ingenieria sismologica

INGENIERIA SISMORRESISTENTE

Fundamentos de Sismologa e Ingenieria Sismolgica

M.I. Jos Velsquez Vargas Maestra en Ing. Sismorresistente e Ing. Sismolgica (Rose School, Italia)

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)

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

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

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.

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.

major eqs 7

LOS TERREMOTOS

MS GRANDES

DESDE 1900

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

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

TERREMOTO DE PAKISTAN M7.6 DE 8 DE OCTUBRE DE 2005

MAPA DE PELIGRO SSMICO DE PAKISTAN

Mo

vim

ien

to d

e la

s p

laca

s te

ct

nic

as

Zona de divergencia

Zona de fallas

Zona de convergencia

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.

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.

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.

Sismos histricos

Terremoto en Chile el 27/02/2010, demagnitud 8.1 en la escala de Richter

Sismos histricos

Terremoto y tsunami en Japn el 11/03/2011, de magnitud 8.9 en laescala de Richter

Sismos histricos

Terremoto en Alaska el 28/03/1964, de magnitud 9 en la escala de Richter

Sismos histricos

Terremoto en Indonesia el 26/12/2004, de magnitud 9.1 en la escala de Richter

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

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

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.

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.

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

LA TIERRA Y SUS TERREMOTOS

Fallas

Terremotos

Fallas activadas por terremotos

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

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


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


DIP-SLIP

FAULTS (3)

earth & earthquakes 30Source: John S. Shelton

NORMAL FAULT: HANGING WALL

DOWN

Key

Bed


NORMAL FAULTS


REVERSE FAULT (CALLED THRUST FAULT IF SHALLOW ANGLE)

Younger

(Hanging wall Up)


REVERSE FAULTS

EARTHQUAKE GENESIS

Posicin originalSIN DEFORMACIN

Almacenamiento de energaDEFORMACIN PROGRESIVA

Ruptura con emisin de energa : TERREMOTORDESPLAZAMIENTO PERMANENTE


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.


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


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


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.


EARTHQUAKE DEPTH AND PLATE TECTONIC

SETTING

Subduction Zones discovered by Benioff

Weakest are the divergent zone earthquakes


TERREMOTOS EN ZONAS DE SUBDUCCIN

Recent example, 9.0 Christmas 2004 Earthquake and Tsunami, Sumatra


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


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.


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

instrumental seismology 44

INSTRUMENTAL

SEISMOLOGY Seismic waves Theory of the seismograph Locating earthquakes Magnitude Fault plane solutions


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.


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.


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.


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)


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


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


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


SUMMARY ABOUT MAGNITUDES


COMPARISON OF THE DIFFERENT MAGNITUDES

Only Mw does not saturate

seismic hazard 54

PELIGRO SSMICO

DSHA

PSHA

Ingredients of PSHA

Hazard maps

Ground motion parameters and maps

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

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

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)

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

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

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)

seismic hazard 61

SEISMIC RISK APPLICATION IN THEDETERMINISTIC-PROBABILISTIC SPECTRUM

McGuire (2001)

seismic hazard 62

EXAMPLES OF EARTHQUAKE DECISIONS

McGuire (2001)

seismic hazard 63

DETERMINISTIC APPROACHES


Historical determinism

Historical probabilism

Seismotectonic probabilism

Non-Poissonian probabilism

Eq prediction


Detailed scenario

Probabilistic approaches Deterministic approaches

Muir Wood (1993)

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.

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


-Empirical attenuation relations

Detailed scenario

-Modeling

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

seismic hazard 67

GENERATIONS OF

PSHA


Probabilistic Approaches

Historical Determinism

Historical Probabilism

Seismotectonic Probabilism

Non-Poissonian Probabilism

Earthquake Prediction

(Muir-Wood, 1993)

Deterministic Approaches

Reference Shaking

Detailed Scenario

seismic hazard 68

THE FIRST HAZARD MAP

(?)

Map of world earthquake occurrence by Robert Mallet in 1854

seismic hazard 69

1ST GENERATION

HISTORICAL

DETERMINISM

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)

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)

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)

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)

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

seismic hazard 75

3RD GENERATION

SEISMOTECTONIC PROBABILISM The 4 steps

of PSHA

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


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


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


seismic hazard 79

3RD GENERATION


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


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

ingenieria sismologica

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