Tectonics Flashcards
(151 cards)
1
Q
Why should we care about mountain building?
A
1) Mountains are higher than oceans; the potential energy gradient between mountains and oceans drive large-scale transport of water, sediment, particulate and dissolved solids
2) Mountains interact with the atmosphere to affect both short-term and long term weather patterns, which control flood hazards.
3) Affects long term climate leading to persistent spatial differences in rainfall which in turn affects…
4) Mountains built by EQs, a primary natural hazard, so mountains are essentially a EQ record- prediction
5) Many erosional processes- landslides, debris flows, water floods
6) Beautiful
2
Q
What are the basic ideas of plate tectonic theory?
A
1) Thin, rigid plates (lithosphere); works well for oceanic plates, less so for thicker, heterogeneous continents
2) All deformation occurs at plate boundaries
3) Relative motion driven by atmospheric convection, gravitational sliding
4) Rates of relative motion are 1-100mm per year which is about the same as fingernail growth
3
Q
What is absolute motion?
A
- The term used to describe the fact that all plates move relative to the centre of the earth
4
Q
What is the relative motion?
A
- The term used to describe how plates behave in relation to each other and what determines their behaviour at plate boundaries.
5
Q
What are the two ways that rock uplift can occur?
A
1) tectonic uplift
2) Isostatic upift
6
Q
What is tectonic rock uplift
A
- Occurs via EQs and movement on faults.
- The word tekton means ‘builder’
7
Q
What is isostatic rock uplift?
A
- Occurs via gravity, due to buoyancy differences
8
Q
What is important to note about relative plate motion vectors?
A
- They are constant even over millions of years
9
Q
If it is the case that relative plate motion is constant, how does motion occur along the fault lines?
A
- The classical view of this is the EQ cycle which was conceived by Harry Reid after the 1906 San Francisco EQ
10
Q
What is the structure of the plates like?
A
- They are elastic
- However, the deformation caused by an EQ is permanent
- How does that work?
11
Q
What is the San Andreas Fault?
A
- Extensively studied fault line.
- California
- Diagrams can not be relied upon to represent a fault line- EQs are too unpredictable
12
Q
What did Reid note about fault lines and EQs?
A
- Observed a pattern of absolute offsets that could be mapped continuously along the fault; he inferred that this represented the release of elastic stress that had built up on the fault over time, and then ‘rebounded’.
13
Q
Why did Reid observe absolute offsets which represented rebounded stress?
A
- The frictional properties of the earth’s brittle upper crust gives rise to stick-slip behaviour as the sides of the fault are loaded by relative plate motion.
14
Q
What phases are there in the process of fault rebound?
A
1) Interseismic phase
2) Coseismic phase
15
Q
What happens in the Interseismic phase of plate rebounds?
A
1) A farmer builds a wall across a right-lateral strike-sip fault a few years after its last rupture
2) Over the next 150 years, the relative motion between blocks on either side of the locked fault causes the ground and the stone wall to deform.
3) Just before the next rupture, a new fence is built across the already deformed land
16
Q
What happens in the Coseismic phase of plate rebound
A
4) When the stress exceeds the strength of the fault a rupture begins at the first point of failure- the focus- beneath the epicentre on the surface. The rupture expands rapidly across the fault.
5) The rupture displaces the fault, lowering the stress and the elastic rebound restores to their pre-stressed state. Both the fence and the wall have shifted equal amounts. The rebound strengthens the wall, but the fence exhibits a reverse curve.
17
Q
What is the problem with the wall and fence illustration of EQs and fault lines?
A
- Overly simplistic
- Not as simple as made out to be
- EQs are very unpredictable
- We cannot predict EQs
18
Q
What are the complications of fault lines?
A
1) the ‘local rock strength’ is neither constant (in time) nor uniform (in space) along a fault
2) the rate at which stress accumulates in the crust is not constant
3) each EQ affects the stress on other faults nearby
19
Q
What knowledge would we need to be able to predict EQs?
A
- The maximum amount of stress that could be placed on a particular slip-fault.
20
Q
What is a key point to make about EQs and their affect on fault lines?
A
- An EQ may increase or reduce the strain on a fault.
