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INGENIERIA SISMORRESISTENTE Fundamentos de Sismología e Ingenieria Sismológica

M.I. José Velásquez Vargas Maestría en Ing. Sismorresistente e Ing. Sismológica (Rose School, Italia)

Terremotos

Terremoto de Pisco (15/08/2007)

Terremoto de Haití (12/01/2010)

Terremoto de Chile (27/02/2010)

Terremoto de Japón (11/03/2011)

Fuente: Informe de terremotos ocurridos en el mundo - Colegio de Ingenieros del Perú

¿ Qué es un terremoto? Son vibraciones de la corteza terrestre, generadas por distintos fenómenos, como la actividad volcánica, la caída de techos de cavernas subterráneas y hasta por explosiones. Sin embargo, los sismos más severos y más importantes desde el punto de vista de la ingeniería, son los de origen tectónico. Estos se deben a los desplazamientos más bruscos de las grandes placas en que está subdividida dicha corteza.

Placas que conforman la corteza terrestre

SISMICIDAD GL0BAL Sismicidad global entre 1975-1999 con terremotos de magnitude mayor a 5.5

95% de la energía liberada por terremotos se originan en regiones estrechas alrededor de la Tierra: estas zona marcan los bordes de las placas tectónicas major eqs

4

Cinturón de Fuego del Pacífico Está situado en las costas del océano Pacífico y se caracteriza por concentrar algunas de las zonas de subducción más importantes del mundo, lo que ocasiona una intensa actividad sísmica y volcánica en las zonas que abarca. Tiene 452 volcanes y concentra más del 75 % de los volcanes activos e inactivos del mundo. Alrededor del 90 % de los terremotos del mundo y el 80 % de los terremotos más grandes del mundo se producen a lo largo del Cinturón de Fuego.

¿ Qué 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 fricción que mantienen en contacto los bordes de las placas y producen caídas de esfuerzo y liberación de enormes cantidades de energía almacenada en la roca. La energía se libera principalmente en forma de ondas vibratorias que se propagan a grandes distancias a través de las rocas de la corteza.

LOS TERREMOTOS MÁS GRANDES DESDE 1900

major eqs

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1936-1980 1915-1980 1895-1980 1843-1980 1787-1980 1626-1980 1501-1980 1300-1980 1000-1980 Scelta

10

1

7.0008, 0.18595

0.1

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

Magnitudo

ZS 63

Numero normalizzato (100 anni)

CÁLCULO DEL PELIGRO SÍSMICO

Numero normalizzato (100 anni)

ZS 63

1936-1980 1915-1980 1895-1980 1843-1980 1787-1980 1626-1980 1501-1980 1300-1980 1000-1980 Scelta

10

1

7.0008, 0.18595

0.1

3.7

4

4.3

4.6

4.9

5.2

5.5

5.8

6.1

Magnitudo

6.4

6.7

7

7.3

7.6

7.9

KOBE EARTHQUAKE OF JANUARY 17, 1995 Magnitude: Duration: Number of Injured: Number of Deaths: Epicenter:

6.9 (Mw) 20 Seconds 33,000 5,470

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 SÍSMICO DE PAKISTAN

Movimiento de las placas tectónicas

Zona de divergencia

Zona de fallas Zona de convergencia

Zona de divergencia Se 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 mayoría de las zonas de divergencia están bajo la superficie el magma al entrar en contacto con el agua se enfría y genera un cuerpo sólido, una roca. En esta zona casi no se producen sismos de gran relevancia.

Zona de fallas Se producen cuando las placas van en direcciones opuestas pero paralelamente, es decir, se rozan de lado a lado. Producen sismos menores y actividad volcánica casi nula.

Desde San Francisco (EE. UU.) hasta la península de Baja California en México, es una zona de falla.

Zona de convergencia Son zonas en donde dos placas tectónicas se dirigen al mismo lugar, por lo tanto colisionan, dando lugar a las zonas de subducción. La placa más 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 volcánica. Generalmente son las placas oceánicas las que se hunden bajo las placas continentales.

