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INGENIERIA SISMORRESISTENTE
Fundamentos de Sismologa e Ingenieria Sismolgica
M.I. Jos Velsquez Vargas Maestra en Ing. Sismorresistente e Ing. Sismolgica (Rose School, Italia)
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Terremotos
Terremoto de Pisco (15/08/2007)
Fuente: Informe de terremotos ocurridos en el mundo - Colegio de Ingenieros del Per
Terremoto de Chile (27/02/2010)
Terremoto de Hait (12/01/2010)
Terremoto de Japn (11/03/2011)
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Qu es un terremoto?Son vibraciones de la corteza terrestre, generadas por distintos fenmenos, como
la actividad volcnica, la cada de techos de cavernas subterrneas y hasta por
explosiones. Sin embargo, los sismos ms severos y ms importantes desde el
punto de vista de la ingeniera, son los de origen tectnico.
Estos se deben a los desplazamientos ms bruscos de las grandes placas en que
est subdividida dicha corteza.
Placas que conforman la corteza terrestre
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major eqs 4
SISMICIDAD GL0BAL
95% de la energa liberada por terremotos se originan en regionesestrechas alrededor de la Tierra: estas zona marcan los bordes de las placas tectnicas
Sismicidad global entre 1975-1999 con terremotos de magnitude mayor a 5.5
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Cinturn de Fuego del PacficoEst situado en las costas del ocano Pacfico y se caracteriza por concentrar
algunas de las zonas de subduccin ms importantes del mundo, lo que ocasiona
una intensa actividad ssmica y volcnica en las zonas que abarca.
Tiene 452 volcanes y concentra ms del 75 % de los volcanes activos e inactivos
del mundo. Alrededor del 90 % de los terremotos del mundo y el 80 % de los
terremotos ms grandes del mundo se producen a lo largo del Cinturn de
Fuego.
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Qu es un terremoto?La presiones que se generan en la corteza por los flujos de magma desde el
interior de la tierra llegan a vencer la friccin que mantienen en contacto los
bordes de las placas y producen cadas de esfuerzo y liberacin de enormes
cantidades de energa almacenada en la roca. La energa se libera
principalmente en forma de ondas vibratorias que se propagan a grandes
distancias a travs de las rocas de la corteza.
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major eqs 7
LOS TERREMOTOS
MS GRANDES
DESDE 1900
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CLCULO DEL PELIGRO SSMICO
0.1
1
10
3.7 4 4.3 4.6 4.9 5.2 5.5 5.8 6.1 6.4 6.7 7 7.3 7.6 7.9
ZS 63 1936-1980
1915-1980
1895-1980
1843-1980
1787-1980
1626-1980
1501-1980
1300-1980
1000-1980
Scelta
Nu
me
ro n
orm
aliz
za
to
(10
0 a
nn
i)
Magnitudo
7.0008, 0.18595
0.1
1
10
3.7 4 4.3 4.6 4.9 5.2 5.5 5.8 6.1 6.4 6.7 7 7.3 7.6 7.9
ZS 63 1936-1980
1915-1980
1895-1980
1843-1980
1787-1980
1626-1980
1501-1980
1300-1980
1000-1980
Scelta
Nu
me
ro n
orm
aliz
za
to
(10
0 a
nn
i)
Magnitudo
7.0008, 0.18595
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KOBE EARTHQUAKE OF JANUARY 17, 1995
Magnitude: 6.9 (Mw)
Duration: 20 Seconds
Number of Injured: 33,000
Number of Deaths: 5,470
Epicenter: 20 km underneath the island of Awaji
Across a strait from Kobe
Direct and Indirect Costs:
$200 Billion in damages (4% of Japan's GDP)
$100 Billion to restore basic functions
$50 Billion in losses due to economic dislocation and business interruption
$50 Billion in losses of private property
Structural Damage (Buildings):
144,032 Buildings destroyed by ground shaking
7,456 Buildings destroyed by fire
82,091 Collapsed buildings
86,043 Severely damaged buildings
Structural Damage (Highways/ Bridges/Ports):
All Kobe ports shut down to international shipping
Damage to containing loader piers
All access to Kobe via highway and railway blocked
Miscellaneous Facts:
Largest peak accelerations 0.8g to greater than 1g
300,000 People were left homeless
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TERREMOTO DE PAKISTAN M7.6 DE 8 DE OCTUBRE DE 2005
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MAPA DE PELIGRO SSMICO DE PAKISTAN
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Mo
vim
ien
to d
e la
s p
laca
s te
ct
nic
as
Zona de divergencia
Zona de fallas
Zona de convergencia
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Zona de divergenciaSe generan cuando las placas van en direcciones opuestas, por lo tanto se
separan. Al separarse dejan el camino abierto para que ingrese el magma desde
el centro de la tierra. Como la mayora de las zonas de divergencia estn bajo la
superficie el magma al entrar en contacto con el agua se enfra y genera un
cuerpo slido, una roca.
