1
Seismology
ieso
2010
2002 Denali Earthquake
From: http://www.citiesoflight.net/AlaskaQuake.html
Seismology – What is a Wave
Seismology is primarily concerned with determining the structure of the earth – on all scales.
To accomplish this it uses the ability of seismic waves to propagate through the earth.
What is a wave?
From: Mussett and Khan, Looking into the earth
Wavelength: The length between two crests or troughs
Amplitude: The maximum height relative to the zero position
Frequency: The number of “wavelenghts” that pass a point in one second
Frequency
λ
*
f
v
=
Velocity = frequency x wavelength
Frequencies in seismology range from less than 10 to perhaps 100s of Hz (cycles per second).
Ancient Seismographs
F
rom
T
a
rb
uck
and Lut
gens
, 2005 The Chinese made the first
Earthquake
Nowadays, if an earthquake occurs, how do we detect it, and how do the waves travel – in the next few slides I will attempt to answer these questions.
F
Detecting Seismic Waves
It is easy to visualize the motion of an ocean wave, and how we might measure its wavelength, amplitude, and frequency, but how do we do this with the earth?
On the left are two basic seismometers. When the ground moves the
pendulums moves either horizontally (top) or vertically (bottom). The movement is damped so that subsequent motion of the earth is not obscured by the pendulum oscillating.
On the right is a more conventional seismometer. Motion of the magnet through the coil generates a current in the coil which is amplified and recorded.
Building A Seismometer
A basic seismometer is actually very simple. Shown here is a simple seismometer that with the addition of some
electronics (amplifier etc) will happily record earthquakes. Refer to http://www.iris.edu/edu/AS 1.htm for more details.
Snell’s Law
The earth is not a uniform sphere. Broadly speaking, it is made up of layers. When wave fronts cross from one rock type into another with a higher velocity they turn.
Wavefront
The time between successive wavefronts remains unchanged, so the wavelength must increase in the second rock in proportion to the increase in velocity.
Trigonometry
tells us that:
sin
Snell’s Law
Answer the following question:
A ray traveling in a rock with a seismic velocity of 3 km/s encounters an interface with a rock of 4 km/s at an angle of 45o. At what angle from the normal does it
leave the interface?
F
Snell’s Law – Multiple Horizons
3
Snell’s Law – Curved Layers
The differences between the angles also depends not on the velocities of the layers, but only on the geometry of the triangle ABO. Snell’s law determines how the angle of a ray changes on crossing an interface, while geometry determines the change of angle between interfaces. Now,
p
The parameter pis known as the ray parameter and has the same value all along the path of any given ray provided that v,i, and r are measured at the same place.
Velocity-Depth Structure
Using an approximate velocity model, travel times can be calculated for the distance to actual seismic receivers and compared with observed times. The difference between the two is then minimized by adjusting the velocity-depth curve. This is repeated for millions of earthquakes and hundreds of seismometers all over the world. From this, a velocity depth model can be derived.
Body Waves
There are two types of body wave (waves which travel through the earth).
P-waves – Travel through the earth in a series of dilations and compressions. Akin to sound through air.
S-waves -- Shear wave, do not travel through fluids, travel at about half the speed of P-waves.
F
rom
Mus
s
es
tt
an
d Khan, 2
000
P, Primary (Body) Wave
•
Deformation parallel to direction of propagation, e.g. like sound wave
heard by human ear or pressure wave in a liquid. P waves can travel
through solids, liquids or gases.
•
Speed 1 km/s (in water) ~ 14 km/s (Lower part of mantle)
Axial Compression
P
WAVE
Direction of propagation
radial expansion
radial compression
S, Secondary (Body) Wave
•
Deformation perpendicular to direction of propagation, shear wave that
cannot travel through gases or liquids
•
Speed 1 km/s (in unconsolidated sediments) ~ 8 km/s (Lower part of
S
WAVE
Body Waves
S-Waves cannot travel through water. The passage of an S-wave depends on the medium restoring its shape after initially being sheared. Water does not do this.
The S-wave velocity is always less than the P-wave velocity (vs= 0.55 vp).
As the velocity of the S-wave is different to the P-wave, the angle of reflection of a converted wave is not equal to the angle of incidence of the P-wave. Also, an S-wave is refracted at a different angle to a P-S-wave.
Surface Waves
Water waves are an example of a surface wave.
They are slower than P- and S-waves and often have larger amplitudes.
Particle motion is a vertical elipse. It has both vertical and horizontal motion.
