EARTHQUAKES AND SEISMOLOGY
An earthquake is a naturally produced shock event which causes the Earth to vibrate.
Of interest are:
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their effect
why they occur
where they occur
scientific study of the Earth's interior and dynamics:
the structure of the Earth,
composition of the Earth
kinematics and dynamic of plate tectonics.
How many Earthquakes?
EQs (earthquakes) are very common, many thousands per day all over the world., e.g. map for 22-29th Oct 2003:
Most are weak (low energy) and undetected. Here are those with Mag > 2.5 (see later for definition) for the past
week:
Update time = Wed Oct 29 12:00:04 UTC 2003
MAG DATE UTC-TIME LAT LON
y/m/d h:m:s
deg deg km
DEPTH
region
map 2.8 2003/10/29 11:21:33 61.650 -150.210 45.0 SOUTHERN ALASKA
map 2.8 2003/10/29 10:19:08 63.087 -144.253 5.0 CENTRAL ALASKA
map 3.5 2003/10/29 07:25:52 57.460 -143.110 1.0 GULF OF ALASKA
map 3.1 2003/10/29 07:18:29 34.659 -116.295 1.6 SOUTHERN CALIFORNIA
map 2.5 2003/10/29 03:34:52 62.972 -152.859 180.0 CENTRAL ALASKA
map 2.9 2003/10/29 02:54:35 63.585 -147.866 1.0 CENTRAL ALASKA…….
…………………………………………………
map 3.5 2003/10/22 19:23:16 51.479 -176.185 23.7 ANDREANOF ISLANDS, ALEUTIAN IS., ALASKA
map 3.0 2003/10/22 17:57:27 51.223 -178.156 14.4 ANDREANOF ISLANDS, ALEUTIAN IS., ALASKA
Large Earthquakes
Large energy EQs are rare but cause wide scale social disruption.
July 1976 Tangshan, China 650,000 fatalities
May 1970 Lima, Peru 66,000 fatalities
May 1927 Nan-Shan, China 200,000 fatalities
Sept. 1923 Tokyo, Japan 143,000 fatalities
Largest Recorded Earthquake
Chile 1960 May 22 19:11:14 UTC, Magnitude 9.5
More than 2,000 killed, 3,000 injured, 2,000,000 homeless, and $550 million damage in southern
Chile;
Tsunami caused 61 deaths, $75 million damage in Hawaii;
138 deaths and $50 million damage in Japan;
32 dead and missing in the Phillippines; and
$500,000 damage to the west coast of the United States.
Why Earthquakes?
EQs result from sudden displacement of crust, usually along faults.
Often come in a series of quakes - "minor" aftershocks common.
The earth rings like a bell after a large earthquake occurs.
Very long wavelength surface waves circle the globe and interfere constructively to set up harmonic
oscillations.
The shape of an oscillation is determined by the wavelength of the waves, and the frequency of the oscillation
by the internal velocity structure.
Analyzed by spherical harmonics….
Shocks give rise to landslips, turbidity currents,…..
….and tsunamis:
Discuss:
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earthquake cause and mechanism
earthquake locations and distribution
earthquake size: magnitude and intensity
seismic waves and the interior of the earth
seismotectonics
earthquake prediction and control
MEASUREMENT OF SEISMIC WAVES
Earthquake waves recorded on a SEISMOMETER -> SEISMOGRAM.
Seismometer originally consisted of a rigid frame attached to the Earth, a chart recorder attached to frame, a
heavy mass suspended from frame by a pivot and a pen attached to mass.
Modern ones digitised, etc.
When frame is shaken by quake, the mass and pen remain stationary. The scale of the displacement is recorded
on chart.
Mass is stationary because of inertia.
Pivot restricts recording to just one plane.
Need 3 seismometers to measure EQ.
One for vertical movements and 2 for horizontal movements.
Often have more seismometers with different masses to record shocks with different frequencies - seismic
vibrations have spectrum of frequencies.
Typically record waves with short-periods - 12s,
and long-periods - 20s.
EARTHQUAKE CAUSES AND MECHANISMS
Major EQs occur at plate boundaries - infer that cause of EQs is relative motion of sections of the lithosphere.
Explanation of EQs is the ELASTIC REBOUND THEORY, put forward by H. F. Reid in 1906 after San
Francisco EQ.