En esta zona casi no se producen sismos de gran relevancia.
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Zona de fallasSe producen cuando las placas van en direcciones opuestas pero paralelamente,
es decir, se rozan de lado a lado. Producen sismos menores y actividad volcnica
casi nula.
Desde San Francisco (EE. UU.) hasta la pennsula de Baja California en Mxico,
es una zona de falla.
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Zona de convergenciaSon zonas en donde dos placas tectnicas se dirigen al mismo lugar, por lo tanto
colisionan, dando lugar a las zonas de subduccin. La placa ms densa
comienza a penetrar debajo de la placa menos pesada, se produce entonces una
zona de contacto directo entre ambas placas que genera gran cantidad de sismos
y actividad volcnica. Generalmente son las placas ocenicas las que se hunden
bajo las placas continentales.
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Sismos histricos
Terremoto en Chile el 27/02/2010, demagnitud 8.1 en la escala de Richter
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Sismos histricos
Terremoto y tsunami en Japn el 11/03/2011, de magnitud 8.9 en laescala de Richter
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Sismos histricos
Terremoto en Alaska el 28/03/1964, de magnitud 9 en la escala de Richter
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Sismos histricos
Terremoto en Indonesia el 26/12/2004, de magnitud 9.1 en la escala de Richter
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Sismos histricos
Megaterremoto registrado en Chile (Valdivia) el 22/05/1960, con una intensidad de 9.4 en la escalade Richter. Es considerado el peor terremoto en la historia de la humanidad
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Magnitud e Intensidad de un terremoto
Magnitud: La magnitud de un sismo corresponde a la energa liberada por la rotura o el desplazamiento de rocas en el interior terrestre. Se mide mediante la escala
de Richter; es una escala objetiva porque se basa en los datos extrados del registro de
sismgrafos.
Intensidad: La intensidad de un sismo corresponde a los efectos producidos por la accin de las ondas superficiales. Se puede medir mediante la escala MSK o
mediante la escala de Mercalli. Las dos son medidas subjetivas porque dependen de la
apreciacin de las personas
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ESCALA RICHTER (Se expresa en nmeros rabes)Representa la energa ssmica liberada en cada terremoto y se basa en el registro
sismogrfico.
Es una escala que crece en forma potencial o semilogartmica, de manera que cada punto
de aumento puede significar un aumento de energa diez o ms veces mayor. Una magnitud
4 no es el doble de 2, sino que 100 veces mayor.
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ESCALA MERCALLI Se expresa en nmeros romanos.Creada en 1902 por el sismlogo italiano Giusseppe Mercalli, no se basa en los
registros sismogrficos sino en el efecto o dao producido en las estructuras y en la
sensacin percibida por la gente. Para establecer la Intensidad se recurre a la
revisin de registros histricos, entrevistas a la gente, noticias de los diarios pblicos
y personales, etc. La Intensidad puede ser diferente en los diferentes sitios
reportados para un mismo terremoto (la Magnitud Richter, en cambio, es una sola) y
depender de:
a)La energa del terremoto,
b)La distancia de la falla donde se produjo el terremoto,
c)La forma como las ondas llegan al sitio en que se registra (oblicua, perpendicular,
etc,)
d)Las caractersticas geolgicas del material subyacente del sitio donde se registra la
Intensidad y, lo ms importante,
e)Cmo la poblacin sinti o dej registros del terremoto.
