Download Earthquakes

Earthquakes
Earth is a dynamic planet of a pretty dangerous sort
Terremoto Haiti 2010. Duecentovetimila vittime
Earthquakes occur along faults. A fault is a planar fracture or discontinuity in
a volume of rock, across which there has been significant displacement. Large
faults within the Earth's crust result from the action of tectonic forces. Energy
release associated with rapid movement on active faults is the cause of most
earthquakes. There are three main types of faults:
A normal fault occurs
when the crust is
extended. The hanging
wall moves downward
relative to the footwall
A thrust fault occurs
when the crust is
compressed. The
hanging wall moves
upward relative to the
footwall
The fault surface is usually
near vertical and motion
results from shearing forces.
Doglioni et al., 2014
An earthquake is the result of a sudden release of energy in the Earth's crust
that creates seismic waves. The elastic rebound theory is an explanation for
how energy is spread during earthquakes. As rocks on opposite sides of a
fault are subjected to force and shift, they accumulate stress energy and
slowly deform (strain) until their internal strength is exceeded. At that time, a
sudden movement occurs along the fault, releasing the accumulated energy,
and the rocks snap back to their original undeformed shape.
In geology, the elastic rebound theory was the first theory to satisfactorily
explain earthquakes.
Following the great 1906 San Francisco earthquake, Harry Fielding Reid
examined the displacement of the ground surface around the San Andreas
Fault. From his observations he concluded that the earthquake must have
been the result of the elastic rebound of previously stored elastic stress
energy in the rocks on either side of the fault. In an interseismic period, the
Earth's plates move relative to each other except at most plate boundaries
where they are locked.
Suppose that rocks in the region of the locked fault have bilt up elastic stress
energy in the form of elastic deformation (strain) over a time period of many
years.
When the accumulated strain is
great enough to overcome the
strength of the rocks,
an earthquake occurs on the
fault plane at Time 0.
During the earthquake, the portions of the rock around the fault that were
locked and had not moved 'spring' back, relieving the strain (accumulated
over several years) in a few seconds. Like an elastic band, the more the
rocks are strained the more elastic energy is stored and the greater
potential for an event. The stored energy is released during the rupture
partly as heat, partly in damaging the rock, and partly as elastic waves.
Modern measurements using GPS largely support Reid’s theory as the
basis of seismic movement, though actual events are often more
complicated.
An aftershock is an earthquake that occurs after a previous earthquake,
the mainshock. An aftershock is in the same region of the main shock but
always of a smaller magnitude. If an aftershock is larger than the main
shock, the aftershock is redesignated as the main shock and the original
main shock is redesignated as a foreshock. Aftershocks are formed as
the crust around the displaced fault plane adjusts to the effects of the
main shock.
An earthquake's hypocenter is the position where the strain energy stored in the rock
is first released, marking the point where the fault begins to rupture. This occurs at
the focal depth below the epicenter.
The epicenter is the point on the Earth's surface that is directly above the hypocenter,
the point where an earthquake originates.
There are two types of seismic waves, body wave and surface waves. Body
waves originate in the hypocenter and propagate spherically through the
interior of the Earth. They follow raypaths refracted by the varying density
and modulus (stiffness) of the Earth's interior. The density and modulus, in
turn, vary according to temperature, composition, and phase. There are
two types of body waves: P-waves and S-waves.
Surface waves are analogous to water waves and travel along the Earth's
surface. They travel slower than body waves. Because of their low
frequency, long duration, and large amplitude, they can be the most
destructive type of seismic wave. There are two types of surface waves:
Rayleigh waves and Love waves.
The P-wave, where P stands for Primary wave or Pressure wave, can travel
through gases, solids and liquids, including the Earth. It has the highest
velocity (5-8 km/s during an earthquake) and is therefore the first to be
recorded, and it is formed from alternating compressions and rarefactions. In
isotropic and homogeneous solids, the polarization of a P-wave is always
longitudinal; thus, the particles in the solid have vibrations along (or
parallel to) the travel direction of the wave energy.
The velocity of P-waves in a
homogeneous isotropic medium
is given by
where K is the modulus of
compressibility (resistance to
volume change), μ is the modulus of
rigidity or shear (resistance to
change in shape due to shear), ρ is
the density of the material through
which the wave propagates.
