ْ َ ُ َ َ ْ َّ َ َ ْ َ َ
ِ‫ون بإذنه‬
ِ ‫يا منِ استقرتِ اْلرض‬
Fundamentals of Earthquake Engineering
Engineering Seismology
Mojtaba Mahsuli
mahsuli@sharif.edu
1
Myth
2
•
•
•
•
•
Greek: When Poseidon is in a bad mood, he strikes the ground with a trident, causing earthquakes
Hindu: When one of the eight elephants that carry the Earth gets tired …
Mongolian: When a frog that carries the world moves …
African: When the giant on whose head people all live, sneezes or scratches …
Japanese: When the attention of Kashima (who looks after the giant catfish Namazu that supports
the Earth and prevents it to sink into the ocean) weakens and Namazu moves …
• Native American: When the god Maimas decides to count the population in Peru, his footsteps
shake the Earth. Then natives run out of their huts and yell: “I’m here, I’m here!”
2
Seismic Waves
3
• Body waves
• Travel through the Earth’s interior
• Surface waves
• Result from the interaction between body waves and the surficial material
• Travel along Earth’s surface
3
Seismic Wave Propagation
4
• Seismic wave propagates from the rupture location to all directions
4
Seismic Waves: Body Waves
5
Body waves
• p-waves: Primary, compressional, longitudinal waves
• Analogues to sound waves
• Particle motion is parallel to wave direction
• Can travel through fluid and solid
• s-waves: Secondary, shear, or transverse waves
• Cause shearing deformation
• Particle motion is perpendicular to wave direction
• Fluids cannot sustain s-waves
• Can be divided into two components: SV (vertical plane movement) and SH (horizontal
plane movement)
• The s-wave on bottom-left (Figure c) is SV, because it causes vertical particle movement
• Figure d shows the combination of p- and s-waves travelling towards the ground surface
• Geologic material are stiffest in compression: p-waves travel faster than s-waves and are first to
arrive at a site
• The speed of s-waves is typically around 60% of that of p-waves in any given material
• Earthquake advance warning is possible by detecting the non-destructive p-waves that travel more
quickly
• The time of advance warning depends on the delay between the arrival of the p-wave and other
destructive waves
→ Generally on the order of seconds up to about 60–90 seconds for deep, distant, large
earthquakes such as the one Tokyo would have received before the 2011 Tohoku earthquake
and tsunami
5
General s-wave
SH component
(Horizontal plane movement)
Particle
SV component
(Vertical plane movement)
6
• SV and SH components of the s-wave
6
Body Wave Propagation
p-wave
s-wave
7
• Right: Unidirectional propagation of p- and s-waves
• Left: Propagation of a p- and s-waves in a 2D grid
7
Seismic Waves: Surface Waves
8
Surface waves
• Result from the interaction between body waves and the surficial material
• Amplitude decreases roughly exponentially with depth
• More prominent at distances farther from the source of the earthquake
• Because of their low frequency, long duration, and large amplitude, they can be the most
destructive type of seismic wave
• Surface waves are slower than body waves, roughly 90% of the velocity of s-waves for typical
homogeneous elastic media
• Rayleigh waves:
• Interaction of p- and SV-waves with Earth’s surface
• Involve both vertical and horizontal particle motion
• Similar to waves produced by throwing a rock in a pond
• Love waves:
• Interaction of SH-waves with a soft surficial layer
• No vertical component
• Slightly faster than Rayleigh waves
8
Surface Wave Propagation
9
• Top: Propagation of the Rayleigh wave
• Bottom: Propagation of the Love wave
9
Wave Arrival
10
• Each ground motion recorded at a station has two horizontal components and one vertical
• Note the lower frequency and higher amplitude of the surface waves
• Surface waves have lower speeds than s-waves (roughly 10% less); therefore, they arrive at the site
later than body waves
• Love waves are the most destructive, and appear in the horizontal components of recorded ground
motions, but do not appear in vertical components (Q: Why?)
