ES204 Plate Tectonics Lecture Eli Silver X 2266 Email: esilver@ucsc.edu Room: A142 EMS

Outline

1.  What is a plate? How Thick? 2.  Why does the Earth have Plate Tectonics?

3. Are all tectonics a result of plate edge effects?

Topography of the Earth’s Surface

What is a Plate?

Plate thickness can be measured:

• Seismically

• Thermally

• Elastically

Heat Flow through the lithosphere is governed by Fouriers’s Law:

q = -k ∂T/ ∂z Where q is the rate of heat flow/area k is thermal conductivity z is positive down and q positive upward T is Temperature

This describes conductive heat flow

Thermally

For the upper mantle, thermal conductivity, k, Is about 3 Watts/meter/°C

And q is generally expressed as mW/m2

For 140 my old lithosphere, the temperature is 1000 °C at 100 km. If k = 3 W/m/ °C, what is q?

Ans: 0.03 W/m2 or 30 mW/m2

Temperature at base of TBL ~ 1200 oC

Elastic Thickness Of the Lithosphere

from Watts, 2001

wo

w(x) = w0e(-x/α) [cos(x/α) + sin(x/α)]

Where w0 is the maximum deflection at the load

α = [4D/g(ρm – ρw)]1/4

Known as the flexural parameter Where D = Eh3 / 12(1-υ2) D is the flexural rigidity of the plate h is the elastic thickness of the plate υ is Poisson’s ratio E is Young’s Modulus g is gravity ρm and ρw are mantle and water densities

To solve for the elastic thickness, h:

Choose a value for h, solve for D, then α. Next solve for w at a number of x locations. Plot, and compare your curve with the observed data. Change h to a higher or lower value of h, depending on this comparison.

Constants: E = 1011 Pa υ = 0.282 (ρm – ρw) = 2400 kgm/m3

g = 9.8 m/s2

wo

-2500

-2000

-1500

-1000

-500

0

500

0 50000 100000 150000 200000 250000 300000 350000

30 Km 30 Km

-2500

-2000

-1500

-1000

-500

0

500

0 20000 40000 60000 80000 100000 120000 140000 160000

wo

Estimating Lithospheric Thickness, z, as a function Of Plate Age, t:

With z in km, and t in Ma, z ~ 11√t

t = 1 My, z = 11 km

t = 10 My, z = 35 km

t = 100 My, z = 110 km

What thicknesses do you get from Crustal Flexure studies?

Less than half these numbers.

Often 10 km or less, and 25 to 30 km is Definitely on the high end for Oceanic Crust.

Why the large difference???

Rock strength varies with depth in the Crust and upper mantle depending on:

• Temperature • Rock composition • Crustal Thickness • Strain rate • Water content

Strength of the Lithosphere

The Jelly Sandwich Crust – Upper Mantle

Top: Variable Crustal Thickness

Middle: Variable Temperature

Lower: Variable Strain rate

Wet vs. Dry

East African Rifts: Earthquake depths and Crustal Rheology

Albaric et al., 1009; Tectonophysics

Effects of crustal composition and heat flow

Earthquake Depth-Frequency● Yield Strength Envelopes

Frequency-Depth distribution of Earthquakes In California – A function of:

• Thermal structure • Crustal Thickness • Petrology and Geochemistry • Strain rate • Water content