21
Q
What happens in a subduction zone?
A
- The plates move towards each other but the fault remains locked in the Interseismic phase. This causes subsidence of the upper plate close to the fault, and uplift farther inland.
22
Q
What consequence does an EQ have on the fault?
A
- The locked fault slips, releasing seismic energy and reverses the pattern of uplift and subsidence.
- This gives rise to a repeated predictable pattern of uplift and subsidence at any one point near the fault.
- Similar process to that of sea-level change.
23
Q
What are the three phases in the EQ cycle?
A
1) pre-seismic- mostly elastic strain accumulation; no fault movement- can last several hundred years
2) Coseismic- rapid strain release in an EQ (seconds to hours)
3) Post seismic- Relaxation and more rapid strain accumulation but decaying with time (hours to years).
24
Q
What happens to the ground inbetween EQs?
A
- Ground moves up and down
- Pattern of displacement. EQ changes land life but gradually returns to the previous state.
25
What area is affected in the coseimic phase of a small EQ?
- Only a part of the fault moves, so only part of the surface is affected e.g. Nepal EQ
26
What area is affected by the coseismic phase of a large EQ?
- Most of the fault moves, so a much larger area is affected and the uplift is greater (2008 Wenchuan EQ)
- More on magnitude in a bit
27
What is the perio-distic or characteristic EQ model?
- the same size EQ occurs after the same amount of stress has accumulated; thus the EQs occur at a constant interval.
- If we know this interval, we can predict both the time of the next EQ and its magnitude
28
What is the time predictable model?
- The strain required to cause an EQ stays constant but the size of the EQ can vary; after a large EQ it takes longer to reach that threshold strain again.
- Thus the time to the next EQ can be estimated )based on the size of the last one) but not its magnitude.
- Key point is that we still can't predict how large an EQ might be
29
What is the slip-predictable model?
- The strain required to cause an EQ varies but the EQ always releases enough energy to get back to the same state, thus the longer it's been since the last event, the larger the EQ.
- Thus the magnitude of the next EQ can be estimated (based on how long it's been since the last one), but not its timing
- Shows that the longer there hasn't been an EQ, the larger the EQ is likely to be
- Potentially the most useful model
30
What is the clustered model?
- In areas where we have sufficient data, EQs seem to occur in clusters of lots of events, separated by times of relative quiet that may be 10-10000 years long.
- Individual clusters may follow one of the first three models, or may be apparently random
- Essentially a model based on EQ history.
31
What is the best way of assessing the magnitude of an earthquake?
- How much energy is released
| - This is proportional to the seismic moment Mo
32
If the magnitude is increased by +1, how much more energy is released?
- 30 x the amount
33
What is the advantage of a conversion to moment magnitude?
- Allows the comparison of different EQ sizes.
34
Name a famous EQ situation
- Lost River Range, Idaho, USA, 1983 Borah Peak EQ
35
Describe the EQ at Borah peak
- Clear from the pattern of slip that the EQ (which formed a break or scarp up to 2-3m high) that the mountains were uplifted over time by many such events,
- Scarp formed in 1983 and EQ fault is now visible.
- 'Unzipped the ground surface', 2-3mm of slip from one EQ
36
In the simplest of terms, how are mountains built?
- Built by repeated, small earthquakes- a process which occurs over long periods of time
37
Describe the relationship between a fault and a mountain range
- Mountain belts are composed of multiple faults and folds so once it is understood how a single fault grows and accumulates displacement, we can understand the dynamics of the entire range.
38
What is the difference between tectonic rock uplift and surface uplift?
- Tectonic rock uplift is caused by movement on the faults.
- Surface uplift builds mountain ranges.
- This is because we must also allow for erosion or denudation
- Essentially surface uplift takes into account the impact of erosion
39
What is the equation for surface uplift?
Surface uplift= rock uplift- denudation
40
What happens if denudation (erosion) occurs faster than rock uplift?
- There may be negative surface uplift ie the elevation of the mountain may go down even if there is tectonic activity.
41
What is isostatic uplift?
- There's another problem
- The continental crust 'floats' at the surface of the denser mantle and so adding mass to the crust like a mountain range causes the crust to sink.