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El movimiento ssmico del suelo se transmite a los edificios que se apoyen sobre ste. La
base del edificio tiende a seguir el movimiento del suelo, mientras que, por inercia, la masa
del edificio se opone a ser desplazada dinmicamente y a seguir el movimiento de su base.
Las fuerzas de inercia que se generan por la vibracin en los lugares donde se encuentran
las masas del edificio se transmiten a travs de la estructura por trayectorias que dependen
de la configuracin estructural. Estas fuerzas generan esfuerzos y deformaciones que
pueden poner en peligro la estabilidad de la construccin.
EFECTOS SSMICOS EN LOS EDIFICIOS
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LA TIERRA Y SUS TERREMOTOS
Fallas
Terremotos
Fallas activadas por terremotos
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FALLAFRACTURA EN LA ROCA QUE
MUESTRA DESPLAZAMIENTO
RELATIVO
Falla por deslizamiento:el sentido prinicipal del
movimiento en el plano de
falla es horizontal
Falla por inmersin: el sentido principal del
movimiento en el plano de
falla es vertical
Falla Emerson en California:
Produjo el terremoto de Landers
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earth & earthquakes 27
FALLAS POR INMERSIN
Dip-slip
Faulting that produces vertical displacements along the strike of the fault.
90 dip is vertical.
Two types of dip-slip faults: normal fault and reverse fault.
Normal fault: when the rock on that side of the fault hanging over fracture (the hanging wall) plane slips downward.
Reverse fault: when the hanging wall moves upwards over the footwall.
A thrust fault is a special type of reverse fault in which the dip of the fault is small (shallow). Subduction zones (e.g., Cascadia in the Pacific North West) are the sites of many thrust earthquakes.
NormalReverse
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earth & earthquakes 28
FALLAS POR INMERSIN
1) Terms: Hanging wall and footwall
2) Normal faults
(a) Grabens
(b) Horsts
3) Reverse faults
a) low angle called Thrust faults
4) Oblique-slip faults
Thrust
Oblique
Blind thrust
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earth & earthquakes 29
DIP-SLIP
FAULTS (3)
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earth & earthquakes 30Source: John S. Shelton
NORMAL FAULT: HANGING WALL
DOWN
Key
Bed
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earth & earthquakes 31
NORMAL FAULTS
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earth & earthquakes 32
REVERSE FAULT (CALLED THRUST FAULT IF SHALLOW ANGLE)
Younger
(Hanging wall Up)
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earth & earthquakes 33
REVERSE FAULTS
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EARTHQUAKE GENESIS
Posicin originalSIN DEFORMACIN
Almacenamiento de energaDEFORMACIN PROGRESIVA
Ruptura con emisin de energa : TERREMOTORDESPLAZAMIENTO PERMANENTE
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earth & earthquakes 35
TEORA DEL REBOTE ELSTICO
QuickTime e undecompressore
sono necessari per visualizzare quest'immagine.
Harry Fielding Reid postulated that the forces causing earthquakes were not close to the earthquake source but very distant. The earthquake is, then, the result of the elastic rebound of previously stored elastic strain energy
in the rocks on either side of the fault.
After the devastating 1906 San Francisco, California earthquake, a fault trace was discovered that could be followed along the ground in a more or less straight line for 270 miles. It was found that the Earth on one side of the fault had slipped compared to the Earth on the other side of the fault by
up to 7 m.
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earth & earthquakes 36
REBOTE
ELSTICO
Mechanism for earthquakes
Rocks on sides of fault are deformed by tectonic forces
Rocks bend and store elastic energy
Frictional resistance holding the rocks together is overcome by tectonic forces
Earthquake mechanism
Slip starts at the weakest point (the focus)
Earthquakes occur as the deformed rock springs back to its original shape (elastic rebound)
The motion moves neighboring rocks
And so on
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earth & earthquakes 37
RPLICAS
-The change in stress that follows a mainshockcreates smaller earthquakes called aftershocks
- The aftershocks
illuminate the fault
that ruptured in the mainshock
Red dots show location ofaftershocks formed by 3earthquakes in Missouriand Tennessee in 1811/1812
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earth & earthquakes 38
PROFUNDIDAD DE LOS TERREMOTOS
Earthquakes originate at depths ranging from 5 to nearly 700 kilometers.