Sismos históricos

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

Sismos históricos

Terremoto y tsunami en Japón el 11/03/2011, de magnitud 8.9 en la escala de Richter

Sismos históricos

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

Sismos históricos

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

Sismos históricos

Megaterremoto registrado en Chile (Valdivia) el 22/05/1960, con una intensidad de 9.4 en la escala de 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 energía 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 extraídos del registro de sismógrafos.

Intensidad: La intensidad de un sismo corresponde a los efectos producidos por la acción 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 apreciación de las personas

ESCALA RICHTER (Se expresa en números árabes) Representa la energía sísmica liberada en cada terremoto y se basa en el registro sismográfico. Es una escala que crece en forma potencial o semilogarítmica, de manera que cada punto de aumento puede significar un aumento de energía diez o más veces mayor. Una magnitud 4 no es el doble de 2, sino que 100 veces mayor.

ESCALA MERCALLI Se expresa en números romanos. Creada en 1902 por el sismólogo italiano Giusseppe Mercalli, no se basa en los registros sismográficos sino en el efecto o daño producido en las estructuras y en la sensación percibida por la gente. Para establecer la Intensidad se recurre a la revisión de registros históricos, entrevistas a la gente, noticias de los diarios públicos 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 dependerá de: a)La energía 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 características geológicas del material subyacente del sitio donde se registra la Intensidad y, lo más importante, e)Cómo la población sintió o dejó registros del terremoto.

EFECTOS SÍSMICOS EN LOS EDIFICIOS El movimiento sísmico del suelo se transmite a los edificios que se apoyen sobre éste. La base del edificio tiende a seguir el movimiento del suelo, mientras que, por inercia, la masa del edificio se opone a ser desplazada dinámicamente y a seguir el movimiento de su base. Las fuerzas de inercia que se generan por la vibración en los lugares donde se encuentran las masas del edificio se transmiten a través de la estructura por trayectorias que dependen de la configuración estructural. Estas fuerzas generan esfuerzos y deformaciones que pueden poner en peligro la estabilidad de la construcción.

LA TIERRA Y SUS TERREMOTOS

• • •

Fallas Terremotos Fallas activadas por terremotos

FALLA FRACTURA EN LA ROCA QUE MUESTRA DESPLAZAMIENTO RELATIVO •

Falla por deslizamiento: el sentido prinicipal del movimiento en el plano de falla es horizontal

•

Falla por inmersión: el sentido principal del movimiento en el plano de falla es vertical

Falla Emerson en California: Produjo el terremoto de Landers

FALLAS POR INMERSIÓN • 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.

Normal

Reverse earth & earthquakes

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FALLAS POR INMERSIÓN Thrust

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

earth & earthquakes

Oblique

Blind thrust

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DIP-SLIP FAULTS (3)

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NORMAL FAULT: HANGING WALL DOWN

Key Bed

Source: John S. Shelton

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NORMAL FAULTS

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REVERSE FAULT (CALLED “THRUST FAULT” IF SHALLOW ANGLE) (Hanging wall Up)

Younger

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REVERSE FAULTS

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EARTHQUAKE GENESIS Posición original SIN DEFORMACIÓN

Almacenamiento de energía DEFORMACIÓN PROGRESIVA

Ruptura con emisión de energía : TERREMOTOR DESPLAZAMIENTO PERMANENTE

TEORÍA DEL REBOTE ELÁSTICO 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. 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.

QuickTime™ e un decompressore sono necessari per visualizzare quest'immagine.

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REBOTE ELÁSTICO • 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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RÉPLICAS -The

change in stress that follows a mainshock creates smaller earthquakes called aftershocks - The aftershocks “illuminate” the fault that ruptured in the mainshock Red dots show location of aftershocks formed by 3 earthquakes in Missouri and Tennessee in 1811/1812

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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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EARTHQUAKE DEPTH AND PLATE TECTONIC SETTING Weakest are the divergent zone earthquakes

Subduction Zones discovered by Benioff earth & earthquakes

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TERREMOTOS EN ZONAS DE SUBDUCCIÓN Recent example, 9.0 Christmas 2004 Earthquake and Tsunami, Sumatra

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SAN FRANCISCO EARTHQUAKE APRIL 18, 1906 Example of a strike-slip fault

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.

