Plate Tectonics

Plate tectonics is the grand theory that explains how Earth's outer shell moves and deforms. It's the unifying theory of geology that explains earthquakes, volcanoes, mountain ranges, ocean basins, and the distribution of fossils and rocks around the world.

Historical Development of the Theory

Continental Drift Hypothesis

In 1912, Alfred Wegener proposed continental drift based on several lines of evidence:

• Geological fit: The coastlines of South America and Africa fit together remarkably well
• Fossil evidence: Identical fossils of Mesosaurus, Glossopteris, and Lystrosaurus found on now-separated continents
• Glacial deposits: Evidence of ice age deposits from Gondwana glaciation that required continents to be connected
• Rock correlations: Matching geological formations across ocean basins

Despite compelling evidence, Wegener's hypothesis was initially rejected because he couldn't explain the mechanism.

Seafloor Spreading

In the 1960s, Harry Hess and Robert Dietz proposed seafloor spreading based on new oceanographic data:

• Mid-ocean ridges: Underwater mountain ranges with volcanic activity
• Paleomagnetic stripes: Symmetric patterns of magnetic anomalies on either side of ridges
• Age progression: Ocean floor becomes progressively older with distance from ridges

The process follows this model:

Plate Boundaries

Divergent Boundaries

At divergent boundaries, plates move away from each other. This process creates new oceanic lithosphere:

Characteristics

• Mid-ocean ridges: Underwater mountain chains with rift valleys
• Continental rifts: Continental extension zones (e.g., East African Rift)
• Volcanism: Basaltic magmatism from decompression melting
• Earthquakes: Shallow focus, low magnitude

Spreading Rates

• Slow spreading (<5 cm/year): Mid-Atlantic Ridge, rugged topography
• Fast spreading (>9 cm/year): East Pacific Rise, smooth topography
• Intermediate: Examples include Mid-Indian Ridge

Convergent Boundaries

At convergent boundaries, plates move toward each other. The outcome depends on the types of lithosphere involved:

Oceanic-Continental Convergence

• Subduction: Oceanic plate descends beneath continental plate
• Features: Deep oceanic trenches, volcanic arcs (Andes-type)
• Processes: Sediment accretion, metamorphism, partial melting

Oceanic-Oceanic Convergence

• Subduction: Older/denser oceanic plate subducts
• Features: Island arcs, trenches (e.g., Japan, Indonesia)
• Processes: Back-arc spreading, metamorphism

Continental-Continental Convergence

• Collision: No subduction due to buoyancy of continental crust
• Features: Mountain ranges, crustal thickening (Himalayas)
• Processes: Metamorphism, crustal melting, isostatic response

Transform Boundaries

At transform boundaries, plates slide past each other horizontally:

• Transform faults: Connect segments of ridges or trenches
• Characteristics: Strike-slip motion, shallow earthquakes
• Examples: San Andreas Fault, Alpine Fault

Mantle Convection

Convection Mechanism

Mantle convection drives plate motion through thermal circulation:

Where:

• $g$ = gravitational acceleration
• $\alpha$ = thermal expansion coefficient
• $\Delta T$ = temperature difference across layer
• $d$ = layer thickness
• $\nu$ = kinematic viscosity
• $\kappa$ = thermal diffusivity

Forces Driving Plate Motion

Ridge Push

• Mechanism: Gravitational force due to elevated ridge topography
• Formula: $F_{ridge} = \rho g h A$
• Contribution: Up to 30% of driving force

Slab Pull

• Mechanism: Gravitational force of dense, sinking oceanic lithosphere
• Formula: $F_{slab} = (\rho_{slab} - \rho_{mantle}) g V_{slab}$
• Contribution: Primary driving force (up to 70%)

Mantle Drag

• Mechanism: Friction between plate base and convecting mantle
• Direction: Can either aid or oppose motion

Triple Junctions

Where three plates meet, the configuration must satisfy the force balance:

Common triple junction types:

• R-R-R: Three ridges (unstable)
• T-T-T: Three trenches (unstable)
• R-R-T: Two ridges, one trench (stable)
• R-T-T: One ridge, two trenches (stable)

Plate Motion Models

Euler's Fixed-Axis Rotation

Plate motion can be described as rotation about a fixed axis:

Where:

• $\vec{v}$ = velocity vector
• $\vec{\omega}$ = angular velocity vector
• $\vec{r}$ = position vector

Relative vs Absolute Motion

• Relative motion: One plate relative to another
• Absolute motion: Plate motion relative to a fixed reference frame (e.g., hotspots)

Present-Day Tectonics

Major Tectonic Plates

• Pacific Plate: Most oceanic, rapid motion
• North American Plate: Mixed continental and oceanic
• Eurasian Plate: Largest continental component
• African Plate: Stable core with surrounding activity
• Antarctic Plate: Covers the South Pole region

Microplates and Small-Scale Tectonics

• Scotia Plate: Between South America and Antarctica
• Caribbean Plate: Between North and South America
• Anatolian Plate: Caught between major plates

Real-World Application: Himalayan Orogeny

The collision between the Indian and Eurasian plates provides an excellent example of continental collision processes.