EQ derives from FAULT, that separate two blocks which are attempting to move relative to each
other.
Friction or cementing will resist the movement.
Under these conditions crustal stresses do not move blocks, but a state of STRAIN builds up in the region of
the fault.
If crustal stresses increase (because of movement elsewhere on fault, etc.) will reach a level where they
overcome frictional restraint, and the two blocks will slip relative to each other -> EQ.
This process can occur time after time, so called stick-slip movement.
Time between movements can be years.
The longer the time, the larger the stress and strain, the larger the EQ.
There are three main types of fault movement, each give distinctive EQ patterns (see below):
normal fault
thrust fault
strike-slip fault
EARTHQUAKE LOCATION AND DISTRIBUTION
see http://vcourseware2.calstatela.edu/eec/Earthquake/
FOCUS- The source - a small part of a fault (approx. a few
kms3) - can be regarded as a point .
EPICENTRE - The point on the surface, vertically above the
focus.
FOCAL DEPTH - The distance from the epicenter to the
focus.
Shock waves radiate out from focus in all directions.
They are first felt at the surface at the epicentre.
Location of epicentreIf we have seismographs from 3 stations relatively close to the epicentre, we can deduce the position
of the epicentre by the time intervals between the P and the S waves at each station - given a
knowledge of P and S wave velocities.
If local P and S near-surface velocities are Vp and Vs and the station is X km from epicentre, then
Time for P wave arrival (tp) = X / Vp
Time for S wave arrival (ts) = X / Vs
Therefore interval between P and S arrival
Δt = ts-tp = X / Vs - X / Vp
Thus re-arranging to find X gives
X = Vs.Vp.(Ts-Tp) / (Vp - Vs)
Units - Vp,s in kms-1; Δt in s; X in km
To locate epicentre need values of X from THREE stations -> Triangulation.
Epicentre at intersection of 3 circles of radii X1, X2 and X3
based at stations 1, 2 and 3.
World-wide have approx. 1000 stations.
Often arranged as SEISMIC ARRAYS in well defined geometrical
distribution.
Can use arrays to give near-surface data and information about deeper structure of Earth.
Depth of focus (h) can also be deduced, but needs a more refined approach.
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First, need to determine epicentral angle – Δ
This is done from travel time curve, as ts-tp is a simple function of Δ:
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Then, a plot of ts-tp v. tp for several stations give t0, the time the earthquake occurred.
Then, if V is the P-wave velocity, distance of detector (D) to focus is:
D = (tp-t0)V
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Now can obtain h, since:
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X = R . Δ . (2π/360) and so:
h ~ √(D2 – X2)
Global Distrubition
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All earthquakes occur at depths < 700 km and are confined to the rigid lithosphere.
Have 3 classifications of EQs -
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Shallow focus 0-70 km
Intermediate focus 70-300 km
Deep focus 300-700 km
With large Earthquakes (magnitude > 7 ):
o 75% Shallow,
o 90% Intermediate ,
o Approx. 100% Deep occur around the
margins of the Pacific
Those not in circum-Pacific belt occur in AlpineHimalayan belt.
Deep Earthquakes largely from subducted slabs:
Also high concentration of shallow Earthquakes
(mag. 4-6) along ocean ridge system.
Intra-plate Earthquakes are rarer (but do occur, e.g.
Lisbon 1755).
Shallow Earthquakes much more common than
Intermediate and Deep.
Most surface damage is caused by Shallow
Earthquakes.
EARTHQUAKE SIZE : MAGNITUDE AND INTENSITY
Earthquake magnitude is an "ABSOLUTE" measure of size, and is related to the energy released.
Determined from seismic wave amplitude.
C.f. Earthquake intensity refers to amount of damage caused – more subjective.
Magnitude
Magnitude, given by general equation:M = log10 A/T + 
M = magnitude
log - base 10
A = max. amplitude of wave in µm (= 10-6m)
T = period of wave, (P or S) in secs. (time taken for one wavelength to pass a fixed point)
= factor correcting for epicentral distance, focal depth and type of wave. These can be read from
published tables. However, since  needs to be obtained from observation the "absolute" measure of
Earthquake magnitude is still subject of debate. Error in magnitude should be < ± 0.3.
Recall, epicentral distance from the point of measurement to the epicentre is measured by the angle subtended
by these 2 points at the centre of the Earth - the epicentre angle ().
