Seismology – What is a Wave

  1 From: http://www.citiesoflight.net/AlaskaQuake.html

  2010 ieso Seismology

  2002 Denali Earthquake Note: Animation only visible in powerpoint

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? Wavelength: The length between two crests or troughs Amplitude: The maximum height relative to the zero _{From: Mussett and Khan, Looking into the earth} position

  It is important to note that although the waves Frequency: The number of travels through the earth, the material itself does not “wavelenghts” that pass a – in the same way as water. point in one second Frequency v = f λ *

  Velocity = frequency x wavelength Frequencies in seismology range from less than 10 to perhaps 100s of Hz (cycles per second).

  Ancient Seismographs , 2005 _gens The Chinese made the first seismographs over 2000 years ago. _{and Lut} This seismograph will tell the _{a rb uck} observer the direction of the first _T motion of the ground during an _{F rom} earthquake

  Earthquake _{, 2005 F rom T a rb uck and Lut} gens

  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.

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. Three seismometers oriented vertically, N-S and E-W are required to measure the full ground motion. _{Figures from: Mussett and Khan, Looking into the earth}

Building A Seismometer

  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.

  _Mus rom _{s es tt an d Khan, 2} 000

  Rearranging gives: ^{F rom Kear ey et al., 2002 F}

  AB = =

  ' i AA i BB

  1 sin ' sin '

  2

  Trigonometry tells us that:

  Wavefront The time between successive wavefronts remains unchanged, so the wavelength must increase in the second rock in proportion to the increase in velocity.

  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 ' '

  1 AB AA i AB

  2

  ' sin

  ' ' sin '

  = = λ λ

  1 AA BB v v

  2

  1

  2

  BB i = = Snell’s Law

  2

  4 37 sin

  . At what angle from the normal does it leave the interface? ^F

  o

  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 45

  o

  = 48.8

  2

  So i

  2 = =

  2

  5 sin 5 sin

  2

  4

  37 sin

  o o i i

  , the equation can be rearranged to Snell’s Law

  

2

  and v

  1

  As BB’ and AA’ are in proportion to the velocities v

  1 sin sin v i v i =

  1

  _Mus rom _{s es tt an d Khan, 2} 000

Snell’s Law – Multiple Horizons

  3

  As i’

  The ratio (sin i/v) thus remains unchanged

  _Mus rom _{s es tt an d Khan, 2} 000

  , and so on ^F

  2

  = i

  2

  , I’

  1

  = i

  1

  1 = = =

v

i v i v i

  2 '

  1

  2

  2

  3

  3

  = = constant sin sin sin

  1 sin sin sin sin v i v i v i v i

  1 '

  2

  2 '

  2

  3 Snell’s Law – Curved Layers

  However, in the real earth, the layers are curved, so it is not true that i

  2

  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. _F

  Velocity-Depth Structure

  The parameter p is 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.

  1

= = =

  1

  1

  2

  2

  2

  p v i r v i r constant sin sin

  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,

  F rom _{Mus s es tt an d Khan, 2} 000

  2 , etc.

  = I’

  _Mus rom _{s es tt an d Khan, 2} 000 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 Mus an tt s} rom _{d Khan, 2 es} 000

  P, Primary (Body) Wave

Direction of propagation

Axial Expansion

Axial Compression

  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) •

P WAVE

  S, Secondary (Body) Wave radial compression

Direction of propagation

radial expansion

  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 • mantle)

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 (v = 0.55 v ).

  s p i i _F sin sin _{P S}

  1

  1 rom

  = _Mus reflection : v v _{s es}

  1P

  1 S i r _tt sin sin _{P S an}

  1

  2 = _{d Khan, 2} refraction : v v S ₀₀₀

  1P

  2 As the velocity of the S-wave is different to the P-wave, the angle of reflection of a

  converted S-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-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. _F Particle motion is a vertical elipse. It

  rom _Mus

  has both vertical and horizontal _{s es 000 d Khan, 2 an tt} motion.

  Particle motion is horizontal and transverse. It has only horizontal motion Surface wave amplitude decreases rapidly with depth, similarly to water waves.

  Rayleigh WAVE Love (Surface) Wave Love Surface wave

  Multiple reflections of (horizontal component) SH wave trapped by surficial layer creates Love wave

  S wave front

• Deformation (in plane of surface) eg. side to side motion, not recorded on vertical seismometer.
• Speed 1 ~ 7 km/s

  Surface Waves F _{d Khan, 2 an tt es s Mus} rom 000 Seismic Velocities mass e appropriat force restoring waves of velocity =

  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 κ is also involved.

