ICTP Diploma Programme

Earth System Physics

Fabio ROMANELLI

Dept. Mathematics & Geosciences

Università degli studi di Trieste

romanel@units.it

Seismology

Seismic hazard

Some basic definitions:

Seismic Hazard: describes the potential for dangerous, earthquake related phenomena, such as ground shaking, fault rupture or soil liquefaction.

Seismic Risk: probability of occurrence of these consequences.

Leon Reiter, 1990

Some basic definitions

Seismic Hazard: any physical phenomenon (e.g. shaking) associated with an earthquake that may cause an adverse effect on human activity.

Seismic Risk: a probability that social or economic consequences will exceed a specified value.

John Anderson, 2006

Some basic definitions

Seismic Hazard: a physical effect associated with an earthquake, such as ground shaking, that MAY produce adverse effects.

Seismic Risk: the probability that consequences of an earthquake, such as structural damage, will equal or exceed specified values in a specified period of time.

Carlos Ventura, 2006

Hazard, Risk & Vulnerability

Risk Hazard Vulnerability*=

Nature decided, and can be assessed

Man decided, and can be reduced

set of i-events with possible adverse consequences

associated intolerable

consequences

associated probabilities of their occurrence

R=⟨Ni, Pi,Ci⟩

Earthquake zoning - history

13

Oldest seismic hazard map, compiled by Mallett in 1853-1855

Earthquake zoning - history

Moscow Institute of Physics of the Earth, 1937

These maps were first incorporated into the building code for the Russian Federative Republic. Later, the Institute of Physics of the Earth prepared more detailed maps, which were incorporated in the 1957 Zoning (Rayonirovanye) of the Soviet Union. These maps

became an official part of the Earthquake Building Code SN8-57 of the U.S.S.R.

112 EARTHQUAKE ZONING

Fig.9.1. Earthquake zoning map of the U.S.S.R. (Normy i pravila stroitel' stva v seismicheskikh raionakh SN8-57, Stroiizdat, 1958).

(a) Compilation of seismicity maps, i.e. maps showing the incidence of earthquake epicenters in different regions. These seismicity maps combine plots of epicentral loca-tions with geological data on recent faulting and other crustal movements.

(b) Mapping of soil conditions affecting seismic intensity; such mapping is usually done through the study of isoseismals of past earthquakes, plus geologic evidence.

The combination of these two steps cannot be done as yet in a rigorous way. Specific regional conditions which are taken into account include local peculiarities of the seismic process, relations between geology and seismicity, uncertainty factors which involve the relative availability of data, and "other factors" such as economic and human consider-ations (Medvedev). The final zoning maps show the areas where intensities of 6, 7, 8, and 9 on the Mercalli Scale (or on the roughly equivalent GO ST 6249-52 scale) may be expected to occur. In some instances these zoning maps are superposed on geotectonic maps. They may contain information about the relative frequency of earthquakes, e.g. "low" (once every 150-200 years), "moderate" (once every 50 years), or "high" (once every 15 years).

EARTHQUAKE ZONING IN THE U.S.A.

The development of zoning concepts in the United States has been closely connected with the development of building codes. As long as each city or district has its own building regulations there is little incentive for zoning. In California, statewide rules on earthquake design existed only for school buildings, as a result of the Field Act of 1933. After considerable efforts by the engineering profession a conference of Pacific Coast

“Earthquake Hazard Analysis”, Reiter, 1990

SHA dualism: P & D

SHA global map

http://www.seismo.ethz.ch/static/GSHAP/

SHA global map (1999)

http://www.seismo.ethz.ch/static/GSHAP/

Response spectra

Response Spectrum

Modelling of spectral amplificationResponse spectra can be computed using synthetic seismograms as input motion.

To estimate the spectral amplification due to a change in the model, computations of thesynthetic seismogram can be repeated changing any parameter of the model.

Example: two synthetic seismograms are generated modifying the properties of the structuralmodel. The ratio between their response spectra will show the relative amplifications dueto the change of the structure.

Usually, one synthetic seismogram is generated for a bedrock model, and kept as a reference.The second synthetic seismogram is computed considering a structural model representativeof the site conditions, possibly taking into account lateral heterogeneities.