Magnitude scale is Logarithmic, therefore M = 7.0 is 100 times larger than M = 5.0
There are many definitions of magnitude, depending on what is being measured:
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Richter was amongst first to develop a scale for earthquakes in 1935 based on P-wave amplitudes.
An earthquake's Richter magnitude was originally defined to be the amplitude of shaking on a WoodAnderson seismometer of an earthquake 100km away. Since there are very few working WoodAnderson seismometers around these days, scientists approximate the magnitude using calibration
scales based on the distance from the source and the amplitude of seismic waves.
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The Richter local magnitude is given by:
MR = log10(A/T) + g(d,h) + a
o
o
o
o
o
o
o
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where M is the magnitude
A is the maximum wave amplitude
T is the wave period
g is a function that corrects for the decrease in wave amplitude(A)
d is the angular distance from seismometer to epicenter
h is the focal depth of the earthquake
and (a) is an empirical constant
BODY-WAVE magnitude - At large distances from epicentre use body-wave amplitude (usually Pwave), because body-wave attenuation is less than surface-waves.
MB = log10 (A/T) + 0.01 + 5.9
where T approx. 12 secs.
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The surface wave magnitude is given by
MS = log10 (A/T) + 1.66 log10  + 3.3
o
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o
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where T is between 17 and 23 seconds
d is between 20 degrees and 160 degrees
and h (depth of focus) is less than 50 km
For extremely deep earthquakes the magnitude must be corrected to compensate for the increased
distance due to depth. This correction is:
M corr = MS + bMS(h)
b comes from a table.
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The seismic moment is given by
MO = G.A.
o
o
o
where G is the rigidity
A is the surface area of the fault
and  is the average fault displacement
and the moment magnitude is given by
MM = 0.666log10MO - 6
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The moment magnitude depends on the surface wave magnitude:
log10MO = 1.5MS + 16.1
Largest Earthquakes in the World Since 1900
Date
Location
Mag
Coordinates
1. Chile
1960 05 22
9.5
38.26 S
2. Prince William Sound, Alaska
1964 03 28
9.2
61.02 N 147.65 W
3. Andreanof Islands, Aleutian Islands 1957 03 09
9.1
51.57 N 175.34 W
4. Kamchatka
1952 11 04
9.0
52.75 N 159.50 E
5. Off the Coast of Ecuador
1906 01 31
8.8
6. Rat Islands, Aleutian Islands
1965 02 04
8.7
7. India-China Border
1950 08 15
8.6
1.0 N
72.15 W
81.5 W
51.23 N 178.52 E
28.5 N
96.5 E
8. Kamchatka
1923 02 03
8.5
54.0 N
161.0 E
9. Banda Sea, Indonesia
1938 02 01
8.5
5.25 S
130.5 E
1963 10 13
8.5
44.9 N
149.6 E
10. Kuril Islands
Energy and Magnitude
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The energy released by an earthquake (E in Joules) is related to magnitude.
An empirical relation between ENERGY and MAGNITUDE is given by:
Log10 E = 1.5Ms + 4.8
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An increase in magnitude by 1.0 units in Ms gives approx. x 30 increase in energy.
Estimated annual energy loss via Earthquakes is 1018 J.
Most of this comes from the few quakes with Ms = 7 or 8.
Energy of Earthquake is turned largely into heat via friction of vibrating rock particles, etc.
Total contribution of Earthquake to heat loss is small.
Total Earth heat flow approx. 1021 J per y. Total U.S.A. energy consumption approx. 10 19 Jy-1!
Intensity
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The intensity of an earthquake is based on its effects at the surface.
For a given location intensity is reported as Roman Numerals according to the modified Mercalli
Scale:
INTENSITY ----DESCRIPTION
I----Not Felt.
II----Felt by persons at rest on uppper floors.
III----Felt indoors---hanging objects swing. Vibration like passing of
light trucks.
IV----Vibration like passing of heavy trucks. Standing automobile rock.
Windows, dishes, and doors rattle; wooden walls or frame may creak.
V----Felt outdoors. Sleepers wakened. Liquids disturbed, some spilled;
small objects may be moved or upset; doors swing; shutters and pictures
move.
VI----Felt by all; many frightened. People walk unsteadily; windows and
dishes broken; objects knocked off shelves, pictures off walls. Furniture
moved or overturned; weak plaster cracked. Small bells ring. Trees and
bushes shaken.
