Efectos de la Geología Superficial en las Características de los Temblores

Francisco J. Sánchez-SesmaInstituto de Ingenieria, UNAM

Factors that affect seismic ground motionSOURCE PATH LOCAL GEOLOGY

Significant influence of surface geologySignificant influence of surface geology

Andalucía Earthquake Imax=X (MSK)Alhama de Granada Dec. 23th, 1884

•Taramelli and Mercalli (1885)•Taramelli and Mercalli (1885)

Arenas (Now Arenas del Rey)

Empirical remarks regarding soil type

Soil type Increase in Intensity (MM)

Quarz, granite 0Basalts, piroclastic 1-2Consolidated sand 1-3Dry alluvial soil 2Saturated alluvion 3Fills, lacustrine 3-4

•Tiedemann (1992)•Tiedemann (1992)

+ 17.000 muertos

Michoacán (México) Earthquake Ms = 8.1September 19, 1985

Se evidencia de forma dramática la relación geología superficial-amplificación del movimiento del suelo

Loma-Prieta (U.S.A.) Earthquake M = 7.1October 17th, 1989

+ 6 Billones $

Seismic Records

Characterization of Local Site Response- empirical/experimental approach- numerical/theoretical methods

Ground motion main characteristics forvarious surface geology conditions

- amplitudes- duration- spectral content

•Razones espectrales de terremotos•Análisis espectral de microtremores

Empirical and/or Experimental Methods

R1

S2S1R1

S2S1

f f

f

f f

S1 / R1 S2 /R1

s(t) = recorded signalf(t) = source historyc(t) = wave propagation

along path g(t) = local geology

Signals Spectral Ratios

s(t) = f(t)*c(t)*g(t)

S1( f ) = F ( f ) ·C ( f ) ·G ( f )

R1( f ) = F ( f ) ·C ( f )

R1

S2S1R1

S2S1

f f

f

f f

S1 / R1 S2 /R1

)()()(

)()()()()(

1

1 fGfCfF

fGfCfFfRfS =

⋅⋅⋅=

•Borcherdt (1970)•Chávez-García et al. (1999)

Parkway valley•Triantafyllidis et al. (1999)

Thessaloniki

•Borcherdt (1970)•Chávez-García et al. (1999)

Parkway valley•Triantafyllidis et al. (1999)

Thessaloniki

Spectral Analysis of Microtremors

• It is based upon the use of ambient noise records• Considering origen and frequency band of interest, the

ambient seismic motion is divided in:– microtremors, mainly due to human activity (trafic,

machinery, etc.)– microseisms, due to natural activity (atmospheric

perturbations, sea waves, etc.)

• The used aproximations can be grouped in:- Methods in which dominant frequencies are sought- Spectral Ratios

Station

Station in Hard rock

Trafic

Microseism

IndustryWind Action

•Katz (1976)•Morales et al. (1991)Zafarraya Basin

•Katz (1976)•Morales et al. (1991)Zafarraya Basin

Numerical and/or Analytical MethodsModeling Seismic Ground Motion

Caracterization of Local Seismic Response: 1D Approximation

Hβ 1 ρ1

β 2 ρ2

Resonant Frequencies

1,2,3,...=n1)-(2n4H

=fβ1

• Thompson (1950)• Haskell (1953;1960;1962)

Método de Thompson-Haskell• Kennet (1983)

• Thompson (1950)• Haskell (1953;1960;1962)

Método de Thompson-Haskell• Kennet (1983)

H = 100 m; β1 = 400 m/s

Modeling Seismic Ground MotionAnalytical Solutions

2D MODELS

tu =f +

x xu )+( +

x xu

2i

2

iji

j2

jj

i2

∂∂

∂∂∂

∂∂∂ ρρµλµ

Navier Equation:

zv=1

tv

2

2

22

2

∂∂

∂∂

β

Scalar Equation:

SH waves

Variable Separation

•Trifunac (1973)

•Wong andTrifunac (1974a)

•Trifunac (1971)

•Wong andTrifunac (1974b)

x

Modeling Seismic Ground MotionAnalitical Solutions

Solution for an infinite wedge topographical profile (SH Waves)

•Sánchez-Sesma (1985)