The S-wave, where S stands for Secondary wave orShear wave, moves as
a shear or transverse wave, so motion is perpendicular to the direction of
wave propagation: S-waves are like waves in a rope. S-waves can travel
only through solids, as fluids (liquids and gases) do not support shear
stresses. S-waves are slower than P waves, and speeds are typically around
60% of that of P waves in any given material.
The velocity of S-waves in a
homogeneous isotropic medium
is given by
where μ is the modulus of
rigidity or shear, ρ is the
density of the material
through which the wave
propagates.
Nafe-Drake curve
An important empirical relation
exists between P and S
waves velocity and density.
P and S velocities increase
with density of medium, i.e., in
less dense sedimentary rocks,
waves travel slower (black
dots for S waves) than in
denser igneous and
metamorphic rocks (white dots
for S waves).
Seismic waves travel more
quickly through denser
materials and therefore
generally travel more
quickly with depth.
P
S
However, as noted from the velocity equations, if density increases, P and
S waves velocity decrease:
Thus, the other properties, incompressibility K and rigidity or shear µ must
increase with depth in the Earth at a greater rate than density increases.
This explain the experimantal results illustrated in the Nafe-Drake
curve.
However, anomalously hot areas slow down seismic waves. Seismic
waves move more slowly through a liquid than a solid. Molten areas within
the Earth slow down P waves and stop S waves because in a liquid, rigidity
or shear µ = 0; shearing motion cannot be transmitted through a liquid).
Partially molten areas may slow down the P waves and attenuate or
weaken S waves.
Therefore, the actual velocity of P and S waves depends on the
interplay between rock type, depth, and temperature.
Velocità onde P (a) e onde S (b)
Dipendono dalle caratteristiche del mezzo in cui
viaggiano:
K = modulo di incompressibilità del mezzo
µ = modulo di rigidità o di taglio (shear) del mezzo
r = densità del mezzo
La velocità delle onde S è sempre minore della velocità
delle Onde P in quanto manca il termine K. Le onde P
vengono avvertite (arrivano) prima delle S.
In un mezzo fluido (liquido o gas), K≠0, µ = 0
ovvero i fluidi sono comprimibili ma non
ammettono taglio. Quindi:
K
b=0
Le onde P possono
viaggiare nei solidi, liquidi e
gas
Le onde S possono
viaggiare nei solidi, ma NON
nei liquidi e gas
La velocità delle onde P e S tende ad aumentare
all’aumentare della densità r del mezzo (curva di
Nafe-Drake) poichè all’aumentare della densità r di una
roccia i moduli di incompressibilità K e rigidità o shear µ
della roccia aumentono in proporzione maggiore.
Ciò avviene ad esempio all’aumentare della profondità
nella crosta: aumenta la pressione litostatica e
l’incompressibilità K e rigidità µ delle rocce aumentano
maggiormente dell’aumento di densità r
…Ma la velocità delle onde P e S tende a diminuire
all’aumentare della temperatura poichè aumentando la
temperatura del mezzo i moduli di incompressibilità K e rigidità
o shear µ del mezzo diminuiscono maggiormente rispetto alla
densità r. Ciò avviene ad esempio all’aumentare della
profondità nella crosta (gradiente geotermico).
Dunque l’aumento di velocità in profondità legato
all’aumento di pressione litostatica è contrastato dalla
diminuzione di velocità causata dall’aumento di
temperatura.
LA VELOCITA’ DELLE ONDE E’ CONTROLLATA DALLE
CONDIZIONI GEOLOGICHE ‘LOCALI’
Surface waves - Rayleigh and Love waves - are generated by the interaction of P- and Swaves at the surface of the earth, and travel with a velocity that is lower than the P-, S- wave
velocities.
They emanate outward from the epicenter (surface projection of hypocenter, where P- and Swaves are generated) of an earthquake.
Rayleigh
Love
Love waves are surface seismic waves that cause horizontal shifting of the
earth during an earthquake. The particle motion of a Love wave forms a
horizontal line perpendicular to the direction of propagation (i.e. are transverse
waves). The amplitude, or maximum particle motion, often decreases rapidly
with depth.