• Rayleigh waves do appear in the vertical component, because they involve vertical particle motion
as well
• Note that surface waves have a lower frequency than body waves, because they are the response
of the soil layer to body waves
• Therefore, soil damps out the high frequency waves and amplifies the lower frequency waves due
to resonance, because the frequency of the latter is closer to the natural frequency of the soil
• In this slide, due to the large distance to epicenter (~2000 km), the time difference between arrival
times of different waves is large
10
Wave Arrival
Up-Down
N-S
E-W
P
S
Surface waves
11
Q: Identify the waves
11
Earth Layers
12
Chemical Layers: Crust, mantle, outer core, inner core
• Crust 24-40km
• As thin as 5km beneath oceans
• As thick as 60-70km under young mountains
• Distinct change in the wave propagation velocity marks the boundary between the crust
and the mantle, called Mohorovičić discontinuity, or Moho
• Named after Croatian seismologist, who discovered it in 1909
• Moho reflects and refracts the seismic waves
• Two types of crust shown on top-right: Continental crust and oceanic crust
• Mantle = 2850 km (1770 miles) thick
• Upper mantle: About 650 km (404 miles)
• Lower mantle: No earthquakes have been recorded in the lower mantle, which appears to
be chemically homogeneous
• The mantle is cooler near the crust than at greater depths but still has an average
temperature 2200°C
• As a result, the mantle materials are in a viscous, semi-molten state
• They behave as a solid when subjected to rapidly applied stresses, such as those associated
with seismic waves, but can slowly flow like a fluid in response to long-term stresses
• The mantle material has a specific gravity of about 4 to 5
• Outer core and inner core in the next slide …
12
Earth Chemical Layers
13
Lehman
Gutenberg
• Outer core, or liquid core = 2260km
• As a liquid, it cannot transmit s-waves
• Note the drop to zero in Vs
• Note the sharp drop in Vp
• Boundary between mantle and outer core is called Gutenberg discontinuity
• Primarily consists of molten iron, with density of 9-12
• Flow of the outer core produces the Earth’s magnetic field
• Inner core, or solid core = 1220 km
• Very dense; density up to 15
• Boundary between inner and outer cores: Lehman discontinuity
• Nickel-iron material compressed under tremendous pressure
• 5000-6000°C
13
Earth Mechanical Layers
14
• Mechanical layers: Lithosphere, Asthenosphere, Mesosphere, outer core, inner core
• Lithosphere: Crust + upper parts of mantle
• Uppermost 50-100 km
• No strict boundary between lithosphere and asthenosphere
• Behaves rigidly over very long periods of time
• Consists of tectonic plates
• Asthenosphere: Weakest part of mantle
• Depth of 100-200km, sometimes up to 600 km
• Solid in short time scales, fluid in long term
• Decouples the tectonic plates from the rest of the mantle
• Mesosphere: Hot, but stronger than asthenosphere due to high pressure
14
Reflection and Refraction
15
• Seismic wave paths are shown in this slide, which illustrates reflection and refraction of seismic
waves
• p- and s-waves can reach the earth's surface between 0° and 103°
• Outer core allows only p-waves to reach the surface between 143° and 180°
• Shadow zone: Between 103° and 143°, only the few waves that are reflected from the inner core
can reach the earth's surface; hence, no significant waves are recorded in this zone
15
Wave Path
16
• Q: The travel path of the waves is curved, because the density increases with depth
16
Continental Drift
17
• All the continents had once been one super-continent (Pangaea), and have since broke apart and
drifted, and are still drifting
• This would mean that massive continents pushed through the seas and across the ocean floor
• However, the ocean floor is too strong to permit such motion, and the theory was originally
discredited by most earth scientist
• From this background, however, the modern theory of plate tectonics began to evolve
17
Plate Tectonics
18
•
•
•
•
Earth's surface consists of a number of large, intact blocks called plates
Tectonic plates are large parts of litosphere floating on the astenosphere
Plates move with respect to each other
Earth's crust is divided into
• 6 continental-sized plates: African, American, Antarctic, Australia-Indian, Eurasian, and
Pacific
• About 14 of sub-continental-sized plates, e.g., Caribbean, Cocos, Nazca, Philippine, etc.