• = _{s p}

  ρ μ ρ μ κ

  =

  v v

  3

  In a liquid,

  μ is

  zero, so v

  s

  is always zero. ^F

  _Mus rom _{s es tt an d Khan, 2} 000

  Seismic Velocities (P-wave)

  Rock Velocities (m/sec)

Influences on Rock Velocities

• In situ versus lab measurements
• Frequency differences
• Confining pressure
• Microcracks • Fluids – dry, wet

  Wave Propagation on Inhomogeneous Medium Reflection & Refraction

  Refracted SV wave Refracted P wave Reflected P wave I ncident P wave

  Reflected SV wave or SV wave 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 Refracted SH wave Reflected SH wave

  I ncident 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 Surface P & S vertically orientated

  P & S

• Refraction tends to cause P and S waves to become vertically orientated as they approach the surface.

  Scattering of P and S waves

City

Epicenter

  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

  μ is 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.

  400 km discontinuity: Velocity increase abruptly – olivine and pyroxene reorganize to more compact forms. 600 km discontinuity: Additional phase/composition change. 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 _{F named PcP, etc. These are referred to as phases.} is called PKP. A P-wave reflecting of the core is _{Mus an tt es s} rom _{d Khan, 2}

  o

  There are no main P-wave arrivals in the interval 98

  o

  to 144 . This is the P-wave shadow zone. There are ₀₀₀

  o no S-wave arrivals beyond 98 . o

  There are some weaker arrivals between 98 and

  o

  144 , 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).

Phases

  Receiver gather for station 36 and shot line 8+23 (Gulf of Corinth, Greece). Data are bandpass filtered between 3–8 Hz and reduced at 8 km/s. Horizontal axis is shot-receiver offset. Strong, late phase between 10.6–13.0 s is Ps, interpreted as a reflection from the subducting African slab. Weaker phase around 7 s is probably PmP. Inset shows location of receiver (black dot) and shot line (black line) in relation to other stations and shots.

  Ray Paths in the Earth

  A theoretical travel time plot for an earthquake. Earthquakes that arrive at a distance of greater than 18

  o

  are 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

  _Mus rom _{s es tt an d Khan, 2} 000 2002 Denali Earthquake _From

  : http://www _{.c it ies o} flig _{ht.net/Alas k aQ u a k e.ht} m _l Note: Animatio n onl y visi ble i n po w e rp oint

  Earthquakes

  As both sides of the fault move, strain _F builds up across the

  rom _Mus

  fault – fences may be _{es s} bent, etc. Once the _{an tt d Khan, 2} strain becomes more than the fault can ₀₀₀ support the strain is released by elastic rebound. Energy is released as friction, block movement, and seismic waves. 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

  _Mus rom _{s es tt an d Khan, 2} 000 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 46

  o

  . 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 _F

  _Mus rom _{s es tt an d Khan, 2} 000 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

  _Mus rom _{s es tt an d Khan, 2} 000 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. ^F

  _Mus rom _{s es tt an d Khan, 2} 000

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? ^F

  _Mus rom _{s es tt an d Khan, 2} 000 Beachballs

  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.

  The above beachball defines a fault plane with a roughly NW-SE strike and a dip of either 25

  o

  ~NE or 65

  o ~SW. ^F _Mus rom _{s es tt an d Khan, 2} 000 Making A Beachball _{F Mus} rom _{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 Mus} rom _{s es tt an d Khan, 2} 000

  Earthquakes in PNG Earthquake Intensity _{T a rb uck and Lut gens} , 2005 _F rom

  The Mercalli Intensity Scale is a measure of what people reported. This is useful for areas where there were few seismometers, or in study of ancient earthquakes.

  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).
• 6 •Magnitude = log (max amplitude of oscillation, in units of 10 m).

  10

• 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 _{T a rb uck and Lut gens} , 2005 _F rom

  Seismic Moment

  Though the Richter magnitude scale is the most commonly quoted, a later and better measure is the seismic moment, M

  o .

  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.

  F b = =

= =

  = μ μ couple of moment

• strain and strain, A F As

  2 * couple of moment

  o M Ad d

  , 2b

  How do we determine rupture area?

  _Mus rom _{s es tt an d Khan, 2} 000 Seismic Moment

• Aftershocks What is the maximum seismic moment of an earthquake limited by? ^F

  F ^{rom T a rb uck and Lut gens , 2005}

  Here we can see both the along strike extent of the subducting plate (shown by the earthquake distribution), and the down-dip distribution. The area of the plate rupturing in a given earthquake is a limiting factor in the moment magnitude of the earthquake.

  Seismic Moment

  Fortunately, only distinct parts of the subduction zone slip at one time, limiting the size of the earthquake. ^{F rom T a rb uck and Lut gens , 2005}

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). ^{F rom T a rb uck and Lut gens , 2005}

  References Used

  1. Basic seismic theory: Kearey, P., M. Brooks, and I. Hill, An Introduction to Geophysical •

  rd Exploration, 3 edition., 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

  4. Plus additional html references as listed in this presentation.