- Therefore eroding mass from the crust should cause it to rise.
- If we lose surface uplift, we get isostatic uplift where the crust actually rises.
42
What does denudation lead to?
- Additional component of rock uplift, called isostatic rock uplift or isostatic rebound- just as a ship floats higher when its cargo is removed
- This can be 80% of the total denudation so that the net surface lowering is much smaller than you'd expect.
43
What happens if material is moved disproportionately?
- If a Valley was dug out, the parts of the landscape might change while others might stay the same- erosion has a huge impact.
44
What happens to mountain ranges if the erosion if non-uniform?
- Isostatic uplift can actually cause the peaks to rise higher than their original elevation even without any tectonic activity
- Erosion can actually cause surface uplift and build mountains
45
What do mountains balance?
- The tectonic flux of material into a mountain range and the erosion all flux of material out of it.
46
What is the most common form of plate boundary for erosion?
- Convergent plate boundary
47
What is the effect of isostatic uplift on denudation?
- Reduces its impacts.
48
What would happen if there was a collision between two plates where the wind and thus the precipitation fall on the pro side of the mountains- the downgoing plate?
- Would mean that erosion is concentrated on the pro-side and that the material is pulled up from shallows depths
- No erosion on the back side
- But if the wind comes from the back side, erosion would be concentrated on that side.
- This pulls material deep through the Origen to the back side. No erosion on pro-side
- This is the pro graphic exhumation, a model prediction, but it is hard to find evidence for it in the real world.
49
What important things does the topography impact on?
- Influences atmospheric circulation and thus the pattern of precipitation.
- An excellent example of this is in the South Asian monsoon which owes its strength to the Tibetan plateau
50
Describe the Tibetan Plateau in the summer?
- Hot air rises over the Tibetan plateau, forms low; draws in moist air from Arabian Sea/Bay of Bengal, rain in N India.
51
Describe the Tibetan Plateau in winter?
- Cold, dry air over the Tibetan plateau forms high blocks of moist air masses to south. Dry in Northern India.
52
What is one of the ways that we can estimate the importance of mountains in controlling precipitation?
- Comparing global climate model results with and without topography.
- This is a map of the differences between such models- peak differences over SE Asia are 4.8mm/day or 1.5m/year
53
How do glaciers affect erosion?
- Cause very non-uniform patterns of erosion
54
What are the 4 main ways that sediment is removed from mountain ranges?
1) Suspended load
2) Solute load
3) Bed load
4) Aeolian transport
55
What is suspended load?
- Found in rivers:fine particles that are transported to the river flow and slowly settle out in the oceanic water column. Easy to measure
56
What is the solute load?
- Ions and dissolved components
57
What is the bed load?
- Coarse particles that are transported along the river bed. Very hard to measure
58
What is aeolian transport?
Sand, silt, clay, transported by wind
59
What is the sediment load?
- Mass of sediment leaving a catchment per unit
60
What is sediment yield?
- The load divided by the catchment areas.
- Provides a way of comparing the different basin size
- There wouldn't be any meaning in saying that a bigger river has more sediment than a smaller one so we use sediment yield instead.
61
Where do we find the largest sediment loads?
- India-Asia collision
62
Where do we find the largest yields?
- Small, wet, steep places
| - Taiwan, NZ, Papa New Guinea
63
What river has the largest annual sediment load?
- The amazon
64
What happens to sediment load as the drainage area increases?
- Sediment load also increases
| - Millman and Syvitski (1992)
65
What happens to sediment yield as drainage area increases? Why?
- sediment yield decreases
- Elevation has a significant impact on mountains
- Mountain rivers have high yields for a given runoff, and they carry high ratios of suspended (silt-clay) to solute (dissolved ions) loads.
66
Why is it useful to know what the suspended sediment load from a drainage basin is likely to be?
Tells us:
- Rates of erosion in the catchment
- Rates of sediment transfer
- Baseline for understanding effects of climate change
- Baseline for understanding anthropogenic effects.
67
Besides elevation, what other factors are likely to be important in setting the suspended sediment load?
- Topography
- Lithology (rock type)
- Geology (different erosion rates)
- Precipitation, temperature
- Vegetation
- Anthropogenic e.g. agriculture
68
What could we look for to learn more about tectonics and in this case deltas?