Amplificación: 2/ν θ = νπ

Solution for a hemispherical alluvial basin

Modeling Seismic Ground MotionAnalitical Solutions

•Lee (1984)P and S Waves

•Todorovska and Lee (1990)Rayleigh Waves

•Lee (1984)P and S Waves

•Todorovska and Lee (1990)Rayleigh Waves

3D MODELS

x

y

z

•Ray Theory•Domain Approaches•Boundary Methods

Modeling Seismic Ground MotionNumerical Solutions

Ray Theory (ω >>)

• Cerveny (1985)2D Simulation

• Kato et al. (1993)3D Simulation

• Davidson & Braile (1999)Vibroseis Records Simulation

• Cerveny (1985)2D Simulation

• Kato et al. (1993)3D Simulation

• Davidson & Braile (1999)Vibroseis Records Simulation

Modeling Seismic Ground MotionNumerical Solutions

Domain Approaches

• Finite-Differences

•Pseudoespectral Method

•Finite Elements

2

2

2

2

21

xv

tv

∂∂=

∂∂

β

∫=∂

∂ dketkvikx

txv ikx),(21),(π

211

22221

xvvv

tvvv t

mt

mt

mtt

mt

mtt

m

∆+−=

∆+− −+

∆−∆+

β

• Alterman and Karal (1968)• Sato et al. (1999)

3D Simulation. Tokyo

• Alterman and Karal (1968)• Sato et al. (1999)

3D Simulation. Tokyo

• Kreiss and Oliger (1972)• Tessmer et al. (1992)

2D Topography

• Kreiss and Oliger (1972)• Tessmer et al. (1992)

2D Topography

• Olsen et al. (1995)San Andreas Fault

• Piatanesi and Tinti (1998)Tsunamis

• Olsen et al. (1995)San Andreas Fault

• Piatanesi and Tinti (1998)Tsunamis

Complete Systems of SolutionsDiscrete Wavenumber Method

⋅Boundary Integrals

Modeling Seismic Ground MotionNumerical Solutions

Boundary Methods

• Aki and Larner (1970)• Bouchon and Barker (1996)

3D Topography

• Aki and Larner (1970)• Bouchon and Barker (1996)

3D Topography

• Sánchez-Sesma (1978)• Pérez Rocha and

Sánchez-Sesma (1989)Symmetrical 3D Structures

• Sánchez-Sesma (1978)• Pérez Rocha and

Sánchez-Sesma (1989)Symmetrical 3D Structures

- Formulación directa -Indirect Formulation:IBEM

∫ −=S

dSTuGtcu )( ∫=S

GdSu φ• Sánchez-Sesma and Campillo (1993)

2D Topographic profiles• Luzón et al. (1999)

3D Topography

• Sánchez-Sesma and Campillo (1993)2D Topographic profiles

• Luzón et al. (1999)3D Topography

i i i(d)u = u +u(0)

i(d)

Sj iju (x) = ( )G (x, ) dS∫φ ξ ξ ξ

Indirect Boundary Element Method (IBEM)

X 1

X3i r

d

i i(i)

i(r)u = u +u(0)

i(d)

p=1

N

j p ij lu (x)= ( )g (x, )∑φ ξ ξ ij pS

ijg (x, )= G dSp

(x, )ξ ξ ξ∆∫

i( )

i(d)t +t =00

Boundary Condicions:

• Diffracted WaveFront

• Point emmiting secondary waves

IBEM Current State

Modeling Seismic Ground Motion in 2D Geological Structures

Valley of México

•Luzón et al. (1995)•Luzón et al. (1995)

IBEM Current State

Modeling Seismic Ground Motion in 2D Geological Structures

Zafarraya (Granada) Basin

•Luzón (1995)•Luzón (1995)

IBEM Current State

Modeling Seismic Ground Motion in 3D Geological StructuresIrregular Geometry

ββββr= 1 km/s ββββe= 2 km/s ννννr = 0.35ννννe = 0.25ρρρρr= 0.8 ρρρρe

49 stations

49 stations

IBEM Current State

Modeling Seismic Ground Motion in 3D Geological StructuresIrregular Geometry

IBEM Current State

Modeling Seismic Ground Motion in 3D Geological StructuresSynthetic Seismograms in two Perpendicular Profiles

•Sánchez-Sesma and Luzón (1995)

•Luzón et al. (1997)

•Sánchez-Sesma and Luzón (1995)

•Luzón et al. (1997)

IBEM Current State

Modeling Seismic Ground Motion in 3D Geological Structures

IBEM Current State

Modeling Seismic Ground Motion in 3D Geological Structures

IBEM Current State

Modeling Seismic Ground Motion in 3D Geological Structures

IBEM Current State

Modeling Seismic Ground Motion in 3D Geological StructuresComplete Simulation of Surface Motion

Video Clip

Development Lines

•Realistic Considerations•Seismic Source•Path•Local Geology

•Application to Real Structures•Granada’s Basin

•Realistic Considerations•Seismic Source•Path•Local Geology

•Application to Real Structures•Granada’s Basin

Development Lines: Seismic Source.