Definite patterns exist:
shallow focus occur along mid ocean ridges;
deep earthquakes occur in Pacific landward of oceanic trenches;
central continent (intraplate) earthquakes of various causes: some causes still uncertain.
Devastating earthquakes less than 60 kilometers because cold rock more elastic, transmits waves better than warmer rock below.
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earth & earthquakes 39
EARTHQUAKE DEPTH AND PLATE TECTONIC
SETTING
Subduction Zones discovered by Benioff
Weakest are the divergent zone earthquakes
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earth & earthquakes 40
TERREMOTOS EN ZONAS DE SUBDUCCIN
Recent example, 9.0 Christmas 2004 Earthquake and Tsunami, Sumatra
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earth & earthquakes 41
SAN FRANCISCO EARTHQUAKE APRIL 18, 1906
Fault trace 2 miles north of the Skinner Ranch at Olema. View is north.
Fence offset by the causative fault on ranch of E.R. Strain, 1 1/2 miles north of Bolinas Lagoon, looking northeast. The sheer offset is 8 1/2 feet; the total displacement, shown partly by crooking of fence, is 11 feet.
Example of a strike-slip fault
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earth & earthquakes 42
ALASKA EARTHQUAKE OF MARCH 27, 1964
Example of a thrust fault
Hanning Bay fault scarp on Montague Island, looking northwest. Vertical displacement in the foreground, in rock, is about 12 feet. The maximum measured displacement of 14 feet is at the beach ridge near the trees in the background.
Hanning Bay fault on Montague Island, looking southwest from the bay. The fault trace on the ridge is marked by active landslides.
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earth & earthquakes 43
SAN FERNANDO EARTHQUAKE OF FEBRUARY 9, 1971
Example of a reverse fault
Trace of the main reverse fault where it crosses Little Tujunga Road. By the time this photograph was taken a dirt ramp at right had been built up the scarp. The scarp indicates more than 1-meter reverse dip-slip movement. The fence indicates little strike-slip displacement at this place, which is near the last end of the line of surface rupture.
Compression of freeway
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instrumental seismology 44
INSTRUMENTAL
SEISMOLOGY Seismic waves Theory of the seismograph Locating earthquakes Magnitude Fault plane solutions
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instrumental seismology 45
ORIGIN OF SEISMIC WAVES
A wave is a disturbance that transfers energythrough a medium.
Seismic waves are generated by manydifferent processes:
earthquakes, volcanoes,
explosions (especially nuclear bombs),
wind,
planes (supersonic),
people,
vehicles.
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instrumental seismology 46
MAGNITUDE (1)
Magnitude measures the strenght of the earthquake.It is proportional to the elastic energy released by the quake.It is measured on the basis of the wave amplitude on the seismogram considering the epicentral distance.The most utilized magnitudes in the last century were the following:
1) original magnitude for local shocks obtained using the standardWood-Anderson torsion seismometer indicated as ML, or MAW according tothe Karnik nomenclature (circular of 1976);2) magnitude from body waves obtained using short or long periodinstruments, for epicentral distance greater than 1800 km, called mB if itis derived from the long period recording and mb if derived from the shortperiod one, respectively MPV and M according to the Karnik nomenclature(circular of 1976);3) magnitude from surface waves recorded by long periodseismometers, for epicentral distance greater than 2200 km, indicated asMS, or MLH according to the Karnik nomenclature (circular of 1976).
There is also a magnitude calculated from the duration of the recording of a local shock.
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instrumental seismology 47
MAGNITUDE (2)
Kanamori (1977) has recently developed a standard magnitude scale that iscompletely independent of the type of instrument. It is called the momentmagnitude, indicated with M or MW, and it comes from the seismic moment M0.
