Seismology: Short Introduction

A. Rietbrock

Seismology

Seismology is the science that studies seismic waves radiated by earthquakes and what they can tell us about the Earth structure and the physics of earthquakes. It is the primary means by which scientist learn about Earth’s deep interior, where direct observations are impossible, and has provided many of the most important discoveries regarding the nature of our planet.

Velocity and Density

Vp & Vs versus depth

• decrease at core-mantle boundary

Density versus depth

• increase at core-mantle boundary

Earthquake distribution

NEIC catalogue 2008, M > 4

•Earthquakes are not randomly distributed •Mostly associated with plate boundaries •Events not deeper than 700km •One of the main observations supporting plate tectonics

Chile, February 2010

Damage

Displacement

Displacement at surface station in Concpecion

Slip distribution on the fault (mega thrust)

Magnitude-frequency relationship

• Over 10,000 with Magnitude >4 occur each year. • About 20 earthquakes with Ms or Mb > 7 occur

worldwide every year. • About 1 “great earthquake” Magnitude > 8 occurs

every year.

N is the number of earthquakes exceeding M and a and b are constants.

Gutenberg-Richter relationship

log(N) ab M

Felzer, 2006

Felzer, 2006

Stress & Strain (Continuum mechanics)

pij

pxx pxy pxz

pyx pyy pyz

pzx pzy pzz

ij

xx xy xz

yx yy yz

zx zy zz

Stress Strain

Symmetric tensors 6 independent variables p=pT =T

Definition of elastic moduli

v p K 4 /3

1/ 2

2/1

sv

2/1

)21(

)1(2/

sp vv

Equilibrium condition

The equilibrium condition for an arbitrary finite volume V in a deformed body requires that the resulting forces and moments are vanishing.

F dV P df 0S

V

x F V

dV x P S

df 0

Resulting force

Resulting moment

0

dV

x

n

P

F

V S

F Volume forces including inertia (dimension force/volume) Stress on S (normal direction to the outside)

P

Equation of motion

Fi dV Pi df S

V

Fi dV V

pij n j

Pin

df 0S

Using Gauss theorem:

Pin df P iV

S

dV

Fi P i dVV

this gives us

which has to be full filled for an arbitrary volume element

003

3

2

2

1

1

j

ij

iiii

ix

pFor

x

p

x

p

x

pF

Equation of motion (2)

ii

i fdt

udF

2

2

t

A

t

x

x

A

t

A

dt

dA

uAgrad

i

i

i

j

iji fx

p

t

u

2

2

Equation of motion

Decomposition of Fi into inertia and all other Volume forces.

Infinitesimal movements leads to partial differentiation

Stress-strain relations

klijklij cp Ideal elasticity ijklc Elasticity constants

Linear elasticity theory • Infinitesimal deformation • Stress-strain relation is linear

A 11

p11

p11 = E 11 B

C

Hook’s law Cijkl tensor of rank 4, 81 components, Symmetry of deformation and stress tensor leads to 36 components Energy conservation leads to 21 components Isotropic body only 2 parameters

Stress-strain relation (isotropic)

ijijijp 2

and are the Lame parameter and can be function of the location

= 11 + 22 +33 is the cubic dilatation

i

j

iji fx

p

t

u

2

2

Into equation of motion:

Equation of motion

2ui

t 2

x j

ij 2 ij f i

x i

x j

ui

x j

u j

x i

f i

i

i

iii

i

i fx

u

x

u

x

u

xx

u

x

u

x

u

xt

u

3

3

2

2

1

1

2

3

2

2

2

2

2

1

2

2

2

ii

i

i fuxt

u

2

2

2

)(

and are independent of there location then:

Wave equation

Wave propagation in 2 layers

Earthquake distribution

NEIC catalogue 2008, M > 4

•Earthquakes are not randomly distributed •Mostly associated with plate boundaries •Events not deeper than 700km •One of the main observations supporting plate tectonics

Velocity and Density

Vp & Vs versus depth

• decrease at core-mantle boundary

Density versus depth

• increase at core-mantle boundary

The seismic source

• Location and Origin Time

• What other parameters describe the earthquake source: – Magnitude

– Radiation pattern (moment tensor)

– Spectral Parameters (e.g. source corner frequency)

– Stress release (stress drop)

– ……..

Fault Source

Equivalent body forces

Single couple representation

Fault plane solutions

Seismic properties

Seismic tomography