Fault trace 2 miles north of the Skinner Ranch at Olema. View is north. earth & earthquakes

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ALASKA EARTHQUAKE OF MARCH 27, 1964 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.

Example of a thrust fault

Hanning Bay fault on Montague Island, looking southwest from the bay. The fault trace on the ridge is marked by active landslides. earth & earthquakes

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SAN FERNANDO EARTHQUAKE OF FEBRUARY 9, 1971 Example of a reverse fault Compression of freeway

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.

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INSTRUMENTAL SEISMOLOGY

• • • • •

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

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ORIGIN OF SEISMIC WAVES

• A wave is a disturbance that transfers energy through a medium. • Seismic waves are generated by many different processes:

•

earthquakes,

• • • • • •

volcanoes, explosions (especially nuclear bombs), wind, planes (supersonic), people, vehicles. instrumental seismology

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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 standard Wood-Anderson torsion seismometer indicated as ML, or MAW according to the Karnik nomenclature (circular of 1976); 2) magnitude from body waves obtained using short or long period instruments, for epicentral distance greater than 1800 km, called mB if it is derived from the long period recording and mb if derived from the short period one, respectively MPV and M according to the Karnik nomenclature (circular of 1976); 3) magnitude from surface waves recorded by long period seismometers, for epicentral distance greater than 2200 km, indicated as MS, 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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MAGNITUDE (2) Kanamori (1977) has recently developed a standard magnitude scale that is completely independent of the type of instrument. It is called the moment magnitude, indicated with M or MW, and it comes from the seismic moment M0. M0 = µAd where µ is the shear strength (rigidity modulus) of the faulted rock (about 3.31010 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 

log M 0 10.7 1.5

with M0 in dynexcm.

 instrumental seismology

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LOCAL MAGNITUDE 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.

QuickTime™ e un decompressore sono necessari per visualizzare quest'immagine.

Charles F. Richter (1900-1985)

ML  logA  logA0



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DURATION MAGNITUDE

There is also a magnitude calculated from the duration of the recording of a local shock: the equation has to be derived empirically by comparison with actual ML estimates. Duration magnitude is indicated with MD and the general relation has the form:

MD  a  blog  c where  is the duration of the signal, computed from the P-wave arrival to the moment when the earthquake wave amplitude has the same amplitude as the background noise,  is the epicentral distance and a, b, and c are  by regression analysis. In practice, c is very small parameters calculated indicating a slight dependence of MD on distance.

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BODY-WAVE MAGNITUDE

The general formula recommended from the IASPEI's Committee of Zurich 1967 is the following, given by Gutenberg in 1945:

A  m  log max Q   T  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.

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SURFACE-WAVE MAGNITUDE The magnitude from surface waves can also be computed using different waves and vertical or horizontal components. The most common is the one computed with the waves of maximum amplitude having period from 10 to 30 seconds. The magnitude expression, given by Karnik (1962) is:

A  M  log max1.66logd  3.3 T 

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.



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SUMMARY ABOUT MAGNITUDES

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COMPARISON OF THE DIFFERENT MAGNITUDES

Only Mw does not saturate

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PELIGRO SÍSMICO

• DSHA • PSHA • Ingredients of PSHA • Hazard maps • Ground motion parameters and maps

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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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DETERMINISTIC AND STATISTICALPROBABILISTIC MODELS • Determinism = the process IS KNOWN and it is possible to write the equation E.g.: gravity law s = 1/2 g*t2



Probabilism = the process IS NOT KNOWN and it is possible to approximate it from observations E.g.: exit poll

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APPROACHES FOR SHA SEISMIC HAZARD ASSESSMENT

Probabilistic approaches

Deterministic approaches

Historical determinism Reference ground motion Historical probabilism Seismotectonic probabilism

Detailed scenario

Non-Poissonian probabilism Eq prediction Muir Wood (1993) seismic hazard

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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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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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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 RISK APPLICATION IN THE DETERMINISTIC-PROBABILISTIC SPECTRUM