VII----Difficult to stand. Furniture broken. Damage to weak materials,
such as adobe; some cracking of ordinary masonry. Fall of plaster, loose
bricks, and tile. Waves on ponds; water muddy; small slides along sand or
gravel banks. Large bells ring.
VIII----Steering automobiles affected. Damage to and partial collapse of
ordinary masonry. Fall of chimneys, towers. Frame houses moved on
foundations if not bolted down. Changes in flow of springs and wells.
IX----General panic. Frame structure shiffted off foundations if not
bolted down; frames cracked. Serious damage even to partially reinforced
masonry. Underground pipes broken; reserviors damaged. Conspicuous cracks
in ground.
X----Most masonry and frame structure destoryed with their foundations.
Serious damage to dams and dikes; large landslides. Rails bent slightly.
XI----Rails bent greatly. Underground pipelines out of service.
XII----Damage nearly total. Large rock masses shifted; objects thrown into
the air.
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Factors that tend to increase intensity:
o magnitude of Earthquake
o distance to focus
o
substrate
SEISMOTECTONICS
Earthquake Focal Mechanisms
o
o
In any given direction P waves radiate from focus as compression or dilatation. The pattern of initial
motion (first motion) characterizes the nature of the fault motion that produced the EQ (normal,
reverse, strike-slip)
Thus of a strike slip fault:
Can define the fault plane from the plane normal to fault (the auxiliary plane)
o
The first shock reveals a good deal about the nature of the fault. Depending on whether a particular
area is compressed or extended by movement along the fault, the first motion p-wave will be
upwards (positive) or downwards (negative), respectively.
o
The pattern of first motions obtained from a number of seismic stations can be summarized on a
stereogram, depicting quadrants of compression and dilation.
o
o
o
On a stereonet there are two planes, drawn along great circles, separating the compressional (positive)
p-waves from the extensional (negative) p-waves.
These planes are known as nodal planes.
From this can infer nature of faulting - FOCAL MECHANISM SOLUTIONS (black- compression,
white- dilatation).
o
o
o
Note: the observed pattern of arrivals does not uniquely determine the orientation of the fault.
From P waves alone cannot tell fault plane from auxiliary plane:
If the source is a single- couple one, can tell from S-waves distribution:
o
But if movement on the fault is complex (“double couple”), then the solution is still ambiguous:
o
To determine the correct plane, the locations of aftershocks and/or surface geology and regional
tectonics may be necessary.
Mixed Faults
It is very unusual to find a pure strike-slip, normal or thrust fault in nature. Most faults consist mainly of one
motion with a small component of another. Pure strike-slip faults have first motion diagrams with nodal planes
that intersect in the center of the stereonet (as pictured above). Strike-slip faults that have some component of
thrust or normal faulting intersect off-center.
This is either a left-lateral or right-lateral strike slip fault with a component of thrust
faulting. The nodal planes for pure normal faults and pure thrust faults intersect along the
primitive circle (as pictured previously). Strike-slip faults can have components of either
normal or thrust faulting, but normal and thrust faults can only have components of
strike-slip faulting. Here's the first motion patterns of an oblique normal fault and an
oblique thrust fault with a small component of strike slip motion.
Oblique
thrust
The first motion pattern for thrust faulting with a small component of left lateral
strike-slip motion would look the same (except the compression and extension circles
would be reversed).
Oblique
normal
Earthquakes and Plate Tectonics
Different earthquakes are characteristic of different tectonic setting.
Revealed by study of focal mechanisms.
Divergent boundaries - shallow focus EQ's, normal and strike slip faults along mid-ocean ridge:
Convergent bounday- EQ at all depths, all magnitudes. Extentional or Compressional depending on position:
o
o
Thrust faults in upper part of subducting slab,
normal faults at depth
Continental collision zones show only shallow and intermediate depth EQ.
EARTHQUAKE PREDICTION
Social impact of EQ in regions of high pop. are obvious.
If we could predict when EQ will occur, could reduce effect of quake on death toll, etc.
U.S.A., Japan and China have large programmes.
Tokyo and Peking are "at risk" cities.
Current results in prediction are poor - still need more data on EQ processes.
Prediction at several levels
(1)
Most large EQs will occur at plate boundaries.