- Volume- how much sediment produced?
- Lithology- what are the grains made of?
- Sediment discharge over time/via stratification
- Size- indicates transport distance
- Other constituents e.g. organic matter
- Determine age and isotopic condition
69
What do offshore records show?
- How much? Mass shows fluxes
- What kind? Transport processes
- From where? Provenance
70
Describe Cenozoic mass accumulation around the India-Asia Collison
- Cenozoic era started 65 million years ago.
- Deepest sediment accumulations close to the land but large area of sediment accumulation in the gap between India and Indonesia.
71
Describe some key points about sediment accumulation
- It takes a long time for accumulation rates to begin.
- Very gradual process
- India-Asian collision began 50 million years ago.
- There is only an increase in accumulation rates over a long period of time.
72
Describe some confusion regarding the India-Asia collision?
- Wasn't just a simple increase throughout the Cenozoic.
- Onset of rapid accumulation doesn't seem to coincide with India-Asia collision at 50Ma
- Glacial rates of last 2-3 million years are not always higher than mid- Cenozoic rates.
73
Describe some important controls on sediment flux?
- Large-scale tectonics and climatic shifts are not the only important controls on sediment flux- rivers can be diverted or captured during mountain building and this leaves a record in deep-sea sediments.
- Best evidence is found offshore.
- Sediment from rivers often ends up in the sea.
74
What did Clift et al (2005) use differences in neodymium isotope ratios to show?
- Show that sediment from the Himalayas became more important in the Indus fan after about 5 million years.
- This coincided with a drop in the sedimentation rate by a factor of 2.
- Different rocks have very different identities- like a human fingerprint
- We can learn a lot from this about provenance and age.
75
describe the history of Mexico's drainage basin
- Relatively low accumulation rates before 60 million years ago.
- Suggestion that the drainage basin in the gulf of Mexico was expanded which allowed greater accumulation.
76
What is a good example of large-scale drainage diversion?
- The 'Three Rivers' area of south-eastern Tibet
- Home to the famous Tiger Leaping Gorge.
- Sediment from the mouth of the red river show that until about 40 million years ago, it carried a lot of Yangtze Craton rocks
- Clift et al (2006)
77
What can we infer from the load change of the Red river?
- Until about 40 million years ago, most of eastern Tibet drained through what is now the Red river.
- The other rivers were progressively captured and diverted, so that the modern Red River is relatively small.
- This is an enormous change in the river system.
78
Describe river system changes at the three gorges?
- Yangtze river cuts through 3000m high mountains.
- If model of capture is correct, we should see evidence that the river grew in size and that the rocks were gradually eroded (and thus cooled) more rapidly, starting about 40 million years ago.
- If we knew when the gorge was created, we could then establish when the river was established also.
- When did the rock begin to cool?
79
What actually happened at the three gorges?
- Three gorges began to be cut about 40 million years ago, as the Yangtze river reversed itself and began to flow to the east rather than towards the southwest.
- Shows that even large river systems are transient things and can be diverted, blocked or captured.
- This changes the pathways by which sediment and nutrients are delivered to the sea, and can change the distributions of plants and animals e.g. fish
- There's a fundamental shift in where sediment goes and by extension where everything in sediment goes.
80
What do offshore records do?
- Preserve info on past sediment fuxes and sediment sources and can be used to reconstruct mountain belts through time.
- Sediment volumes, type and composition or provenance all tell us different parts of the puzzle.
81
What is important to remember about mountains, river and the earth?
- NOT STATIC
| - The earth is dynamic and constantly changing albeit very slowly!!
82
What is one way of studying sediment routing systems?
- Looking at model landscapes- a 'mountain in a box'
- These models try and show how we get mountain topography.
- Good because it is a completely controllable setting
- Can test different variables
83
What are model landscapes particularly good for?
- Such experiments are good for showing us the effects of varying different parameters
- For example, increasing the rate of rock uplift leads to steeper, higher , rougher topography
84
What can we do at the most basic levels in terms of landscape and topography?
- Divide the landscape into channels which concentrate flow
- Hillslopes can be considered everything else.