Particle motion is horizontal and transverse. It has only
horizontal motion
Surface wave amplitude decreases rapidly with depth, similarly to water waves.
F
rom
Mus
s
es
tt
an
d Khan, 2
000
Love (Surface) Wave
• Deformation (in plane of surface) eg. side to side motion,
not recorded on vertical seismometer.
• Speed 1 ~ 7 km/s
S wave front
Love Surface wave
Multiple reflections of (horizontal component) SH wave trapped by surficial
layer creates Love wave
Surface Waves
F
rom
Mus
s
es
tt
an
d Khan, 2
Seismic Velocities
The velocity depends on two main things – the restoring force (analagous to the strength of a spring), and the mass (analagous to the mass of the spring). As the restoring force increases, the velocity increases. However, as the mass increases, this will slow the spring, reducing the velocity. The mass in the case of a rock is its density (mass per unit volume).
S-waves involve a change in shape – this requires a shear force. The size of the force depends on the shear, or rigidity modulus, μ. A P-wave also involves a change in size, so the compressibility modulus κis also involved.
Rock Velocities (m/sec)
Influences on Rock Velocities
• In situ versus lab measurements
• Frequency differences
• Confining pressure
• Microcracks
Wave Propagation on
Inhomogeneous Medium
Reflected P wave Refracted P wave
Reflected SV wave Refracted SV wave
Reflection & Refraction
•
P and SV (vertical component) waves, reflects and refracts at
boundary layer between two rock/soil layer: producing both SV
and P waves
Reflection & Refraction
I ncident SH wave Reflected SH wave Refracted SH wave
•
SH (horizontal component) waves, reflects and refracts at
boundary layer between two rock/soil layer but no P reflected or
refracted waves are produced.
Refraction through stratified layers near
surface
• Refraction tends to cause P and S waves to become vertically orientated as they approach the surface.
Surface
P & S
Scattering of P and S waves
• Reflection and refraction, add complexity to seismograph recorded at the city.
Identification of seismic phases
2008, May 12, M7.9,
Eastern Sichuan,
China
Seismology of the Earth
As S-waves do not travel through liquid, they do not travel through the outer core. As μis reduced to zero in a liquid, the P-wave velocity is reduced.
Mohorovicic discontuity: P-wave velocity jumps to more than 7.6 km/s. This defines the crust mantle boundary. The depth of this boundary varies from 5-6 km under the ocean floor to 70 km or more below major mountains. The average is approximately 40 km.
Low velocity zone: ~100 km depth. Not found everywhere.
Ray Paths in the Earth
A ray is named according to the parts of the earth that it travels through – e.g a P-wave traveling successively through mantle, core, and mantle again is called PKP. A P-wave reflecting of the core is named PcP, etc. These are referred to as phases.
There are no main P-wave arrivals in the interval 98o
to 144o. This is the P-wave shadow zone. There are
no S-wave arrivals beyond 98o.
There are some weaker arrivals between 98oand
144o, because as well as ones reflected into it such
as PP, the inner core reflects some rays into it (hence the discovery of the inner core).
F
Ray Paths in the Earth
A theoretical travel time plot for an earthquake. Earthquakes that arrive at a distance of greater than 18oare termed teleseismic. These are important as they not only
sample deep parts of the earth, but they come back to the surface at a steep angle, spending as little time as possible in the highly variable crust.
F
2002 Denali Earthquake
Earthquakes
As both sides of the fault move, strain builds up across the fault – fences may be bent, etc. Once the strain becomes more than the fault can support the strain is released by elastic rebound. Energy is released as friction, block movement, and seismic waves.
F
rom
Mus
s
es
tt
an
d Khan, 2
Where was that Earthquake?
Unless we see rupture at the surface, which is rare, we do not know where the earthquake occurred. Using first arrivals is limited – we can tell which station the earthquake was closest to, but we do not know how long it took to get there.
It is as if we are trying to tell how far away a storm is but we are not seeing the lightning – we have only thunder to judge by.
F
Where was that Earthquake?
What if we use both the P- and S-wave (the thunder and the lightning)?
As S-waves travel more slowly than P-waves, the more distant the earthquake from the receiver, the greater the lag of the S- after the P-arrival. There are standard curves for this purpose:
In this case a P-S arrival time difference of 6.5 minutes equates to a epicentral angle of 46o. We
also know that the earthquake occurred about 8 minutes before the first P-arrival. If this procedure is repeated for multiple earthquakes we can triangulate the location
How Deep was that Earthquake?