M0 = Adwhere is the shear strength (rigidity modulus) of the faulted rock (about 3.31010
N/m2), A is the area of the fault (i.e.: the product of its length and width), and d is the average displacement on the fault (i.e.: the slip which is the length of the slip vector of the rupture measured in the plane of the fault).There is a standard way to convert a seismic moment to a magnitude (Hanks and Kanamori, 1979). The equation is:
Mw logM0
1.510.7
with M0 in dynexcm.
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instrumental seismology 48
LOCAL MAGNITUDE
QuickTime e undecompressore
sono necessari per visualizzare quest'immagine.
The concept of magnitude was introduced by Richter (1935): the magnitude of any shock is taken as the logarithm of the maximum trace amplitude with which the standard torsion seismometer would register that shock at an epicentral distance of 100 km.
ML logA logA0
Charles F. Richter (1900-1985)
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instrumental seismology 49
DURATION MAGNITUDE
There is also a magnitude calculated from the duration of the recording of alocal shock: the equation has to be derived empirically by comparison withactual ML estimates. Duration magnitude is indicated with MD and thegeneral relation has the form:
where is the duration of the signal, computed from the P-wave arrival tothe moment when the earthquake wave amplitude has the same amplitudeas the background noise, is the epicentral distance and a, b, and c areparameters calculated by regression analysis. In practice, c is very smallindicating a slight dependence of MD on distance.
MD ablog c
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instrumental seismology 50
BODY-WAVE MAGNITUDE
The general formula recommended fromthe IASPEI's Committee of Zurich 1967is the following, given by Gutenberg in1945:
where A is the maximum true amplitude and T the period of the used wave, Q is the Gutenberg-Richter's correction value for hypocentral depth and distance and is the station correction obtained by statistical analysis of the resulting systematic divergences.
m logA
T
maxQ
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instrumental seismology 51
SURFACE-WAVE MAGNITUDE
The magnitude from surface waves can also be computed using different waves andvertical or horizontal components. The most common is the one computed with thewaves of maximum amplitude having period from 10 to 30 seconds. The magnitudeexpression, given by Karnik (1962) is:
where A is the maximum true amplitude of the wave used, computed as the square root of the sum of the squares of the two horizontal components, T is the period and d is the epicentral distance in degrees.
M logA
T
max1.66logd 3.3
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instrumental seismology 52
SUMMARY ABOUT MAGNITUDES
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instrumental seismology 53
COMPARISON OF THE DIFFERENT MAGNITUDES
Only Mw does not saturate
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seismic hazard 54
PELIGRO SSMICO
DSHA
PSHA
Ingredients of PSHA
Hazard maps
Ground motion parameters and maps
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seismic hazard 55
RISK = HAZARD * VULNERABILITY * EXPOSED VALUE
RISK = probability to observe a certain damage or loss of operativity
HAZARD = probability to observe a certain ground shaking
(acceleration, intensity, etc.)
in a fixed time period
VULNERABILITY = tendency of the study item (building, complex system, etc.)