McGuire (2001) seismic hazard

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EXAMPLES OF EARTHQUAKE DECISIONS

McGuire (2001)

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DETERMINISTIC APPROACHES SEISMIC HAZARD ASSESSMENT

Probabilistic approaches

Deterministic approaches

Historical determinism Reference ground motion Historical probabilism Seismotectonic probabilism

Detailed scenario

Non-Poissonian probabilism Eq prediction Muir Wood (1993) seismic hazard

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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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DETERMINISTIC APPROACH SOURCE CHARACTERISATION Focus = historical & instrumental seismicity Mechanism = geology, instrumental seismicity Magnitude = geology, instrumental seismicity

Reference ground motion Empirical attenuation relations

PATH DESCRIPTION Intensity attenuation = historical seismicity acceleration attenuation = instrumental seismicity

SITE EFFECTS Stratigraphy = geology, instrumental seismicity Morphology = geology seismic hazard

Detailed scenario Modeling

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PSHA AND DETERMINISTIC SCENARIO FOR A SITE

Deterministic Scenario Regional max mag = 6.4 (Kijko and Graham 1999 method) PGA 0.23 0.30 0.30

attenuation relation for rock Ambraseys et al. 1996 Sabetta & Pugliese 1987 Chiaruttini & Siro 1981

PSHA 1000-yr PSHA return period PGA on rock 1000-yr return period PGA on rock seismic hazard

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GENERATIONS OF PSHA SEISMIC HAZARD ASSESSMENT

Probabilistic Approaches

Deterministic Approaches Reference Shaking Detailed Scenario

Historical Determinism Historical Probabilism Seismotectonic Probabilism Non-Poissonian Probabilism Earthquake Prediction (Muir-Wood, 1993)

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THE FIRST HAZARD MAP (?)

•

Map of world earthquake occurrence by Robert Mallet in 1854

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1ST GENERATION HISTORICAL DETERMINISM

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2ND GENERATION HISTORICAL PROBABILISM

•

Gumbel approach (1)

The Gumbel approach Given Imax = max Xi, with i=1, …, n and n large Type 1: no upper limit of Xi

P[Imax  i]  FIm ax (i)  exp[eiu] Type 3: upper limit of Xi



P[Imax  i]  F Im ax (i)  exp{[(w i)/(w  u)]k} Application Putting



F X (x)  i /(n 1)

Introducing the reduced variable

y i  ln{ln[ F X (xi)]}

 y i   (xi  u)



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2ND GENERATION HISTORICAL PROBABILISM

•

Gumbel approach (2)

Example of the Gumbel approach Given an eq catalogue, let’s take the maximum annual (extreme) magnitudes and order them x1, x2, …, xn: xi≤ xi+1 " i  let’s assign the annual non exceedence probability:

FX (x)  i /(n 1)

 let’s calculate the Gumbel reduced variable:

y i  ln{ln[ FX (xi )]}  we obtain: yi  (xi  u)  let’s compute  and u by regression analysis:

 let’s compute the hazard estimates (e.g.: extreme exceeded with probability p in T years:

y p,T  u {ln[ ln(1 p)]  lnT} /  seismic hazard

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2ND GENERATION HISTORICAL PROBABILISM

•

The smoothed seismicity approach (1)

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 :

ñi

 ne  e

2

  ij / c

2

j

j

 2ij / c 2

j

The annual rate  (u>u0) of exceeding ground motion u0 at a specific site is determined from a sum over distance and magnitude mu

(u  u0) 

1  ñi  P[u  u0 | di, mj ] fm(m)dm T i m min

where

P[u  u0

 (from Frankel, 1995 and Lapajne et al., 1997)

|

lnu0  lnu(di ,m j )  1    di, m j]    2   2

bln1010b( mm 0 ) fm (m)  110b(mu m 0 ) seismic hazard

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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

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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