If no one lived in these regions, EQs would not be socially v. important. But since people
will not move, how and when will these large, plate boundary quakes occur?
(2) Earthquakes often occur in cycles.
Predict that there will be a large EQ in San Francisco again.
But when - within 200 years - 100% prob.; 50 years - 50% prob.; 5 years ?
(3)
To be socially useful need to be PRECISE as to time and place.
To make progress need to understand:
EARTHQUAKE PRECURSORS.
Geodetic Measurements
Prior to an EQ, does the Earth bulges due to build up of strain, etc.?
These could be detected by geodetic measurements - study of land shape, tilt and position -> periodic
survey :
and GPS monitoring (but need high precision):
Studies in Japan, U.S.S.R. and elsewhere, show that there are changes of height, etc. in regions which
subsequently suffer from EQs. Also water levels in wells change:
Studies show upwelling and downwelling before EQ. However, the time scale can be in 10's of years.
Cannot easily predict when it will happen.
Tide-gauges can also be useful. Large retreats of sea can occur before large submarine EQ. In 1872 shock in
Japan sea went out over 200 m, 20 mins. before shock.
Tide gauge data:
Continuous observation of land level - Tiltmeters (c.f. surveys) e.g. water filled tube 30-40 m. in length.
Find that increase in rate of ground tilting occurs during immediate pre-earthquake period.
Tilting produced by change in volume of rocks during deformation.
As shear rock, open up cracks - dilation - which increases volume.
Big EQ occurs when cracks join up to give large fracture.
Now can use SAR to see land deformation after Earthquake (and bulging before):
7.1 magnitude Hector Mine earthquake of October 16, 1999 40 km
northwest of Barstow, California (edge of Mojave Desert).
Seismic Activity
In seismically active regions, the distribution of seismic activity can give clues as to where large EQs may
occur.
Along San Andreas have areas with lots of small earthquakes (microearthquakes Ms approx. 1 to 3).
These are continuously releasing the strain in rocks and it is unlikely that a large EQ will happen in these
sections.
Some areas are "LOCKED" and show no microseismic behaviour. Expect large build-up of strain in these
Locked Sections.
This will be where the big EQs occur –
e.g. Loma Prieta Earthquake of 17th Oct 1989:
Earthquake filled the gap:
Major damage where the shockwaves where in soft mud – high amplitude:
Still a gap in San Fransico Area – when will it happen?
Changes in SEISMIC WAVE VELOCITY may give the answer.
When rocks deformed get changes in Vp and Vs.
Find Vp/Vs during stress build up.
Have normal Vp/Vs (often approx. 1.7), which drops prior to EQ, then shows rapid increase to
original value of even greater prior to EQ.
Reason:- As stress builds up, get cracks formed.
Air-filled cracks show seismic waves (P affected more than S, since effective bulk modulus
reduced).
When cracks nearly all joined up, water can flow in.
Water replaces air (or vacuum) and increases bulk modulus (water more incompressible than air), but
not shear modulus, therefore Vp/Vs increases.
Water in cracks weakens rock so it now fails, and EQ occurs (stress corrosion, lubrication, etc.).
Theory supported by experiments on rocks. Looks promising a way of predicting EQ.
But ....
The "Dilatancy Cycle" takes longer in areas where rocks are strong - i.e. in areas where EQs are
likely to be of high energy.
The time interval between Vp/Vs drop and the occurrence of EQ increases with increasing
magnitude of quake.
The larger the quake, the longer the warning time - good!
The less precise the estimate of occurrence of quake - bad!
If Ms > 6, Vp/Vs anomaly occurs approx. 3 years before quake!
Other Techniques
Magnetic and electrical effects:
Low frequency magnetic signals recorded for 31 days around the 1989
Due to enhanced water connectivity and so electrical conduction.
Also have strain on quartz in rock that may set up piezoelectric field.
Friction might give heating and enhanced IR immision:
Noble gas escape due to cracking:
Location and radon variations of 6 springs in the vicinity of
a M=2.4 earthquake a few km west of the Abant Lake end of 1990.
Shown are changes relative to 1988.
animals go mad, etc.
State of Art
Still hit and miss, but this is the general sequence:
Elastic strain builds up along a fault due to plate movement:
Stage
All parameters are at their normal state.
I
No uplift, radon increase, etc.
Cracks begin to develop in crustal rocks in the pre-quake area.