Time

Acce

lera

tion

Natural period ofvibration

Input motion

Responsespectrum (SA)

Inputacceleration

Probabilistic Seismic Hazard Analysis (PSHA)

A Primer

Written by Edward (Ned) H. Field

These notes (available at http://www.relm.org/tutorial_materials) represent asomewhat non-standard treatment of PSHA; they are aimed at giving an intuitiveunderstanding while glossing over potentially confusing details. Comments andsuggestion are highly encouraged s (to field@usgs.gov).

The goal of probabilistic seismic hazard analysis (PSHA) is to quantify the rate (orprobability) of exceeding various ground-motion levels at a site (or a map of sites) given allpossible earthquakes. The numerical/analytical approach to PSHA was first formalized byCornell (1968). The most comprehensive treatment to date is the SSHAC (1997) report, whichcovers many important procedural issues that will not be discussed here (such as the use of“expert opinion”, the meaning of “consensus”, and how to document results). Except whereotherwise noted, the SSHAC report represents the best source of additional information (that Iknow of). It’s a must-read for anyone conducting PSHA.

Traditionally, peak acceleration (PGA) has been used to quantify ground motion inPSHA (it’s used to define lateral forces and shear stresses in the equivalent-static-forceprocedures of some building codes, and in liquefaction analyses). Today the preferred parameteris Response Spectral Acceleration (SA), which gives the maximum acceleration experienced bya damped, single-degree-of-freedom oscillator (a crude representation of building response).The oscillator period is chosen in accordance with the natural period of the structure (roughlynumber_of_stories/10), and damping values are typically set at 5% of critical (see Figure 1).

M MM

~~Building Response Mass on a

Leaf Spring W/ ~5% Damping

The FreeOscillation+

Figure 1. The response-spectrum value is the peak motion (displacement, velocity, or acceleration) of a damped single-degree of freedom harmonic oscillator (with a particular damping and resonant period) subjected to a prescribed ground motion.

( )

To keep things simple, PGA will be used as the ground-motion parameter here (the analysis isotherwise equivalent).

PSHA involves three steps: 1) specification of the seismic-hazard source model(s); 2)specification of the ground motion model(s) (attenuation relationship(s)); and 3) theprobabilistic calculation.

34.5

34.0

-116.5 -116.0

20 s 0 Km 30

forward directivity

region

backward directivity

region

epicentre

Rupture propagation

Lucerne Valley

Joshua Tree

Landers, 1992

Source effects... 1156 Y. Hisada and J. Bielak

Figure 1. (a) Map of California with the site location; (b) the surface faults and theepicenter of the 1992 Landers earthquake, together with the location of the observationstation at the Lucerne valley; (c) the velocities; and (d) the displacements at the station.Panel (b) also shows the direction of the strike slip, the directions of the fault-normal and-parallel components, and the directions of the maximum velocity and displacement.

Green’s functions with shallow source points. Therefore, thesecond obstacle is that the integrands of wavenumber inte-grations (equation 2) do not converge with wavenumberwhen the depths of source points are close to or on the freesurface (e.g., Apsel and Luco, 1983; Hisada, 1993, 1995).In particular, the convergence is extremely slow in the caseof the static Green’s function (x ! 0). Therefore, specialtechniques are needed to overcome the two obstacles.

The purpose of this article is to propose a mathematicalmethodology for computing near-fault ground motions ef-fectively and to use it for investigating the effects of flingand directivity in several simple situations. We first carefullycheck the fault integration (equation 1) using the simplestfault model: an axially symmetric circular fault in a homo-geneous full-space. Based on the results from this simplecase, we will then propose a new form of the representationtheorem for calculating the fault integration efficiently formore general cases, involving arbitrary kinematic faultingmodels in layered half-spaces. In addition, we propose anefficient method for calculating the wavenumber integration(equation 2), considering the surface faulting. Finally, wecheck the validity of the proposed method and investigatethe physical basis of the fling and directivity effects.

Efficient Methods for Computing Near-Fault GroundMotions in Layered Half-Spaces

Near-Fault Ground Motions Using an AxiallySymmetric Fault Model in a HomogeneousFull-Space

We first check the basic characteristics of the dynamicand static Green’s functions in the fault integration (i.e.,equation 1) to find efficient ways for computing the near-fault ground motions. In this section, we use the simplestfault model, that is, the axially symmetric circular faultmodel in a homogeneous full-space. In addition, we willcheck the attenuation relation of the static offset using thismodel.