Love waves travel with a slower velocity VL than S waves (b), but faster than
Rayleigh waves (VR): VR
< VL < b
Rayleigh waves, also called ground roll, are surface waves that are confined
to the Earth’s surface where they travel as ripples with motions that are similar
to those of waves on the surface of water. The surface particles move in
ellipses in planes normal to the surface and parallel to the direction of
propagation. At the surface and at shallow depths this motion is retrograde
(unlike water waves). Particles deeper in the material move in smaller ellipses
with an eccentricity that changes with depth.
The speed of Rayleigh waves (VR) on bulk solids, of the order is slightly
less than the Love-waves velocity.
VR<VL< b
The amplitude of Surface
waves decays as function of
1/sqrt(x) whereas the
amplitude of Body waves
decays as function of 1/x2,
where x is the radial distance
from the epicenter for S
waves or from the hypocenter
for Body waves. Surface
waves therefore decay more
slowly with distance than do
body waves, which spread
out in three dimensions from
a point source (hypocenter).
A
Body waves
A = f(x-2)
x
A
Surface waves
A = f(x-0.5)
Surface waves therefore
tend to be more destructive
than body waves.
x
Surficial expression of waves
P waves
Love waves
Rayleigh waves
S waves
Summary Waves
Sismografi Wood-Anderson
Un terremoto viene registrato attraverso un sismografo che consiste
essenzialmente in un pendolo ed un apparato di registrazione. Il
passaggio dell’onda sismica provoca il movimento del supporto del
pendolo.
Sequenza: P – S
The difference of arrival time of P- and
S-waves at a seismograph is function of
distance of earthquake epicenter.
A 11-minute difference equals to a
distance of ~8600 km; a 8-minute
difference equals to ~5600 km; a 3minute difference equals to ~1500 km,
and so on.
The arrival time difference of P- and S-waves measured at three
seismographic stations reveals the location of the epicenter by smallcircles intersection.
The difference in arrival time between P and S waves is used
In Japan for the Early Warning System…it’s a matter of minutes...that
can save your life...
When two or more
seismometers detect Pwaves (upper), the Japan
Metereological Agency
immediately analyzes the
readings and distributes
the warning information to
advanced users such as;
broadcasting stations and
mobile phone companies,
before the arrival of Swaves (lower).
Local Magnitude (ML) or Richter scale. The Richter magnitude of an
earthquake is determined from the logarithm of the amplitude of waves
recorded by seismographs (adjustments are included to compensate for the
variation in the distance between the various seismographs and the epicenter
of the earthquake). The original formula is:
Richter magnitude ML = log10A - log10A0(d)
Where A is the maximum
excursion of the
seismograph; the
empirical correction
function A0 depends only
on the epicentral distance
of the station, δ.
The Richter scale is
obsolete and has been
replaced by the MMS
scale.
The moment magnitude scale (abbreviated as MMS; denoted as Mw) was
developed in the 1970s to succeed the 1930s-era Richter magnitude scale
(ML). The MMS is now the scale used to estimate magnitudes for all modern
large earthquakes. The magnitude is based on the seismic moment of the
earthquake M0, which is equal to the rigidity of the Earth multiplied by the
average amount of slip on the fault and the size of the area that slipped.
µ = rigidity or shear modulus
Seismic moment M0 = µAD
A = LW = fault plane area
in dyne centimeters (10−7 Nm)
D = mean displacement along fault plane
In order to create a moment magnitude scale (Mw) most consistent with
older magnitude scales such as the Local Moment (or "Richter") scale the
seismic moment (M0) is converted into a logarithmic scale using the following
equation:
Moment magnitude Mw = 2/3log10(M0) – 10.7
The Moment Magnitude Scale based on the Seismic moment M0 and
calculated as Mw = 2/3log10(M0) – 10.7 extends from Mw = 0 to Mw = 10
Exercise 1
Exercise 2. Suppose you want to estimate the proportional
difference fΔE in energy release between earthquakes of two
different moment magnitudes Mw1 and Mw2, where Mw1 is
larger than Mw2
Starting from the equation of Moment magnitude
Mw = 2/3log10(M0) – 10.7
and solving for M0 we obtain:
log10(M0) = 3/2(Mw + 10.7)
and
M01 = 103/2(Mw1 + 10.7)
M02 = 103/2(Mw2 + 10.7)
fDE = M01 / M02
= (103/2(Mw1 + 10.7)) / (103/2(Mw2 + 10.7))
= 103/2(Mw1-Mw2)
The difference fΔE in energy release between earthquakes of
two different moment magnitudes Mw1 > Mw2 is:
fDE = 103/2(Mw1-Mw2)
An increase of 1 on the moment magnitude Mw logarithmic scale
corresponds to a 101.5 ≈ 32 times increase in the amount of energy
released, an increase of 2 corresponds to a 103 = 1000 times increase in
energy, an increase of 3 corresponds to a 104.5 = 31622 times increase in
energy etc.