• Relative deformation between plates occurs in narrow zones near their boundaries
• slowly and continuously (aseismic deformation)
• spasmodically in the form of earthquakes (seismic deformation)
• Map of seismic activity supports this theory
18
Seismicity since 1980
19
• Only events with Mw > 5.0 are shown
• Note that the line of earthquake closely follows the boundaries of the tectonic plates
19
Seismicity in 2002
20
• Again, the line of earthquakes closely follows the boundaries of the tectonic plates
20
Convection in Mantle
21
• Plate tectonics is a kinematic theory
• In other words, it explains the geometry of plate movement without addressing its underlying
cause
• Movement of these huge plates requires gigantic forces
• Thermomechanical equilibrium of the earth's materials explains the movement:
• Upper mantle is in contact with cool crust, and lower mantle with hot outer core, which
produces a temperature gradient
• Unstable situation: Denser, cooler material resting on top of less dense, warmer material
• Cooler, denser material begins to sink under the action of gravity and the warmer, less
dense material begins to rise
• Sinking material gradually warms, becomes less dense, moves laterally, and begin to rise
again
• Cooled material begins to sink
• This is called convection
• Convection currents in the semi-molten mantle impose shear stresses on the bottom of the plates,
which drag them in various directions across the Earth’s surface
21
Convection in Mantle
22
• Video illustrating the convection cells within the mantle
22
Plate Interactions
23
• Convergent: Plates collide or subduct
• Divergent: plates move away from each other
• Transform: plates slide one past another
23
Plate Tectonics
24
• Kermanshah 2017 M7.3 earthquake epicenter was due to the movement of Arabian plate towards
the Eurasian plate at 26 mm/year
24
Plate Interactions
25
• Divergent: Bottom-right
• Produces spreading ridges
• Molten rock rises and cools
• Plates grow at spreading ridges (2-18 cm/year)
• Generally weaker earthquakes than subduction
• Convergent: Top
• One Plate subducts beneath the other
• Balances the growth at ridges
• Top-left: Continental-continental collision (orogeny)
• Forms mountain ranges, e.g., Himalayas, Alps
• Top-right: Oceanic-continental collision (subduction)
• Near the edge of continents
• The denser crust goes underneath the less dense one under its own weight
• Produces strong and sometimes very deep earthquakes (up to 700 km)
• Deeper earthquakes are more infrequent, because as the plate subducts, it warms and
becomes ductile
• Huge earthquakes such as the large ones that have occurred in Chile and Japan are
produced by this mechanism
• Produces volcanoes
• Transform: Bottom-left
• Movement along transform faults
• Weak to strong earthquakes
25
Plate Interactions
26
NOTE
• Theory of plate tectonics does not explain all observed tectonic seismicity
• For example, it is known that intra-plate earthquakes (earthquakes that occur within a plate, away
from its edges) have occurred on most continents
26
Inactive Fracture Zones
27
• Fracture zones may be observed over thousands of kilometers
• However, only the segment between the spreading ridges is the transform fault
• Motion on the portions that extend beyond the transform fault is in the same direction on either
side → No relative motion
• These inactive portions of the fracture zone are fossil faults that are not producing earthquakes
27
Faults
φ: Strike angle
δ: Dip angle
λ: Slip angle
28
•
•
•
•
•
On a smaller scale, the movement at a particular location can be quite complicated
Plate boundaries may be broken to platelets or micro-plates trapped between the larger plates
Locally, the movement between two portions of the crust will occur on offsets known as faults
Maybe obvious, maybe difficult to detect
Presence of a fault does not necessarily mean earthquakes are expected → Movement can occur
aseismically, or the fault may be inactive
• Lack of observable surficial faulting does not imply that earthquakes cannot occur → Fault rupture
