12.520 Lecture Notes 24

Growth of Boundary Undulations
• salt domes
• diapirs
• continental delamination
X
3
λ
=
λ
0 cos
2
� x
1
�
=
λ
0 coskx
Figure 24.18
Figure by MIT OCW.
η u
,
� u
η l
,
� l
X
1
General problem: topography on an interface
ξ = ξ
0 cos kx
1 k
=
2
π
λ
(1) If
ρ u
< ρ l
topography decays as
ξ
0 e
− t /
τ
.
(2) If
ρ > ρ u l
topography grows.
Initially
ξ = ξ t /
τ
0 e .
Eventually many wavelengths interact, problem is no longer simple.
Characteristic time
τ depends on
∆ ρ
,
η u
,
η l
, thickness of layers, …

Before glaciation
Subsidence caused by glaciation
Ice Sheet
Surface after melting of the ice sheet but prior to postglacial rebound
Full rebound
Figure 24.19. Subsidence due to glaciation and the subsequent postglacial rebound.
Figure 24.19
Figure by MIT OCW.
•
Weight of ice causes viscous flow in the mantle.
•
After melting of ice, the surface rebounds – “postglacial rebound”.
•
Different regions have different behaviors (e.g., Boston is now sinking).

X
3
�
=
�
0 coskx
Air
X
1
� m
Figure 24.20
Figure by MIT OCW.
Problem: how to reconcile physical boundary conditions with mathematical description?