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Earthquake EngineeringGE / CEE - 479/679

Lecture 2. Plate TectonicsJanuary 24, 2008

John G. Anderson

Professor of Geophysics

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Handout Today

• Chapter 2. Plate Tectonics– Students are advised to read this as your

textbook on this topic.– Solve exercises 3, 4, 5, 6, and 8.– For extra credit, solve exercises 9, 11.– Exercises are due Jan. 31.

Source: Geological Society of America web: http://www.geosociety.org/science/timescale/timescl.htm

Source: Geological Society of America web: http://www.geosociety.org/science/timescale/timescl.htm

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http://www.physics.mcgill.ca/~crawford/PSG/PSG12/204_97_L12.2_earthxn.html

Crust - rocks (granite, basalt); density ~ 3 g/cm3

Lithosphere - "rock-sphere" - rigid layer (includes crust)

Asthenosphere - "weak-sphere" (lower v seismic waves) Convection currents flow in the 'plastic' asthenosphere, and the plates of the lithosphere ride on these.

Mantle - iron-rich, mainly solid rock

Outer core - liquid iron and nickel

Inner core - solid iron, nickel

Distances are in kilometers.

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The radii for the tops of the major layers are more accurate on this plot.

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http://topex.ucsd.edu/marine_topo/gif_images/global_topo_small.gif

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http://www2.ocean.washington.edu/oc540/lec02-1/

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http://www2.ocean.washington.edu/oc540/lec02-1/

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Why believe plate tectonics?

• Geography - matching continental boundaries.• Geology - units match where continental

boundaries match.• Paleomagnetism

– Characteristics of the magnetic field

– Polar wander

– Mid-ocean ridge magnetic anomalies.

– Past and future Earth.

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Why believe plate tectonics?

• Ocean drilling results.

• Hot spots

• Earthquakes

• Direct measurements

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http://www.ngdc.noaa.gov/mgg/fliers/96mgg04.html

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Direct measurement using the Global Position System

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Engineering applications

• Context to understand seismicity

• Quantitative estimate of earthquake rates

• Seismic gaps

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cos sin sin cos cos cos( )Δ = + −φ φ φ φ ψ ψ1 1 1

Distance between two points on the Earth’s surface

Where:(φ, ψ) = (latitude, longitude) of selected point on plate boundary(φ1, ψ1) = (latitude, longitude) of pole of relative rotation

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u a=ω sinΔu = relative rate of plate motiona = radius of Earth, 6370 kmΔ = distance from pole of rotation, in degreesω = rotation rate of plates about their pole

(a different use of the symbol ω)

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( ) ( )okm

cmkm

y

myradians

myu 77sin10637010

deg180

deg98.0 56

⎭⎬⎫

⎩⎨⎧

⎟⎠

⎞⎜⎝

⎛

⎭⎬⎫

⎩⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= −π

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Seismic Moment

• Definition of Seismic Moment

• M0=μAD

– μ is the shear modulus of the rock– A is the area of the fault on which slip takes

place– D is the average slip on the fault

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Application to Japan

• Accept for the time that the plates in Japan converge at u=10.6 cm/yr.– This is a horizontal convergence rate.– .

• The last large earthquake at Tokyo was 1923. – Time past is (2005-1923)=84 years.

• Then accumulated slip is: – 10.6 cm/yr*82 yr=890 cm.

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Application to Japan (cont.)

• Then accumulated slip is: – 10.6 cm/yr*82 yr=890 cm.

• Suppose the fault is 200 km long and the seismogenic zone is from 0 to 30 km depth.– The subduction zone dips, lets say at 40o

– Width = 30 km/cos(dip)=40 km• M0=μAD

= 4*1011 dyne/cm2 * 200 km * 40 km * (105 cm/km)2 * 890 cm

= 2.8 * 1028 dyne-cm

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Moment Magnitude

• MW=(2/3) log M0-10.73

• This is the preferred magnitude scale in the seismological community.

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Application to Japan (cont.)

• M0=μAD=2.8 * 1028 dyne-cm

MW=(2/3) log M0-10.73 =8.24

Conclusion, by these assumptions, there is enough strain accumulated to cause a MW=8.2 earthquake under Tokyo.