Figure 2 shows the fault model and the location of anobservation point. R is the radius of the circular fault model.We assume a uniform slip, D, over the fault plane. The ob-servation point is located at a distance, z, above the centerof the fault. The dynamic displacement, U, in the same di-rection as D, is easily obtained by substituting Green’s func-tion of the homogeneous full-space (e.g., Kane, 1994) intoequation (1),

Michoacan, 1985

Fling & Directivityaka

Near-field & Near-source

Sir Georges Stokes Hugo Benioff

Michoacan 1985 event: way to DF...

Michoacan 1985 event: RSA in DF at SCT

Tenochtitlan and Mexico City (DF)

La ciudad de Tenochtitlan y su entorno en el siglo XVI Pintura de Miguel Covarrubias, Museo Nacional de Antropología, México DF

The actual boundaries of the World Heritage Property follows the boundaries of the Historical Monuments Zones, according to the limits of the city in the 19th century (perimeter A), and a buffer zone (perimeter B)

Chapultepec. This dike was 12 km long and 20 m thick. He also built ChapultepecAqueduct to provide fresh water to the city (Serra Puche, in Kumate and Mazari 1990).

After the Spanish conquest, in 1521, the Aztec city was razed and the colonial capitalwas founded in the same location. Mexica constructions were used as sources of buildingmaterials. Floods and epidemics suggested a need to drain the lakes and this long effortbegan near 1524. In 1607 Enrico Martinez designed a channel and tunnel at Nochistongo todeviate the course of Cuauhtitlan River to the north. Because of continuing disastrousfloods, in 1629 King Charles IV ordered to move the capital elsewhere, but the settlers

Fig. 3 The Mexico Basin Lakes as the Spanish found them in 1392 (D. D. F. 1975). These days, there isonly a small lake near Xochimilco, which is a natural reserve

Nat Hazards (2007) 40:357–372 361

123

Michoacan 1985 event: GM in DF

@ Strong motionseismographs

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27

Michoacan 1985 event: damage in DF

Wreckage of a twenty-one-story building in Conjunto Pino Suarez Complex

Totally destroyed office building in the foreground, while the 44-floor Torre Latinoamericana office building, in the background on the right, stands

Near surface effects: impedance contrast, velocity

geological maps, v30

Basin effects

Basin-edge induced waves

Subsurface focusing

Important issues in SRE

heavy-damagezone

slight-damagezone

650 m apart 1 sec

L.A. BasinSediments

Santa Monica Mountains

Santa Monica

1 km

Bedrock

In SHA the site effect should be defined as the average behavior, relative to other sites, given all potentially damaging earthquakes.

This produces an intrinsic variability with respect to different earthquake locations, that cannot exceed the difference between sites

....may vary greatly among the earthquake scenarios, considering different source locations (and rupture ...)

SCECPhase 3Report

Peak Velocity Amplification from the 3D Simulations of Olsen (2000)

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Figure 1 – Acceleration time history. Rocca NS record. 1971 Ancona earthquake (ML=4.7)

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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15t (s )

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Encyclopaedia of Geology Engineering Seismology

Figure 5. Four horizontal accelerogram components with exactly the same PGA

Bommer & Boore 18

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(a) Overall view of the Kurihara City Municipal Office Building

(b) Fall of ceiling of Municipal Assembly Hall (1)

(c) Fall of finishing tiles on a column (d) Fall of ceiling of Municipal Assembly Hall (2)

Photo 1: Kurihara City Municipal Office Building and non-structural damage

4.2 Kurihara City Municipal Tsukidate Junior High School and Tsukidate Gymnasium Center

Two buildings near the K-NET Tsukidate station were selected for the damage investigation; Kurihara City

Municipal Tsukidate Junior High School (new construction, Photo 2) and Kurihara City Municipal

Tsukidate Gymnasium Center Building (Photo 3), the latter suffered non-structural damage during the

2008 Iwate-Miyagi Inland Earthquake. No damage was observed in both buildings.

Time & Space scales... and actions

Time Space Action

No National Seismic Codes

Decades Regional IT alerts

Seconds Urban Red Alert

MYrs Decades Seconds

Geodynamics Geodesy Seismology

Strain rates Slip rates