Lecture 11

Seismic Tomography and

Mantle Convection

DOI: 10.1126/science.285.5431.1231, 1231 (1999);285 Science

Miaki Ishii and Jeroen Trompin Velocity and Density of Earth's MantleNormal-Mode and Free-Air Gravity Constraints on Lateral Variations

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Discussion paper 3

Kustowski et al., GJI (2008)

-  Large degree of heterogeneity around 100-200 km depth with correlation with surface tectonics

-  Correlation between velocity anomalies and surface

tectonics decreases with depth. Amplitude of heterogeneity also decreases with depth

-  At lowermost mantle (2300-2900 km) amplitude of

heterogeneity becomes larger

-  Amplitude of P-wave anomalies half that of S-wave anomalies

Velocity anomalies have completely different dynamical implications depending on whether their origin is thermal or chemical

Anharmonicity -  Increase in temperature leads to thermal expansion,

so density decreases -  As a result, distance between neighboring atoms

increases, leading to weaker atomic bonding

Anelasticity -  Elastic velocities can vary with frequencies -  For lower frequencies velocities are lower

-  Effect of viscous response of a material on elastic wave propagation

Problems: -  Very extensive partial melting would be predicted

throughout the mantle

-  significantly smaller than values obtained from seismic tomography (~2 - 3.5)

-  = 0.7-1.0 for most materials, while

observed = 0.2- 0.4 and sometimes negative in deep lower mantle

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

5

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

Rr/s,p ⌘dlogr

dlogV

s,p

5

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

Rr/s,p ⌘dlogr

dlogV

s,p

5

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

Rr/s,p ⌘dlogr

dlogV

s,p

R

s/p

=g

s

�1/3

gp

�1/3

gs,p =

∂logws,p

∂logr

5

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

Rr/s,p ⌘dlogr

dlogV

s,p

R

s/p

=g

s

�1/3

gp

�1/3

gs,p =

∂logws,p

∂logr

5

Grüneisen parameter

~ 1.0 – 1.5

~ 1

Observed 2 – 3.5

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

Rr/s,p ⌘dlogr

dlogV

s,p

R

s/p

=g

s

�1/3

gp

�1/3

gs,p =

∂logws,p

∂logr

5

Describes the effect that changing the volume of a crystal lattice has on its vibrational properties

✓∂logV

s,p

∂T

◆=�a(g

s,p �1/3)

6

-  α decreases significantly with pressure

-  ϒ changes only weakly with depth

-  amplitude of velocity anomalies corresponding to same temperature variation will decrease with depth

Decrease in amplitude of velocity anomalies with depth does not imply a decrease in temperature anomalies with depth

Masters et al. (2000)

Problems: -  Very extensive partial melting would be predicted

throughout the mantle

-  significantly smaller than values obtained from seismic tomography (~2 - 3.5)

-  = 0.7-1.0 for most materials, while

observed = 0.2- 0.4 and sometimes negative in deep lower mantle

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

5

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

Rr/s,p ⌘dlogr

dlogV

s,p

5

Nu =Qd

kDT

⇠ 10

Pr =nk⇠ 10

24

—2

f = 0

Y

m

l

(q,f) = Ne

imfP

m

l

(cosq)

P

m

l

(x) =(�1)m

2

l

l!

(1� x

2)m/2

d

l+m

dx

l+m

(x2 �1)l

R

s/p

⌘ dlogV

s

dlogV

p

Rr/s,p ⌘dlogr

dlogV

s,p

5

- At frequency range of seismic waves anelasticity becomes important, which increases temperature sensitivity of seismic wave velocities (#1)

-  This effect larger for S-waves than P-waves (#2)

-  Changes in seismic wave velocity through this mechanism occurs without much change in density (#3)

Effect of Anelasticity