The buildup begins to be visible as an uplift of the area.
Stage The cracked rocks do not propogate P-waves as easily and their velocity slows in the area.
II
Radon gas can escape through the newly formed cracks, and electrical resitivity decreases.
The newly forming cracks and increasing stress may also result in a tiny increase in local
seismicity.
Groundwater from surrounding areas can now flow into the new cracks.
Stage Because the cracks are now filled again, the P-wave velocity can increase back to normal.
III
The ground's uplifing also ceases and radon gas emission decreases.
Electrical resistivity is still decreasing.
Stage
IV
THE EARTHQUAKE
But….
If we could predict an major earthquake, could we handle to social consequences of accurate
prediction??
MAN-MADE EQS - CONTROL AND MODIFICATION
Man produces EQs in several ways.
The study of these "man-made" EQs sheds light on how it may be possible to control natural EQs and so
prevent major, damaging shallow EQs.
Nuclear Explosions
During explosion naturally produce a shock
1 megaton approx. equal Mb approx. equal 6.5
Also find that explosion gives rise to a series of "after shocks". Usually small Mb < 4,but sometimes Mb > 4.
Cause: shock of explosion unsticks locked up faults, and so allows the release of stored strain energy
in form of after shocks.
Conclude: Could release strain in a large fault by explosion.
Problem:-
Unpredictable
Not respectable (Superman stuff!)
Study of shock effects of explosions was not motivated by EQ control, but for nuclear test ban studies, etc.
How to identify a nuclear explosion?
(1)
First motion studies - an explosion only generates compressive first waves, no dilational
first arrivals. Fault plane solution:
(2)
Usual Mb, Ms relations do not hold for nuclear
explosions:
Mb = 0.56 Ms 2.9 for natural EQs not for explosions.
Mb is larger than predicted for a bomb.
Nuclear explosions not transformed so much into surface waves,
therefore Ms smaller than Mb.
Also rock in which explosion occurs affects Mb, Ms. Alluvium adsorbs more energy than granite,
therefore Mb is less in Alluvium explosion than Mb in granite.
State of Art:- approx. 90% of nuclear tests can be distinguished from natural, larger explosions easier to
distinguish than those approx. <Mb = 4.
Reservoirs
Now widely known that filling a dammed reservoir initiates a series of EQs, even in previously aseismic
areas.
Make a lake, cause a quake!
Largest occurred in December 1967 when after filling local reservoir had Ms = 6.4 quake in Koyna, India.
Killed 180 people.
This occurred in area of Indian PreCambrian shield, with no previous seismic history.
Also note:(1)
(2)
(3)
Epicentres of shocks always close to reservoir.
Seismic activity maximum at early stages of filling. Diminishes with time.
Most EQs are <Ms = 4.
Causes:(1)
Increased load of water may change stress loads, therefore -> EQ?
Unlikely because stress due to loading of even 1 or 2 km. of water is small in
comparison with crustal stresses.
(2)
Reservoir -> increase in pore-water pressure in local rocks?
More likely - water enters cracks and lubricates faults to allow strain release (c.f.
Dilatancy Cycle of natural EQs).
Pumping Studies
Similar EQ generation found in areas where chemical waste pumped into ground.
EQs started in previously aseismic area.
Find that often increased pumping pressure increased EQ
activity.
Conclude:(1)
Increase in pore-pressure reduces shear strength of rock, therefore allows release of stored
up strain energy.
(2)
Water acts as lubricant (stress corrosion) and hence allows slip.
Earthquake Control
Aim: To release strain in locked fault zone in a controlled manner. Hence no more damage!
Approach: Use controlled changes in pore pressure to allow limited slip:
Drill holes A -> D along fault.
-----------A---------------------B----------------------C-------------D-----------Pump out H2O at A and C to lock fault still further - dry fault zone.
Pump in H2O at B to allow limited slip (By locking at A and C will prevent catastrophic failure along
whole fault)!
Now repeat, but with centre on C, etc.
Has worked in small scale experiments.
Problems:
(1) don't know what pressure is needed to allow slip;
(2) can't be certain that movement will be stopped at dry wells;
(3) don't know what Ms of EQ will be when it is triggered,
(4) relation of Energy and magnitude means that to release same amount of
energy as and M=6, need to generate ~ 1000 M=4 shocks.