does not reach the earth's surface in most earthquakes
• Fault geometry
• Strike: horizontal line produced by the intersection of the fault plane and a horizontal plane
• Strike angle: Angle between the strike and the direction of the north
• Dip: Downward slope of the fault plane
• Dip angle: Angle between the dip and the horizon
• For vertical faults: Dip angle = 90
• Foot wall: ‫فرودیواره‬
• Hanging wall: ‫فرادیواره‬
28
Fault Types
29
• Dip-slip (‫)شیب‌لغز‬: Movement along the dip
• Normal fault: Tensile stress, lengthening of crust
• Reverse fault: Shortening of crust
• Thrust fault: Very small dip angle; it causes very large movements (e.g., Alps)
• Strike-slip (‫)امتدادلغز‬: Movement along the strike; usually vertical faults that have a dip angle of 90
degrees; cause large movements
• Left-lateral: An observer would observe the material on the other side moving to the left
• Right-lateral: An observer would observe the material on the other side moving to the right
• Oblique-slip: Movement along both the strike and the dip
29
Examples
30
Strike-slip
Dip-slip Normal Fault
30
Event Characteristics
31
EMSC (2017)
• Kermanshah earthquake rupture mechanism was analyzed by several agencies
• They all indicated a reverse, thrust fault as evident from the seismology “beach ball,” which
produces significant motions compared to normal or strike-slip faults
• In seismology beach balls, material moves from white to black; hence, the beach balls in this slide
show compression, which mean reverse faulting
• The interface of white and black also shows the direction of rupture
• The agencies differed in their estimation of the epicenter, depth, and magnitude:
• Epicenter: 34.77N, 45.76E (Geophysics UT), 34.81N, 45.91E (BHRC) → 14.5 km apart
• 7.2<M<7.4 in moment magnitude (Richter local saturates at 6.8~7)
• 15<Depth<25km
• Tehran Geophysics: M7.3 at 18km depth
• Energy: 1.8M ton TNT or 89 Hiroshima atomic bomb; 5.6 Peta Joule (peta = 1015)
• 5 times the energy of Bam earthquake, which was occurred on Dey 8, 1382, M6.6, Depth of 8.6km,
distance to Bam=5km
• However, smaller PGAs at Sarpol compared to Bam because of larger distance and depth
• Bam: Horizontal PGA: 0.82g, Vertical PGA: 1.01g
• Sarpol Zahab: Horizontal PGA: 0.7g, Vertical PGA: 0.36g
31
Elastic Rebound Theory
32
• Elastic rebound theory describes the process of the successive buildup and release of strain energy
in the rock adjacent to faults
• Relative movement of the plates leads to Elastic strain energy being stored in the materials near
the boundary as shear stresses increase on the fault plane
• When shear stress reaches the strength of the rock, it fails → Accumulated strain energy is
released
• Effects of the failure:
• Weak and ductile rock: strain energy released relatively slowly → Movement occurs
aseismically
• Strong and brittle rock: rapid failure; energy released explosively → Heat and stress waves
(earthquakes)
32
Fault Rupture
START
Depth
Surface of the earth

Distance along the fault plane (100km)
33
33
Fault Rupture
Second 2.0
34
34
Fault Rupture
Second 4.0
35
35
Fault Rupture
Second 6.0
36
36
Fault Rupture
Second 8.0
37
37
Fault Rupture
Second 10.0
38
38
Fault Rupture
Second 12.0
39
39
Fault Rupture
Second 14.0
40
40
Fault Rupture
Second 16.0
41
41
Fault Rupture
Second 18.0
42
42
Fault Rupture
Second 20.0
43
43
Fault Rupture
Second 22.0
44
44
Fault Rupture
Second 24.0
45
45
Fault Rupture
Total Slip in the M7.3 Landers Earthquake
46
46
Seismic Moment
M0 =   AD
2
M w = ( lo g10 ( M 0 ) − 9.1)
3
M 0 in N  m
47
• Seismic moment: A measure of the work done by the earthquake
• μ: Rupture strength of the material along the fault
• A: Rupture area
• D: Average amount of slip
• Seismic moment is named for its units of force times length
• It is a measure of the total amount of energy that is transformed during an earthquake
from the built-up stresses to other forms, such as
• Cracks and deformation in rocks
• Heat
• Radiated seismic energy
• Only a fraction of the M0 is converted into radiated seismic energy, Es, which is what
seismographs register: Es=1.6 M0 ∙ 10-5
• Moment magnitude:
• Most magnitude scales are empirical
• As the amount of energy released increases, the ground-shaking characteristics do not
necessarily increase at the same rate
• Saturation: For strong earthquakes, the measured ground-shaking characteristics become
less sensitive to the size of the earthquake than for smaller earthquakes
• Body wave and Richter local magnitudes saturate at magnitudes of 6 to 7
• Surface wave magnitude saturates at about Ms = 8
• The only magnitude scale that is not subject to saturation is the moment magnitude
• This is because it is based on the seismic moment, which is a direct measure of the factors
that produce rupture along the fault
47
Magnitude-Duration Correlation
48
• Earthquake duration is highly correlated with the magnitude
48
Magnitude-Fault Length Correlation
49
• Magnitude is highly correlated with the length of the fault
49
Directivity and Fling
50
• Forward directivity: Focusing of wave energy along the fault in the direction of rupture; produces a
pulse-like record with a large amplitude and short duration (right figure)
• Fling: Pulses of large displacement at sites toward which the rupture is progressing; produced by
constructive interference of waves (right figure)
• Backward directivity: When rupture propagates away from the site, the arrival of the pulses is
distributed in time; produces motions with relatively long duration and low amplitude (left figure)
50
Regional Damage
‫دو ‌ یب‬
‫یب‌ ز‬
‫یب‌متو‬
4.1±1.6
‫یب‌شدید‬
‫یب‌ م‬
‫فروریز‬
4.1±1.6
22.3±3.3
25.7±3.3
700
600
500
10.1±2.5
33.8±4.1
400
300
200
51
100
• This is the result of processing the data of 1198 buildings that experienced the 1396 Kermanshah
earthquake
• Explain each damage state:
• None: 0%
• Slight: 2%
• Moderate: 10%
• Severe: 50%
• Total: 100%
• Collapse
• Most damage in Ezgeleh but in terms of numbers, Sarpol had higher number of damaged and
collapsed buildings because it is a much larger city
• It is clear that when you go towards east, the damage declines quickly
• But towards south and southeast, the directivity caused significant damage and damage does not
decay as quickly
• This is due to directivity
51
Seismic Gap
52
• Seismic gap: A segment of an active fault that has not slipped in an unusually long time compared
with other segments
• 1989 Loma-Prieta earthquake occurred on a segment of the San Andreas fault that had previously
been identified as a gap
52
Geometric Notation
53
•
•
•
•
•
•
Focus or hypocenter: Point at which rupture begins and the first seismic waves originate
Rupture spreads across the fault at velocities of 2 to 3 km/sec
Focus is located at some focal depth (or hypocentral depth) below the ground surface
Epicenter: Point on the ground surface directly above the focus
Epicentral distance: Distance on the ground surface between an observer or site and the epicenter
Hypocentral distance: Distance between the observer and the focus
53
Determination of Location
d=
ts − p
1 / vs − 1 / v p
54
• This is a preliminary method
• More refined estimates of the epicentral or hypocentral location are made using multiple
seismographs, a three-dimensional seismic velocity model of the earth, and numerical
optimization techniques
54
Determination of Location
55
• This is a classic example of an inverse problem
• An inverse problem is a general framework that is used to convert observed measurements into
information about a physical object or system that we are interested in
55
Path
 Combination of source, path and site effects
56
Source: Boore D. M. (2004) Journal of Earthquake Engineering 8(1), pp. 1-41
• An earthquake scenario consists of the source, the path, and the site
• Source: What we talked about thus far
• Path: Travel of waves
• Distance: As waves travel away from a seismic source, geometric spreading reduces their
amplitude; this is called attenuation
• Crustal Structure: Tendency to transmit and absorb the energy in the seismic waves by the
crust and mantle (reflection and refraction)
• Site (next slide)
56
Site Effect
57
Site Effect
• Surface Geology
• Motion at the ground surface is the response of the soil layer to the input motion at the