Collision History

# Himalayan collision analysis
collision_age = 50  # Ma (time when India collided with Asia)
indian_velocity = 15  # cm/year (India's velocity before collision)
current_velocity = 4   # cm/year (India's current velocity relative to Asia)

# Calculate convergence
total_convergence = (collision_age * 1e6) * (indian_velocity - current_velocity) * 1e-2  # meters

print(f"Time since collision: {collision_age} million years")
print(f"India's velocity before collision: {indian_velocity} cm/year")
print(f"India's current velocity: {current_velocity} cm/year")
print(f"Total convergence: {total_convergence/1e3:.0f} km")

# Calculate crustal thickening
# Assuming ~20% shortening is accommodated as crustal thickening
crustal_thickening = 0.20 * total_convergence  # meters
initial_crustal_thickness = 35000  # meters (normal continental crust)
current_crustal_thickness = initial_crustal_thickness + crustal_thickening  # meters

print(f"Estimated crustal thickening: {crustal_thickening/1e3:.0f} km")
print(f"Current crustal thickness: {current_crustal_thickness/1e3:.0f} km")
print(f"Normal crustal thickness: {initial_crustal_thickness/1e3:.0f} km")

Isostatic Response

The thickened crust causes isostatic uplift, contributing to the high topography.

Seismic Hazards

The ongoing convergence creates significant seismic risk across the Himalayan region.

Your Challenge: Transform Fault Analysis

Analyze the motion along a transform fault system and calculate the implications for earthquake risk.

Goal: Calculate the motion along a transform fault system and assess the implications for seismic activity.

Fault System Parameters

import math

# San Andreas Fault system parameters
plate_velocity = 3.5    # cm/year (Pacific plate motion relative to North America)
fault_length = 1200     # km (length of major fault segment)
fault_width = 15        # km (depth of seismogenic zone)
shear_modulus = 30      # GPa (shear modulus of crust)
locking_depth = 15      # km (depth to which fault is locked)

# Calculate total displacement over time
time_period = 100       # years (time since last major earthquake)

# Calculate displacement on fault
total_displacement = plate_velocity * time_period  # cm accumulated over time

# Calculate stress accumulation
# Shear stress = (shear modulus) * (shear strain)
# For transform fault, shear strain = displacement / width
shear_strain = (total_displacement/100) / (fault_width*1000)  # unitless (m/m)
stress_accumulation = shear_modulus * 1e9 * shear_strain  # Pa

# Calculate seismic moment
fault_area = (fault_length * 1000) * (locking_depth * 1000)  # m²
seismic_moment = shear_modulus * 1e9 * fault_area * (total_displacement/100)  # N·m

# Calculate equivalent earthquake magnitude
# Mw = (log10(M0) - 9.1) / 1.5
moment_magnitude = (math.log10(seismic_moment) - 9.1) / 1.5

Analyze the relationship between plate motion, stress accumulation, and potential earthquake size along transform faults.

Hint:

• The displacement that accumulates during the interseismic period is released during earthquakes
• Stress accumulates as long as the fault remains locked
• The seismic moment determines the earthquake magnitude

# TODO: Calculate key parameters for earthquake risk assessment
displacement_accumulated = 0  # meters (displacement accumulated since last major event)
stress_increase = 0           # MPa (stress increase in the crust)
seismic_moment = 0            # N·m (seismic moment if all strain released)
earthquake_magnitude = 0      # Moment magnitude of potential earthquake

# Calculate recurrence interval (if slip_per_eq = 3m, for example)
slip_per_earthquake = 3.0     # meters (typical for large SAF events)
recurrence_interval = 0       # years (average time between major events)

# Print results
print(f"Displacement accumulated: {displacement_accumulated:.2f} m")
print(f"Stress increase: {stress_increase:.1f} MPa")
print(f"Seismic moment: {seismic_moment:.2e} N·m")
print(f"Potential earthquake magnitude: {earthquake_magnitude:.1f}")
print(f"Recurrence interval: {recurrence_interval:.1f} years")

# Assess seismic risk (qualitative)
if earthquake_magnitude > 7.5:
    risk_level = "Very High"
elif earthquake_magnitude > 6.5:
    risk_level = "High"
else:
    risk_level = "Moderate"
    
print(f"Seismic risk level: {risk_level}")

How does the rate of plate motion affect the frequency and magnitude of earthquakes along transform boundaries?