- Each one of these is dominated by a particular set of geomorphic processes.
85
What are the characteristics of a hillslope?
- Have low upslope contributing areas and a range of gradients (flat to steep)
86
What are the characteristics of a channel?
- Start at a given contributing area
| - Gradients decrease downstream
87
What distinguishes channels and hillslopes?
- Their gradient and their upstream area.
88
What is the longitudinal profile?
- Shows the long profile of a river, following a drop of water from the drainage divide to the river mouth.
- The profile can be plotted visually to make the data easier to analyse
89
What happens to the longitudinal profile at the hillslopes?
- On the hillslope above the headwaters and in the headwaters, the elevation drops.
- The profile is a high and nearly uniform slope
90
What happens to the river profile at the river channel?
- In the river channel downstream, the elevation drops much more gradually
- River channel is always low and decreasing slope
91
Give an example of a very geomorphically active area?
- A typical mountain sediment routing system: the Illgraben, Switzerland
- Hillslopes: sediment production and diffusion sediment transport
- Channels: debris flows
92
What controls hillslope evolution?
- The thickness of the soil and the rate at which it is produced by weathering of bedrock. This typically happens at 10s to 100s of microns per year
- Bottom layers continuously weathered to produce the soil layer
- Removable material controls hillslope evolution
- Millions of years process.
93
What happens when soil production is rapid?
- The landscape is covered or 'mantled' by soil, giving rise to smooth, rounded hillslopes. Here the rate of transport is dependent only on the slope and happens grain-by-grain-termed diffusion sediment transport.
- Smooth rounded hillslopes characteristic of areas with lots of sediment e.g. Durham
94
In areas with lots of sediment, how is sediment controlled?
- Controlled or at least meditated by biogenic processes.
- Macrobiology matters to the landscape
- Biology controls how rapidly bedrock is weathered and how much sediment is around e.g. Animals and plants
95
What happens as hillslopes get steeper?
- Loose sediment is transported in discrete shallow landslides rather than grain by grain- this produces hillslopes that are much more planar.
- Steeper hillslopes mean that more sediment is transported.
96
What are shallow landslides efficient at?
- Efficient at removing material from a hillslope, the transport rate (or sediment flux in the diagram) increases very quickly with increasing hillslope gradient (curved line).
- Landslides are much more efficient for transportation than grain by grain.
- Is more variable depending on whether a landslide has occurred or not.
97
What does a shallow landslide require?
- A loose layer of soil at the surface
98
What happens in a shallow landslide?
- If the soil is removed by land sliding faster than it is produced, then the regolith will be stripped and we'll be left with a bedrock hillslope with a thin or discontinuous regolith cover.
- This is definitely not a smooth rounded landscape.
- This is the rule in most mountain landscapes; soil-mantled, high-relief landscapes are very rare.
- In places like Sawrnill Canyon, Sierra Nevada, US a whole piece of bedrock would need to break off for transportation to take place.
99
How do bedrock slopes evolve?
- Via deep seated or bedrock landslides.
- These typically cover a wider range of scales than shallow landslides
- This again produces planar (rather than rounded) hillslopes
- Stronger relief or less landsliding means higher relief and steeper gradients.
100
What happens to the channel if sediment is not transported?
- If it can't be transported, then the bed builds up and the channel aggrades
101
What are debris flows?
- Common in steep channels where slopes are more than 10%
- Particularly in mountainous regions
- They are mixtures of sediment and water that behave as a slurry or semisolid mass, rather than as a simple fluid.
- The sediment may be made up of fine particles or large boulders
- These are distinct events which require a lot of material.
102
What impact can we think of debris flows having?
- They hand off sediment from hillslopes to larger channels.
- As you move lower into the landscape, debris flows become more important and eventually give way to rivers.
103
What is the big picture role of debris flows?
- Provide a key, efficient connection in the sediment routing system- without debris flows, sediment would be trapped on hillslopes (until the next landslide) instead of rapidly delivered to the channel network.
104
What are fluvial channels?
- Transport sediment and incise bedrock through the action of flowing water- they are the final component of our system, and the final downstream link between source and sink
105
What is a key distinction between sediment in hillslopes and in channels?