to suffer damage or modifications
EXPOSED VALUE = (economic, social, etc.) quantification of the study item
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seismic hazard 56
DETERMINISTIC AND STATISTICAL-
PROBABILISTIC MODELS
Determinism = the process IS KNOWNand it is possible to write the equation
E.g.: gravity law s = 1/2 g*t2
Probabilism = the process IS NOT KNOWNand it is possible to approximate itfrom observationsE.g.: exit poll
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seismic hazard 57
APPROACHES FOR SHA
SEISMIC HAZARD ASSESSMENT
Historical determinism
Historical probabilism
Seismotectonic probabilism
Non-Poissonian probabilism
Eq prediction
Reference ground motion
Detailed scenario
Probabilistic approaches Deterministic approaches
Muir Wood (1993)
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seismic hazard 58
DETERMINISTIC APPROACH
Select a small number of individual earthquake scenarios: M, R (Location) pairs
Compute the ground motion for each scenario (typically use ground motion with 50% or 16% chance of being exceeded if the selected scenario earthquake occurs
Select the largest ground motion from any of the scenarios
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seismic hazard 59
PROBABILISTIC APPROACH (1)
Source Characterization Develop a comprehensive set of possible scenario
earthquakes: M, R (location)
Specify the rate at which each scenario earthquake (M, R) occurs
Ground Motion Characterization Develop a full range of possible ground motions for each
earthquake scenario (number of std dev above or below the median)
Specify the probability of each ground motion for each scenario
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seismic hazard 60
PROBABILISTIC APPROACH (2)
Hazard Calculation
Rank scenarios (M,R, ) in order of decreasing severity of shaking
Table of scenarios with ground motions and rates
Sum up rates of scenarios (hazard curve)
Select a ground motion for the design hazard level
Back off from worst case ground motion until the sum of the rates of scenarios exceeding the ground motion is large
enough to warrant consideration (e.g. the design hazard
level)
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seismic hazard 61
SEISMIC RISK APPLICATION IN THEDETERMINISTIC-PROBABILISTIC SPECTRUM
McGuire (2001)
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seismic hazard 62
EXAMPLES OF EARTHQUAKE DECISIONS
McGuire (2001)
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seismic hazard 63
DETERMINISTIC APPROACHES
SEISMIC HAZARD ASSESSMENT
Historical determinism
Historical probabilism
Seismotectonic probabilism
Non-Poissonian probabilism
Eq prediction
Reference ground motion
Detailed scenario
Probabilistic approaches Deterministic approaches
Muir Wood (1993)
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seismic hazard 64
STEPS OF THE DETERMINISTIC APPROACH
1. Identification and characterization of all earthquake
sources capable of producing significant ground
motion at the site.
2. Selection of a source-to-site distance parameter for
each source zone. In most DSHAs, the shortest
distance between the source zone and the site
of interest is selected.
3. Selection of the controlling earthquake (i.e., the
earthquake that is expected to produce the
strongest level of shaking), generally expressed
in terms of some ground motion parameter, at
the site.
4. The hazard at the site is formally defined, usually in
terms of the ground motions produced at the site
by the controlling earthquake. Its characteristics
are usually described by one or more ground
motion parameters obtained from predictive
relationships.
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seismic hazard 65
DETERMINISTIC APPROACH
SOURCE CHARACTERISATION
Focus = historical & instrumental seismicity
Mechanism = geology, instrumental seismicity
Magnitude = geology, instrumental seismicity
PATH DESCRIPTION
Intensity attenuation = historical seismicity
acceleration attenuation = instrumental seismicity
SITE EFFECTS
Stratigraphy = geology, instrumental seismicity
Morphology = geology
Reference ground motion
-Empirical attenuation relations
Detailed scenario
-Modeling
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seismic hazard 66
PSHA AND DETERMINISTIC SCENARIO FOR A
SITE
PSHA
1000-yr return period PGA on rock
Deterministic Scenario
Regional max mag = 6.4
(Kijko and Graham 1999 method)
PGA attenuation relation for rock
0.23 Ambraseys et al. 1996
0.30 Sabetta & Pugliese 1987
0.30 Chiaruttini & Siro 1981
PSHA
1000-yr return period PGA on rock
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seismic hazard 67
GENERATIONS OF
PSHA
SEISMIC HAZARD ASSESSMENT
Probabilistic Approaches
Historical Determinism
Historical Probabilism
Seismotectonic Probabilism
Non-Poissonian Probabilism
Earthquake Prediction
(Muir-Wood, 1993)
Deterministic Approaches
Reference Shaking
Detailed Scenario
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seismic hazard 68
THE FIRST HAZARD MAP
(?)
