (D0  D1 )
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)
The wave energy, Et
8  g  w
3


Et 
 HD  L
3 3
HD ~ H, the wave height near shore (Depth ~ 0)
L = length of wave perpendicular to the propagation direction
wave L = 2r
r