Japan earthquake of Friday, March 11, 2011; Mw1 = 9.0; Depth 32 km
L’Aquila earthquake of Monday, April 06, 2009; Mw2 = 6.3; Depth 8.8 km
Mw1-Mw2 = 2.7
fDE = 103/2(2.7) = 11.220 The Japan quake was eleven thousands times more
energetic than the L’Aquila earthquake
Each earthquake has only one magnitude, but the effects of any one
earthquake can vary greatly from place to place. The Modified Mercalli
Intensity scale generally deal with the manner in which the earthquake is felt
by people. The higher numbers of the scale are based on observed structural
damage.
Peak ground acceleration (PGA) measured in g is equal to the
maximum ground acceleration that occurred during earthquake
shaking at a location.
Unlike the moment magnitude scale, it is not a measure of the total
energy (magnitude, or size) of an earthquake, but rather of how hard
the earth shakes at a given geographic point.
Correlation with the Mercalli scale
1. Focal mechanisms.
Orientation of fault plane can be represented by beach balls
1.Reconsider Elastic Rebound
2. Focal mechanisms
No offset
Earthquake break
No offset
3. Focal mechanisms
Volume
decrease
(compression)
Volume
increase
(dilation)
Volume
increase
(dilation)
Volume
decrease
(compression)
4. Focal mechanisms
Direction of P-wave
first motion
5. Focal mechanisms
Direction of P-wave
first motion
BEACH BALL
6. Focal mechanisms
La Rete Sismica Nazionale (INGV) registra più di 2000 terremoti l'anno in
Italia. Il catalogo sismico strumentale riporta circa 35.000 terremoti
verificatisi in Italia a partire dal 1975. La sismicità crostale rappresenta la
maggior parte dell'attività sismica registrata (Fig. 1). Terremoti intermedi e
profondi (Fig.2) avvengono nella zona del Tirreno meridionale verso i 300
km di profondità, dove i terremoti possono raggiungere anche M = 7. Questi
terremoti suggeriscono un processo di subduzione attiva (Fig. 3).
Fig. 1
Fig. 2
Fig. 3
Peak ground acceleration (PGA) is a measure of earthquake acceleration
on the ground. It is not a measure of a quake magnitude (Richter or MMS
scales) but rather a measure of how hard the earth shakes in a given
geographic area. The PGA scale is
measured by accelerographs
and it generally correlates
well with the Mercalli scale.
La pericolosità sismica, intesa in
senso probabilistico, è lo scuotimento
del suolo atteso in un dato sito con
una certa probabilità di eccedenza
in un dato intervallo di tempo,
ovvero la probabilità che un certo
valore di scuotimento si verifichi in
un dato intervallo di tempo.
Mappa a destra: PGA
con 10% probabilità di
essere superata in 50
Anni; periodo di ritorno T=475
Anni (INGV)
Il rischio sismico,
determinato dalla
combinazione
della pericolosità,
della vulnerabilità e
dell’esposizione, è la misura
dei danni attesi in un dato
intervallo di tempo, in base al
tipo di sismicità, di resistenza
delle costruzioni e di
antropizzazione (natura,
qualità e quantità dei beni
esposti).
Mappa Intensità su scala
MCS da grado V a grado XI
su dati da 1DC a 1992-> utile
per rischio sismico
Rischio = Pericolosità x Vulnerabilità x Esposizione
Per ridurre il rischio possiamo agire sulla vulnerabilità
Prior to the introduction of modern seismic codes in the late 1960s for
developed countries (US, Japan) many structures were designed without
adequate detailing and reinforcement for seismic protection.
Example: Casa dello Studente, L’Aquila
…non sono necessari controlli periodici su palazzi costruiti negli
anni 60 (prima dell’entrata in vigore delle normative in materia di
edilizia anti-sismica) in una zona
a classe di massima pericolosità
sismica.