Map of world earthquake occurrence by Robert Mallet in 1854
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seismic hazard 69
1ST GENERATION
HISTORICAL
DETERMINISM
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seismic hazard 70
2ND GENERATION
HISTORICAL
PROBABILISM
P[Imax i] Im axF (i) exp{[(w i)/(wu)]k}
XF (x) i /(n1)
iy ln{ln[ XF (xi)]}
iy (xi u)
The Gumbel approach
Given Imax = max Xi, with i=1, , n and n largeType 1: no upper limit of Xi
ApplicationPutting
P[Imax i] FIm ax(i) exp[e iu ]
Type 3: upper limit of Xi
Introducing the reduced variable
Gumbel approach (1)
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seismic hazard 71
2ND GENERATION HISTORICAL
PROBABILISM
Example of the Gumbel approachGiven an eq catalogue, lets take the maximum annual (extreme)magnitudes and order them x1, x2, , xn: xi xi+1 " i
XF (x) i /(n 1) lets assign the annual non exceedence probability:
iy ln{ ln[ XF (xi)]}
lets calculate the Gumbel reduced variable:
iy (xi u) we obtain:
lets compute and u by regression analysis:
lets compute the hazard estimates(e.g.: extreme exceeded with probability p in T years:
p,Ty u {ln[ ln(1 p)] lnT}/
Gumbel approach (2)
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seismic hazard 72
2ND GENERATION
HISTORICAL
PROBABILISM
i n je
ij2
/ c2
je ij
2 / c 2
j
(u u0) 1
Ti
i
P[u u0m min
mu
| di,mj] fm(m)dm
The smoothed seismicity approach
The hazard computation is based on the number ni of earthquakes with magnitude greater than Mref in each cell i of a grid: this count represents the maximum likelihood estimate of 10a for that cell. The grid of ni values is then smoothed spatially by multiplying by a Gaussian function with correlation distance c, obtaining :
The annual rate (u>u0) of exceeding ground motion u0 at a specific site is determined from a sum over distance and magnitude
fm(m) bln10 10b(mm 0)
110b(mum 0)
P[u u0 | di,mj] 1
2
lnu0 lnu(di ,m j)
2
where
(from Frankel, 1995 and
Lapajne et al., 1997)
The smoothed seismicity approach (1)
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seismic hazard 73
2ND GENERATION
HISTORICAL
PROBABILISM The smoothed seismicity approach (2)
Options:
the activity rate can be computed considering different seismicity models;
the b-value and Mmax can vary in space;
different attenuation relations can be used.
Seismicity models:
m0 = 3, low seismicity contributes to define hazard
(activity rates normalized over different Ts
according to the zone)
m0 = 5, only high seismicity contributes to define hazard
(activity rates normalized over different Ts
according to the zone)
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seismic hazard 74
2ND GENERATION:
HISTORICAL
PROBABILISM
The smoothed seismicity approach (3)
Zonation models
in each zone b-value and Mmax are constant
Average PGA
with T=475 from
zonation models
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seismic hazard 75
3RD GENERATION
SEISMOTECTONIC PROBABILISM The 4 steps
of PSHA
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seismic hazard 76
3RD GENERATION
SEISMOTECTONIC PROBABILISM The Cornell (1968) approach (1)
P[E] P E | S fs(s)ds
z ii1
N
iP(Z z |m,r) fr o
r
mo
mu
(m) if (r)drdm
T t /ln(1P(ZT z))
The Cornell (1968) approach
Application
The total probability theorem
for all SZs GR distributionSZ geometry
If it is a Poisson process (stationary, independent, non-multiple events)
SF (s) P[S s]
Sf (s) SF (s)/swhere is the PDF of S
is the CDF of Sand
where: T=return period;
t=period of analysis
Attenuation model
P ZT z 1 ezT
Mean annual rate
of exceedence
Mean annual rate
of occurrence
-
seismic hazard 77
3RD GENERATION
SEISMOTECTONIC PROBABILISM The Cornell (1968) approach (2)
Working hypotheses of the
Cornell (1968) approach
The eq magnitude is exponentially distributed
The eq number in time forms a Poisson process
The seismicity is spatially uniform inside the seismic sources (faults,
areas, etc.)