- Channels are more efficient at conveying both water and sediment.
106
What do geomorphic processes in the channel network depend on?
- The gradient of the river
- The distance from the divide
- the presence or absence of sediment
- nature of the substrate
107
What do the long profiles of the majority of mountain rivers show going downstream?
1) Decreasing slope
2) Decreasing exposure of bedrock
3) Increasing sediment cover
4) Decreasing grain size
108
Describe shaping processes in Death Valley?
1) Landslides
2) Debris flow
3) Braided river channel/ fluvial sediment
4) Erosion- grain by grain/diffusive sediment
5) Aeclion
109
What does the term uniformitarianism mean?
- means that the knowledge of the present is key to understanding the past
- This grew from the geological observations of James Hutton but was only popularised by Charles Lyell in 1830
110
Is uniformitarianism the only way of looking at earth's processes?
- We know that some large events for which there is no historical data have had a profound impact on the evolution of the earth system
1) Formation of the moon
2) Impacts and mass extinctions
3) Super volcanoes and plateau basalt eruptions
111
What alternative term could we use rather than uniformitarianism?
- neocatastrophism
112
How can we understand the role of catastrophic events in the Earth system?
- Knowledge about distribution of events in terms of their size and frequency
- Their effectiveness or ability to cause a change in the system
113
How can we describe geographic events?
1) Magnitude
| 2) Frequency
114
What is the relationship between small and large scale events?
- Small scale events occur more frequently with minimal impact
- Large events occur less frequently but can change the form of the landscape.
115
Describe the 2004 Sumatra EQs
- 26th December. M= 9.3 (second largest EQ ever recorded)
- 28th March. M= 8.7
- Length of EQ rupture the distance from the Baltic to Sicily
116
What does the US national EQ Information Centre say about EQ magnitudes and frequencies?
- Average number of EQs above magnitude 8 since 1990 is one.
- Between 7-7.9 is 17
- Between 6-6.9 is 134
- And so on
117
How many magnitude 8 or higher earthquakes were there in 2017?
- Only one
- Only 100 people died
- Central America
118
What does Beroza (2012) say about EQ patterns?
- Describes the problem of the short historical record of EQs and the difficulty of spotting patterns after the fact.
- A major issue is cherry picking- making up rules after the fact.
- If we choose large EQs as thos with magnitudes greater than 8.5, there seems to be some sort of evidence of clustering
119
What happens to EQ patterns if we set the threshold for a large EQ at 7 rather than 8?
- Previous evidence disappears
- 2010 Haiti EQ had a magnitude of 7 so its not as if only the largest EQs are deadly.
- Occurence of large EQs instead seems to be largely random; what matters is how we are exposed to their effects.
- If we can quantify the frequency of EQs, we can estimate the probability of an EQ occurring.
120
What problems appear if we try to plot the frequency of EQs in the last 9 years?
1) The number of small events is under-predicted because they're too hard to hear and locate- more than 40,000 EQs between 2-2.9 magnitude.
2) The number falls off with increasing magnitude, so that magnitudes 6-8 are indistinguishable.
121
How can we resolve the problem that the number falls off with increasing magnitude?
- Plot the number of earthquakes on a logarithmic scale
| - This expands/contracts the vertical scale so that we can see all the data on a single graph.
122
What is interesting about what happens if we plot EQs on a logarithmic scale?
- Seem to decrease with increasing magnitude, following a straight line.
- If we remember the equation of a line (y = n+mx) we can write this as logN=a-bM
- Where M= magnitude, N= number of EQs and a and b are constants.
123
What is the relationship between EQ frequency and magnitude on a logarithmic graph called?
- The Gutenberg-Richter law (same Richter)
- Has been known since the mid 20th century
- Can be defined for global, regional or even local data sets and tells you the number of earthquakes of a given size
- B always has the same value but a has different ones, despite differences in time
- The b value is the best fitting line
124
How can we use the Gutenberg-Richter law?
- Tells us how many earthquakes have occurred of a given magnitude in a specific time period, they can be expressed as the frequency of those earthquakes.