bedrock-soil interface
• Soil deposits amplify the ground motion
• Topography: Presence of topographic features affects the ground motion
• Figure from the Instructor’s master’s thesis
57
Soil-Structure Interaction
58
• Soil-structure interaction: Happens when the wave has arrived at the base of the structure
• This is the due to the presence of a non-rigid soil under the structure
• Kinematic interaction: The structure experiences an average of the motions that are exerted on the
foundation; therefore, the input motion to the foundation differs from the “free-field” motion
• Inertial interaction: Presence of the soil affects the vibration properties of the system, such as its
period and damping; therefore, it affects the response of the structure to the seismic excitation
• Figure from the Instructor’s master’s thesis
58
EXTRA SLIDES
59
59
• K: Bulk modulus
(Incompressibility)
• μ: Shear modulus
(Rigidity)
• ρ: Density
vp =
vs =
K + 43 



60
Thin line is density
Notes:
• The Vs in inner core is not zero in this graph
• There is no jump in Vp at the Lehman discontinuity (see next slide)
1. How different layers were formed?
Heavier, more dense material, tended to sink in the early molten mass, while lighter, less
dense material, rose toward the surface. Separation into layers was based on density. The
separation seems to have taken place shortly after the formation of the planet in an event
called the "Iron Catastrophe".
http://wiki.answers.com/Q/How_did_Earth_separate_into_different_layers#ixzz28Y21xEcx
Therefore, the boundaries between layers are due to presence of different types of materials,
which are detected by the change in the wave propagation pattern.
2. Why mantle acts as rigid under sudden stresses?
Under tremendous pressure, the solid mantle rock can act like a fluid or a solid. It is plastic. If
sudden stresses act upon it, it reacts like a solid, as in the case of s-waves generated by
earthquakes. If allowed enough time, when stressed, it will flow upward like heated water
flows upward through layers of cooler, denser water.
http://www.creationinthecrossfire.com/Articles/CatastrophicPlates3.html
3. Why the wave velocity increases with depth?
The increase is a result of the effects of pressure on the seismic wave speed. Although
60
temperature also increases with depth, the pressure increase resulting from the
weight of the rocks above has a greater impact and the speed increases smoothly
in these regions of uniform composition
http://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/notes/waves_
and_interior.html
Since the density of the Earth increases with depth, you would expect the waves
to slow down with increasing depth. Why, then, do both p- and s-waves speed up
as they go deeper? This can only happen because the incompressibility and
rigidity of the Earth increase faster with depth than density increases.
http://www.bibliotecapleyades.net/tierra_hueca/inner_earth/inner1.htm
3. Why the waves propagate in curved paths?
The waves have curved paths because their velocities increase with depth.
http://www.chm.bris.ac.uk/webprojects1997/JohnH/WELCOME.HTM
5. Why the velocity curve has a jagged shape in upper mantle?
The shallow part of the mantle contains several important well-established and
relatively abrupt velocity changes. In fact, we often divide the mantle into two
regions, upper and lower, based on the level of velocity heterogeneity. The region
from near 400 to 1000 km depth is called the transition zone and strongly affects
body waves that "turn" at this depth and arrive about 20°-30° distant from a
shallow earthquake. In this depth range, the minerals that make up the mantle
silicate rocks are transformed by the increasing pressure. The atoms in these rocks
rearrange themselves into compact structures that are stable at the high
pressures and the result of the rearrangement is an increase in density and elastic
moduli, producing an overall increase in wave speed.
60
Jump in vp in Inner Core Boundary
61
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