Professore dica qualcosa…Seismic retrofitting is the modification of
existing structures to make them more resistant to seismic activity,
ground motion, or soil failure due to earthquakes. With better understanding of
seismic demand on structures and with our recent experiences with large
earthquakes near urban centers, the need of seismic retrofitting is well
acknowledged. Example from San Francisco:
Community Action
Plan for Seismic
Safety (CAPSS)
The CAPSS project will make policy
recommendations to the Department
of Building Inspection (DBI) regarding
the earthquake performance of
most privately-owned, existing
buildings in the city. When enacted,
these policy recommendations would
reduce future earthquake damage
and facilitate the repair of buildings
damaged by earthquakes.
Professore dica qualcosa … 6 Aprile 2009 - L’Aquila
31 Ottobre 2001 - San Giuliano di Puglia - crollo scuola: 27 bambini
morti…"quella sopraelevazione - ha ricordato il procuratore generale della Cassazione,
Francesco Iacoviello - è stata costruita senza rispettare le norme antisismiche
necessarie in una zona, come quella di San Giuliano, ad elevato rischio sismico e il
sindaco non avrebbe dovuto consentire l'apertura di quella scuola senza nemmeno un
certificato di collaudo".
Tsunami can be generated when the sea floor abruptly deforms and
vertically displaces the overlying water. When earthquakes occur beneath
the sea, the water above the deformed area is displaced from its
equilibrium position. More specifically, a tsunami can be generated when
thrust faults associated with convergent or destructive plate boundaries
move abruptly, resulting in water displacement, owing to the vertical
component of movement involved. Movement on normal faults will also
cause displacement of the seabed, but the size of the largest of such events
is normally too small to give rise to a significant tsunami.
Tsunamis in pills:
While everyday wind waves have a wavelength (from crest to crest) of
about 100 metres and a height of roughly 2 metres, a tsunami in the deep
ocean has a wavelength of about 200 kilometres. Such a wave travels at
well over 800 kilometres per hour over deep water.
As the tsunami approaches the coast and the waters become shallow,
wave shoaling compresses the wave and its velocity slows below 80
kilometres per hour. Its wavelength diminishes to less than 20 kilometres
and its amplitude grows enormously. Since the wave still has the same very
long period (time from crest to
crest), the tsunami may
take minutes to reach full
height. Except for the very
largest tsunamis,
the approaching wave does
not break, but rather appears
like a fast-moving tidal bore.
Small amplitude
theory for wave
celerity
Wave celerity (speed):
where g is acceleration of gravity
980 cm/sec2
Wave Period, which is the length of time it takes for a wave to pass a fixed
point (crest to crest), is:
T=L/C
T=L/C
In the open ocean, a Tsunami typical wave lenght L is 200 km. Therefore, the
term d/L is very small, on the order of 0.03; The equation of celerity C
becomes:
C = sqrt(gL/2pi)= sqrt(980 X 2000000/2pi) = 636 km/h (for a 200 km
L wave)
And the Period T of such a wave is:
T = L / C = 200km / 636km/h = 19 min
Whereas a typical amplitude of a Tsunami is of only about 1 metre.
Long periods and small amplitudes make tsunamis difficult to detect
over deep water. Ships rarely notice their passage.
As the tsunami approaches the coast and the waters become shallow,
wave shoaling compresses the wave and its velocity slows below 80
kilometres per hour:
C=
= sqrt(980 X 5000) =
80 km/h (for a 50 m-deep ocean)
Its wavelength L diminishes to less
than 20 kilometres and its amplitude
A grows enormously,
A ~ 1/d1/4
whereas he Period T remains the
same:
T = L / C = 20 / 80 = 15 min
Since the wave still has the same very long period, the tsunami may take
minutes to reach full height. The approaching wave does not usually break,
but rather appears like a fast-moving tidal bore.
Since the wave still has the same very long period, the approaching wave
appears like a fast-moving tidal bore. The whole ocean is coming upon
land! e.g The 2011 Japan tsunami
Note the enormous wavelenght (~200 km) of Tsunami waves
Ancient Mediterranean Tsunami May Strike Again
A map depicts the Mediterranean Sea (green) and the degree of sea-level
displacement caused by a tsunami after the Crete earthqake (magnitude ~8)
that wracked the Mediterranean region in A.D. 365.
Such tsunamis are relatively frequent in the region, striking perhaps as often
as every 800 years.