Point Source. Shear Dislocation

δ

φ :Strikeλ : Rakeδ : Dip

x3

φ

λ

x1

x2

N

E

x’2

x’1x’3

( )u x M G xx

G xx

M Gi j ij ll

j ij ll

j l j l ij l( )' ', , ,= +

= +0 1

2

2

1

0 1 2 2 1β ∂∂

β ∂∂

β β β β

cos cos cos cos cos cos

cos cos

cos cos cos cos cos cos cos

λ φ λ δ φ λ φ λ δ φ λ δ

δ φ δ φ δ

λ φ λ δ φ λ φ λ δ φ λ δ

+ sen sen sen - sen -sen sen

-sen sen sen -

sen - sen sen sen + sen

β β β β =•Aki and Richards (1980)

•Aki and Richards (1980)

x’2

2�x’ 1

F 1

- F 1

-F 2

F 2

Development Lines: Seismic SourceThe Half-space

1 km

6 km

α = 4 km/secβ = 2.3km/secρ = 1.8g/cm3

M0 = 10**22 dyn · cmTriangular 1sec Pulse

N

E z

N

Discrete Wavenumber (Bouchon, 1981)

Boundary Elements

·

·

·

N

Development Lines: Seismic Source

Extended SourceRupture Velocity

Point Source

• Preliminary Results• Preliminary Results

Development Lines: Seismic Source

0 2 4 6 8 10 12-20

-10

0

10

20

30

40

50

60

70

velo

cida

d

0 2 4 6 8 10 12-20

-10

0

10

20

30

40

50

60

70

velo

cida

d

Point Source Extended Source

Tiempo Tiempo

Development Lines: Path

Crustal models between Source and Receiver: Stack of Plane LayersThompson-Haskell’s Method

Lateral IrregularitiesIBEM+Thompson-Haskell

Otther applications: To obtainGeometry and properties of

Geological structures

•Vai et al. (1999)•Vai et al. (1999)

Green’s functions

Green’s function for the complete space

)1()0(11)(

00 z

zzz γα

γγαα +=

++=

)1()0(11)(

00 z

zzz γβ

γγββ +=

++=

nn

zzzz )1()0(

11)(

00 γρ

γγρρ +=

++=

)(4

),( )1(0

0

ωτµ

ω HixG yy Λ=w

n

Rzz τβ

γγ 0

21

0

11

+

++=Λ

Green’s function for inhomogeneos mediumSH case and constant-gradient medium

• Sánchez-Sesma et al. (2001)• Sánchez-Sesma et al. (2001)

)ln()0( 12

12

RRRRh

+−=

βτ

0 2 4 6 0 2 4 6Time Time

Green’s function for inhomogeneos mediumP-SV case and constant-gradient medium

Validation: Displacements produced by a vertical forcewithin an inhomogeneous medium

Some models studied here

RE ρρ 3=

Vertical incidence of SH wavesFrequency Response

Vertical Incidence of SH waves, fp = 0.6 HzTime Domain Response

Development Lines: Path

Other applications: Surface waves in inhomogeneous media

Development Lines: Application to Realistic Structures

Granada’s Basin: exterior and basement

Development Lines: Realistic 3D geometries

Surface Discretization

Granada’s Basin. Incident SV wave

tp = 6.5 sec ts = 40 sec

Granada’s Basin. Incident SV wave

Summary

•XIX CenturyAndalucía, Granada Earthquake 1884(observed local effects)•XX Century

•70’s Qualitative Studies and 1D modeling

•80’sEmpirical approach and 2D modeling

•90’sEmpirical approach and 3D modeling

•XXI CenturyRealistic modeling

•XIX CenturyAndalucía, Granada Earthquake 1884(observed local effects)•XX Century

•70’s Qualitative Studies and 1D modeling

•80’sEmpirical approach and 2D modeling

•90’sEmpirical approach and 3D modeling

•XXI CenturyRealistic modeling