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3RD GENERATION SEISMOTECTONIC PROBABILISM

seismic hazard

• The 4 steps of PSHA

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3RD GENERATION SEISMOTECTONIC PROBABILISM

•

The Cornell (1968) approach (1)

The Cornell (1968) approach The total probability theorem

f S (s)   FS (s)/ s

where

FS (s)  P[S  s]

and Mean annual rate of exceedence

z  for all SZs

P[E] 



 PE | Sf (s)ds s

is the PDF of S is the CDF of S

Application

N

mu r

i1

mo r o

Attenuation model

 i   P(Z  z | m,r) f i(m) f i (r)drdm Mean annual rate of occurrence

GR distribution

SZ geometry

If it is a Poisson process (stationary, independent, non-multiple events)

 P Z  z  1 e z T T

T  t /ln(1 P(ZT  z))

where: T=return period; t=period of analysis

seismic hazard

76

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

77

3RD GENERATION SEISMOTECTONIC PROBABILISM

•

The Cornell (1968) approach (3)

a

b

c Contributing information a = geology, historical & instrumental seismicity b = historical & instrumental seismicity c = instrumental seismicity for PGA historical seismicity for intensity d = statistics e = statistics

d

e

(from Algermissen & Perkins, 1976)

seismic hazard

78

3RD GENERATION SEISMOTECTONIC PROBABILISM

•

The Cornell (1968) approach (4) Gutenberg-Richter law

Uniformely distributed seismicity

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

(from Algermissen & Perkins, 1976)

seismic hazard

Poisson distribution

79

SOURCE-TOSITE 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

80

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

(b)

fL (l)dl  fR (r )dr dl fR (r)  fL (l) dr fL (l)  l / Lf 2 l 2  r 2  rmin

fR (r)  Many single sources, see (a)

(from Kramer, 1996)

seismic hazard

r 2 Lf r 2  rmin

81

FM(M) GUTENBERG - RICHTER LAW

lognm  a  bm  m n m   0e n m   0e  (m m 0 ) with m0 = threshold magnitude   b ln10

 0  10a

•

Gutenberg-Richter recurrence law: a) meaning of a and b parameters; b) application of GutenbergRichter law to worldwide seismicity data

FM (m)  P[M  m | M  m0 ] 

nm0  nm nm0

 1 e  (mm 0 )

d f M (m)  FM (m)  e  (mm 0 ) dm



seismic hazard

82

FM(M) BOUNDED GUTENBERG RICHTER LAW

nm  

exp m  m0  exp mmax  m0  1 exp mmax  m0 

1 e  (mm 0 ) FM (m)  P[M  m | m0  M  mmax ]  1 e  (m max m 0 ) e  (mm 0 ) f M (m)  1 e  (m max m 0 ) where =exp(–m0) is the rate of occurrence of earthquakes exceeding m0

•

seismic hazard

Bounded Gutenberg-Richter recurrence laws for mo=4 and mmax=6, 7, and 8 constrained by constant seismicity rate 83

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

84

SEISMIC HAZARD CURVE • The individual components of the Eq are

PGA with 10% exceedance probability over various exposure times for 14 areas in North America

complicated that the integrals cannot be evaluated analitically: numerical integration is required

P[E] 

 P E | Sf

S

(s)ds

mu r

P[Z  z] 

  P(Z  z | m,r) f i(m) f i (r)drdm

Exceedence probability

mo r o

NS

mu r

Mean annual rate i1 of exceedence

mo r o

z 

 i   P(Z  z | m,r) f i(m) f i (r)drdm Magnitude and distance ranges are divided into segments

NS N M N R

z     iP(Z  z | m j ,rk ) f M (m j ) f R (rk )mr i

i

i1 j1 k1 NS N M N R

z     iP(Z  z | m j ,rk )P[M  m j ]P[R  rk ]

Hazard curve

i1 j1 k1

P ZT  z  1 e z T

Poisson model seismic hazard

85

“Hazard curves” for 4 bridges in Veneto ponti del Veneto

exceedence probability in 50 yrs

1

Fener 0.1

Botteon

Peron 0.01

Spresiano 0.001 0.1

PGA seismic hazard

1 86