- So how often might we expect a magnitude 7 earthquake for example. World: About 1 every 18 days. Southern California: About 1 every decade
125
What is Peak ground acceleration? (PGA
- The maximum shaking in an WQ as a function of Earth's gravity g
126
What is the frequency of exceedance?-
- How often an event of at least that size is expected to occur
127
What is important to observe about different regions in relation to prediction?
- Even different parts of the same fault can show straight lines on diagrams which have different slopes or different b values.
- This is important because it tells us the relative numbers and thus importance of big vs small events
128
What does a small b value signify?
- Larger average size and proportionately more large events
129
What does a large b value signify?
- Smaller average size and proportionately more small events
130
How are b values now being used?
- In order to calculate daily earthquake probabilities- work out likelihood of ground shaking with intensity
- Possible to predict likelihood of EQ occurrence and of probability of shaking.
131
What is the bigger picture of the Gutenberg- Richter law?
- Law belongs to a much larger family of distributions of event size than just EQs
- Together we can call these 'power-law' distributions and they are everywhere.
- Earthquakes, area of forest fires, size of orbiting debris, amount of storm rainfall, volcanic eruption volumes, financial returns, health care costs, war size and intensity, movie revenue, word frequency etc
132
Why does the Gutenberg- Richter law occur?
- Lots of debate about why it happens and why it's so common.
- Seems to characterise systems which are incremental and tightly connected so that information moves through lots of different links (and can be changed or corrupted en route.
133
How can we think of the effect of the Gutenberg-Richter law
- Can think of fault areas this way
- If there is a slip or an EQ in one area, then other faults will also be affected.
- Works in a spiral.
134
What happens in sandpile systems?
1) Behaviour is defined by the movement of individual grains
2) The result is 'greater than the sum of the parts'
3) Simple inputs lead to complex behaviour.
135
What is important about power law distributions?
- They are very common in event magnitudes
| - They are telling us something about the lily hood of very large events.
136
What are underlying distributions?
- Mathematical way of describing the variation in something
| - e.g. Height, exam scores, house prices etc
137
What is the most familiar underlying distribution?
- The normal or Gaussian distribution
138
What properties define the Gaussian distribution?
1) Has a well-defined mean
2) Spread is called the standard deviation
3) Express value in terms of how many standard deviations it is from the mean.
139
Describe the figures within standard variation?
- 68% of the measurements fall within 1 standard deviation of the mean
- 95% fall within 2 standard deviations
- 99.7% fall within 3 standard deviations
140
How does standard deviations relate to the power laws?
- They don't follow the normal distribution
- They are an example of a heavy-tailed distribution where the chances of a very large (or very small) event are much greater than with a normal distribution even if the mean event is the same size.
- On the right hand side of a graph we can see in the overlapping area the chances of a rare but much bigger than average event.
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How can we express the value in relation to power laws?-
- In terms of how many standard deviations from the mean it is- regardless of what these figures are.
- Normal distributions are common and useful - they describe things like measurement errors very well.
- There is a very low chance of something happening that is more than 3-4 standard deviations from the mean in size- ie very large or very small.
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What is important to note about graph patterns?
- Patterns may look very different but may still have the same mean just with different distributions.
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How can we make the differences in graph patterns more clear?
- Rescale the axis to show the size of all the events
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What does a blue colour stand for in graphs?
- Pareto or 'heavy-tailed' distribution
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What does a red colour stand for in graphs?
- Normal or 'light-tailed' distribution
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What does a Pareto or heavy-tailed distribution suggest?
- Most events are very small, but there are some events that are very large.
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What should the distribution of events be?
- We don't actually know what I should be.
| - We can only draw conclusions from past data.
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What are some examples of financial instruments that underpin normal distributions?
- The VIX votality Index (expected range of movement in the S &P 500 stock price index over the next year, at a 68% confidence level
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To understand the role of catastrophic events in the Earth system?
1) the distribution of events, in terms of their size and frequency
2) Their effectiveness or ability to cause change to the system
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How can we calculate geomorphic effectiveness?
- effectiveness (change/year) = frequency (events/years) x amount of change (change/event)
- Wolman and Miller (1960)
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How does water get through vegetation?
- Quite difficult to get through and erode the surface.
- vegetation imposes a threshold that the flowing water must overcome in order to erode the ground surface and remove sediment
