Structure of Earth as imaged by seismic waves

upper mantle

outer core

inner core

D”, core-mantle boundary layer

2000 4000 km 6000 8000 10,000 12,000

lower mantle

core-mantle boundary

transition zone

crust

Structure of Earth as imaged by seismic waves

radius of earth = 6371 km

Seismic waves involve stress, strain, and density

Two important types of stresses and strains:

Pressure, P and volume change per unit volume, V/V

Shear stress and shear strain

For linear elasticity, Hooke’s law applies:

stress = elastic_constant x strain

For elastic waves, two elastic constants are key:

And density of the material,

= mass/volume

Two types of elastic waves

Compressional or P waves involve volume change and shear

Shear or S waves involve only shear

P wave particle motions

S wave particle motions

Click on these links to see particle motions:

http://www.geo.cornell.edu/geology/classes/geol388/p_wave.ppt

http://www.geo.cornell.edu/geology/classes/geol388/s_wave.ppt

Elastic wave velocities determined by material properties

43

p

s

V

V

P wave velocity

S wave velocity

epicenter

expanding wavefront at some instant of time after earthquake occurrence

ray perpendicular to wavefront

seismograph station

Earth surface

Earthcenter

epicenter

ray

seismograph station

= epicentral distance in degrees

Earth surface

Earthcenter

tt() = total travel time along ray from earthquake to station

Globally recorded earthquakes during the past 40 years

earthquake depth 0-33 km 33-70 70-300 300-700

Partial map of modern global seismograph network

2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km.

These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page

distance, degrees

tim

e, m

inu

tes

These lines represent plus or minus one minute errors in reading arrival times

P

diffracted P

PKIKP

PKP

PcP

PP

PPP

ScS

SKS

S

PcS

SS

SSS

PS

PPSPKPPKP

PKKP

PKS

SKKS

PPP

surf

ace w

aves

wat

er w

aves

click on link to P and S phases in the earth

http://www.geo.cornell.edu/geology/classes/geol388/special/phases.ppt

Nomenclature for seismic body phases

c = reflection at core mantle boundary

K

P or S

I or Ji = reflection at inner core-outer core boundary

P wave segments in blueS wave segments in red

inner core

outer core

mantle

PS

Mantle

Inner core

Outer core

Single path refracted through mantle

seismic wave source



distance, degrees

tim

e, m

inu

tes

P

S

P diffracted around core

PP

SS

Mantle

Outer core

Single reflection at surface

Inner core



distance, degrees

tim

e, m

inu

tes

PP

SS

PcP

Single reflection at core-mantle boundary

reflection

ScS

Single reflection at core-mantle boundary

PcS

Single reflection with conversion of P to S



distance, degrees

tim

e, m

inu

tes

PcP

ScS

PcS

PKP

P in mantle, refracting to P in the outer core (K) and out through the mantle as P

PK

P

PKIKP

P segments in mantle, P segments in outer core (K), and P segment in inner core (I)

P

KPK

I



distance, degrees

tim

e, m

inu

tes

PKIKP

PKP

SKSS in mantle, refracting and converting to P in outer core,

then refracting back out and

converting back to S in the

mantle

S

KS

SKKS

S in mantle, refracting and converting to P in outer core, P reflects once at

inner side of core-mantle

boundary, then refracting back out back with

conversion to S in the mantle

S

KS

Kreflection



distance, degrees

tim

e, m

inu

tes

SKS

S

SKKS

outer core

inner core

lower mantle

upper mantlekm/sec

km

transition zone

D’’ layer

0

1000

2000

3000

4000

5000

6000

7000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

dep

th

seismic wave velocity

Compressional (P) and Shear (S) wave velocities, Vp and Vs

43

p

s

V

V

modulus of incompressibility/

shear stressmodulus of rigidity

shear straindensity

(R) = "seismic parameter" derived from Vp(R) and Vs(R)

P

V V

2 24( )

3p sV V R

From Vp and Vs to seismic parameter

For self compression of homogeneous material

(R) = /

= - dP/(dV/V) = dP/(d/)

dP = - g dR

where R = radius to a point in the earth, andg = gravitational acceleration at that radiusg = GMR/R2

where MR = mass within sphere of radius R

d/dR = -/g


d/dR = -/g

This is the gradient in density determined by the seismic wave velocities. To obtain density, one must integrate by fixing the density, , and gravity, g, at the top of the layer and calculating both and g as one proceeds downwards.

The calculation assumes

a simple compression of material that does not change chemistry or phase.

the compression as one goes deeper produces an adiabatic temperature increase.


d/dR = -/g

The method is applied to the following layers:upper mantlelower mantleouter coreinner core

To determine the jumps in density between these layers, the following constraints are used:

Mass of earthMoment of Inertia of EarthPeriods of free oscillations of Earth

Density,

0

1000

2000

3000

4000

5000

6000

0 2000 4000 6000 8000 10000 12000 14000


kg/m3

km

dep

th, k

m

Gravitational acceleration, g

0

1000

2000

3000

4000

5000

6000

0 2 4 6 8 10 12


km

m/s2

dep

th, k

m

Pressure, P


GPa.

km

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200 250 300 350 400

dep

th, k

m

Density vrs pressure

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300 350 400GPa.

kg/m3

Density vrs pressure

0

2000

4000

6000

8000

10000

12000

14000

0 50 100 150 200 250 300 350 400GPa.

kg/m3

compression

compression

com

pos

itio

n

chan

ge

ph

ase

chan

ges liq

uid

to

solid

mantle density

crustal density


Inner core/outer core boundary

fluid, 90% iron

solidified iron

2000 4000 km 6000 8000 10,000 12,000

Mg(Fe) silicates

phase changes

basaltic-granitic crust

chemical stratification and differentiation

cool, strong lithospheric boundary layer

slowly convecting mantle:plate tectonic engine

rapidly convectingouter core:

geomagnetic dynamo

solid inner core

subd

uctio

n

seafloor spreading

core-mantle thermo-chemical boundary layer

2000 4000 km 6000 8000 10,000 12,000

crust

Earth’s convective systems

upper mantle

lower mantle

transition zone

outer core

CMBD”

0 2000 4000 500030001000Temperature, degrees C

iron melting

Adiabatic gradient

near surface thermal boundary layer = lithosphere

D” = Lower mantle thermo-chemical boundary layer

mantle convectionadvective heat flow

conductive heat flow

conductive heat flow

Adiabatic gradient

Temperature in mantle

?

mantle m

elting

Temperature profile through

entire earth

Lowrie, Fundamentals of Geophysics, Fig. 6.26

Mantle convection, hot spots and plumes

Average P-wave velocity perturbation in the lowermost 1000 km of the mantle

abstract

inner core

mantle

The geomagnetic dynamo:• turbulent fluid convection• electrically conducting fluid• fluid flow-electromagnetic interactions• effects of rotation of earth

Generation of Earth’s magnetic field in the outer core

outer core

Geomagnetic field

Documents

Structure of Earth as imaged by seismic waves