The depth of the hypocenter below the epicenter can be found by measuring the difference in arrival of the direct P-wave and the wave that reflects from the surface, pP. As the depth increases the pP-P difference increases.
F
Fault Plane Solutions
Simply put, a fault plane solution tells us the orientation and nature of the fault that caused an earthquake.
In the simple case above, imagine a peg in the ground that is struck by a hammer from the north. Immediately following the impact the ground directly to the north of the peg experiences compression, and that to the south experiences dilation. The magnitude of the compression and dilation decreases off axis (b). S-waves are also generated in the east and west directions.
Fault Plane Solutions
In the above example there is a N-S trending right-lateral(dextral) strike slip fault surrounded by a circle of seismometers. When this fault moves, the seismometers will record a “first motion”. In the top left quadrant this is +ve, or up, in the bottom left quadrant this is –ve, or down. By mapping out the first motions on these seismometers, we can derive what sort of earthquake it is.
However, there is ambiguity, as a left lateral strike slip fault trending E-W would also fit these first motions. This is where we might also consider the local geology – are there any dominant trends? Is there a cluster of aftershocks that illuminates a particular plane?
Traditionally an earthquake fault plane solution is displayed as a beach ball (b). Here we are looking down onto the lower hemisphere of a sphere (a). To create this beachball, earthquakes are plotted an an equal area Lambert projection net using the azimuth, take-off angle, and sense of the earthquake.
Making A Beachball
F
rom
Mus
s
es
tt
an
d Khan, 2
000
First plot azimuth, take-off angle and sense of earthquake. Find a plane that splits two areas of compressional and dilational earthquakes. Plot the pole (P) to that plane, and then find another plane that also splits two area of compressional and dilational earthquakes, but also passes through the pole to the previous plane (ensuring that both planes are perpendicular).
Beachballs for Various Faults
F
rom
Mus
s
es
tt
an
d Khan, 2
Earthquakes in PNG
Earthquake Intensity
F
rom
T
a
rb
uck
and Lut
gens
, 2005
Earthquake Magnitude
In 1935 Richter devised the Richter magnitude scheme for describing the size of earthqauke.
•Measured amplitude in microns of the largest oscillation of a particular type of seismometer 100 km from the source.
•The amplitudes have a very large range, so he took the logarithm (to base 10) to make the numbers more manageable. An increase of 1 in magnitude means the amplitude is 10 times greater (energy release is 30 times greater).
•Magnitude = log10(max amplitude of oscillation, in units of 10-6m).
•-ve values are possible (oscillations < one millionth of a meter). Many –ve magnitude earthquakes have been recorded at the HUGO seismic station half way between Hawai’i and the mainland.
•The scale was originally designed for shallow earthquakes near the receiver and a particular type of seismometer. It has been modified to deal with this.
•It underestimates the biggest earthquakes – many seismometers are not as sensitive to the lowest frequencies.
Earthquake Magnitude
F
rom
T
a
rb
uck
and Lut
gens
Seismic Moment
Though the Richter magnitude scale is the most commonly quoted, a later and better measure is the seismic moment, Mo.Just before a fault ruptures, the shear forces on either side of the fault exert a couple, whose size, or moment, equals the product of the shear forces and the perpendicular distance between them. The force is dependant on the strain, the area of rupture, A, and the rigidity modulus, μ. The strain depends on the fault offset and the width of the strained volume.
o
How do we determine rupture area? •Aftershocks
What is the maximum seismic moment of an earthquake limited by?
F
Seismic Moment
Fortunately, only distinct parts of the subduction zone slip at one time, limiting the size of the earthquake.
F
Risks and Mitigation
What are some of the earthquake risks?
What are some of the ways that we can minimize damage?
Build Sensibly Tsunamis and tsunami warning systems
Using automated seismic triggers to slow trains, etc. (Bullet Train in Japan).
References Used
1. Basic seismic theory:
• Kearey, P., M. Brooks, and I. Hill, An Introduction to Geophysical Exploration, 3rdedition., pages 21-30, 2002.
2. Basic theory, seismology, and earthquakes:
• Mussett, A.E. and M.A. Khan, Looking into the earth: An introduction to geological geophysics, pages 24-64, 2000
3. Really basic theory:
• Tarbuck, E.J. and F.K. Lutgens, Earth: An introduction to physical geology, chapter 11, 2005
