Transcript Horizontal Forces in Isostasy, Pressure, Prelim Review

nonsequitur
Science searches for the true by tying to eliminate the untrue.
“It is a process of separating the demonstrably false from the
probably true.” [Lynton Caldwell]
Authentic science operates on the assumption that a concept
can be shown to be false. Falsification occurs when a concept
either is shown to be logically inconsistent or is demonstrated to
run counter to direct observations.
TJs & Internal Plate Deformation
• (1) Plate Tectonics basic simplifying assumption
that plates are perfectly rigid. However real plates
do sometimes have internal plate deformation
(e.g. Juan de Fuca)
• (2) Triple Junctions (TJs) are places where 3
plates meet. Their kinematic and geometric
evolution can be predicted from plate tectonics
principles as long as the 3 plates maintain
constant velocities.
Juan de Fuca & TJs
Mantle Plumes & Hotspots
• Intraplate volcanism on oceanic plates often forms
a pattern of linear chains of islands/seamounts
• The conventional picture for the formation of these
changes is that they reflect the melting of mantle
that is locally upwelling beneath the focus of
volcanism in a mantle plume
• This hypothesis offers, in particular, a simple
explanation for why the chains on different plates
can all be viewed as being created by plates that
move over multiple nearly stationary mantle plumes
– upwelling plumes that are nearly stationary with
respect to each other…. forming a ‘hotspot’
reference frame with respect to which absolute plate
motions are inferred
Seamoount Trails
Hotspot Tracks
Conceptual model for hotspot
volcanism
On Pressure
• Pressure is a force/area [a stress]
• Pressure is a tensor. (the force depends on the
direction of the surface. However the magnitude of
the force is independent of direction.
Force
Normal vector
P (tensor)
Pressure, Isostasy, and Horizontal Forces
• Each column isostatic equilibrium has the same weight
of overburden at its base (equal pressure)
• If the mean densities and heights of each column are
different, there will be a net horizontal force on the
material (isostasy only reflects a vertical force balance)
2h
Isostasy (same overburden at base)
leads to net horizontal force Ph
/2
Flhs = Ph
P
h

Frhs = Ph/2
P
How big?
• Continental crust is ~40km thick
• Continental shelves and their adjacent oceanic abyssal plains differ in
elevation by ~5-6km (say 5000m for this estimate)
• Mean density of continental crust is 2800 kg/m3 (2.8Mg/m3)
• Pressure at base of continents (compensation depth) is 2800 kg/m3 x
10 m/s2 x 40,000m = 1.1GPa (1.1GN/m2)
• Net horizontal force F ~1.1GPa x 5000m (height difference) = 5.5TN
• Net horizontal stress associated with isostasy  = F/40000m = 0.14GPa
i.e. = ~5,000/40,000 (1/8) of the pressure at the depth of compensation
• Implication: Lithosphere can elastically support stresses at least of
order 0.14GPa (atmospheric pressure = 0.1 MPa, 1400 times less).
In other words, crustal rocks do not typically creep under differential
stresses of order 1400 atmospheres
Review for Prelim 1
• Prelim will be roughly 2/3 non-quantitative questions and 1/3
quantitative ones
• Questions can cover all material to date— but there will be no
mathematical derivations (e.g. ‘show this math expression to be
true’)
• Will be closed book exam, but you will be given a sheet with all
formulas that you would need to use — and many more useless
ones so you will need to recognize what expression is used for
what
• Study suggestions:
– Review notes & problem sets (quantitative problems will be
based on notes & problems)
– Review handouts: e.g. Einstein handout on origin of meanders
– Review the ‘review questions’ at the end of each chapter in the
Marshak assigned reading (some non-quantitative questions will
be taken from these questions)
Review for Prelim 2 – Material Covered
• What is a mineral? What are diagnostic differences
between igneous, sedimentary, & metamorphic
rocks, and how are they formed?
• What is origin of global atmosphere & ocean
circulation patterns? El Nino? Monsoon seasons?
What is global distribution of water? What is the
meaning of residence time?
• Darcy’s Law — what is it? What do various terms
in this relation mean? Groundwater flow & relation to
water table, Aquifers, Artesian Basins & basin-scale
groundwater flow… There will be a quantitative
question or two on some aspect of Darcy’s Law &
groundwater flow
Review for Prelim 3 – Material Covered
• What is the origin of stream meanders? — read the little
handout on Einstein’s explanation for the formation of
stream meanders
• Seafloor spreading, origin of seafloor magnetic anomalies,
Wilson cycle
• Plate tectonics, Transform fault, fracture zones, ridges,
trenches, subduction zones, relative and absolute plate
motions
• Mid-ocean ridge volcanism, arc volcanism, hotspot
volcanism
• Seafloor depth vs. age, thermal model of plate cooling with
seafloor age, volume & density changes associated with
cooling… (quantitative)
• Isostasy, implications for depth vs. age, difference between
ocean & continent heights… (quantitative)
Stress - Generalization of Force to a Volume
• Normal stress (force/area perpendicular to a surface -- like pressure)
• Shear stress (force/area parallel to a surface)
xz or xz
xx
z
x
Direction of normal
vector to surface
Direction of force
Earth’s Rheology: Visco-elastic
• Rock becomes viscous at depth (below lithosphere)
• Rock is elastic/brittle when cold (lithosphere)
F/A
u
D
Analogy to rock deformation:
Bragg’s bubble model
Elastic
 ue  F
z
~1011
Pa (100GPa)
~1021 Pa-s (1ZPa-s)
A
ue = elas tic displaceme nt =
uv 
Viscous
 u&v  F t
z
A
DF  1 
A   
uv
DF  1 
 rate of viscous disp lacement =
t
A   
Earth’s Rheology: Visco-elastic
F/A
u
D
Analogy to rock deformation:
Bragg’s bubble model
Elastic
Viscous
 u&v  F t
 ue  F
z A
z
DF  1 
ue = elas tic displaceme nt =
A   
u
DF  1 
uv  v  rate of viscous disp lacement =
t
A   
A
u = ue +uv
u
DF  1 t 
 ,

A   
Why we know Earth can be viscous
(postglacial rebound)
Main mechanisms for creep: Movement of
imperfections in crystal lattice (dislocations &
vacancies)