(from Algermissen & Perkins, 1976)
-
seismic hazard 78
3RD GENERATION
SEISMOTECTONIC PROBABILISM The Cornell (1968) approach (3)
a b
c
d e
Contributing information
a = geology, historical & instrumental
seismicity
b = historical & instrumental
seismicity
c = instrumental seismicity for PGA
historical seismicity for intensity
d = statistics
e = statistics
(from Algermissen & Perkins, 1976)
-
seismic hazard 79
3RD GENERATION
SEISMOTECTONIC PROBABILISM The Cornell (1968) approach (4)
The actual steps
in PSHA computation
A) Definition of SZs
B) Seismicity characterisation
Attenuation relation
C) Probability of ground motion
exceedence
D) Probability of ground motion
exceedence in T yrs
Uniformely distributed seismicity
Gutenberg-Richter law
Poisson distribution
(from Algermissen & Perkins, 1976)
-
seismic hazard 80
SOURCE-TO-
SITE
DISTANCE
Arcs of circles with centers at the site approximate in Seisrisk III the area of the quadrilater.
Examples of different earthquake source geometries: a) short fault that can be modelled as a point source; b) shallow fault that can be modelled as a linear source; c) 3D source zone modelled as an area source
(from Kramer, 1996)
-
seismic hazard 81
FR(R)
Variations of source-to-site distance for different source zone geometries. The shape of the PDF can be visualized by considering the relative portions of the source zone that would fall between each of a series of circles (or spheres for 3D problems) with equal differences in radius
(from Kramer, 1996)
fL(l)dl fR(r )dr
fR(r) fL(l)dl
dr
fL(l) l /Lf
l2 r 2 rmin2
fR(r) r
Lf r2 rmin
2
(b)
Many single sources, see (a)
-
seismic hazard 82
FM(M)
GUTENBERG - RICHTER
LAW
lognm abm
nm 0em
nm 0e (mm0 )
with m0 = threshold magnitude
b ln10
0 10a
FM (m) P[M m | M m0] nm0 nm
nm0
1 e (mm0 )
fM (m) d
dmFM (m) e
(mm0 )
Gutenberg-Richter recurrence law: a) meaning of a and b parameters; b) application of Gutenberg-Richter law to worldwide seismicity data
-
seismic hazard 83
FM(M)
BOUNDED GUTENBERG -
RICHTER LAW
Bounded Gutenberg-Richter recurrence laws for mo=4 and mmax=6, 7, and 8 constrained by constant seismicity rate
where =exp(m0) is the rate of occurrence of earthquakes exceeding m0
nm exp m m0 exp mmax m0
1 exp mmax m0
FM (m) P[M m |m0 M mmax ] 1 e (mm0 )
1 e (mmax m0 )
fM (m) e (mm0 )
1 e (mmax m0 )
-
seismic hazard 84
CHARACTERISTIC
EARTHQUAKE
Youngs & Coppersmith developed a generalized magnitude-frequency PDF that combined an exponential magnitude distribution at lower magnitudes with a uniform distribution in the vicinity of the characteristic earthquake.
Comparison of recurrence laws from bounded Gutenberg-Richter and characteristic earthquake models (from Youngs & Coppersmith, 1985).Inconsistency of mean annual rate of exceedance as determined from seismicity data and geologic data (from Schwartz and Coppersmith, 1984).
-
seismic hazard 85
SEISMIC HAZARD
CURVE The individual components of the Eq are
complicated that the integrals cannot be evaluated analitically: numerical integration is required
P[E] P E | S fS (s)ds
P[Z z] iP(Z z |m,r) f
r o
r
mo
mu
(m) if (r)drdm
z ii1
NS
iP(Z z |m,r) fr o
r
mo
mu
(m) if (r)drdm
z ik1
N R
j1
NM
i1
NS
P(Z z |m j ,rk ) fM i (m j ) fR i (rk )mr
z ik1
N R
j1
NM
i1
NS
P(Z z |m j ,rk )P[M m j ]P[R rk ]
P ZT z 1 ezT
Magnitude and distance ranges are divided into segments
Poisson model
PGA with 10% exceedance probability over various exposure times for 14 areas in North America
Mean annual rate
of exceedence
Hazard curve
Exceedence
probability
-
seismic hazard 86
0.001
0.01
0.1
1
0.1 1
ponti del Veneto
exc
ee
de
nce
pro
bab
ilit
y in
50
yrs
PGA
Spresiano
BotteonPeron
Fener
Hazard curves for 4 bridges in Veneto