L2 - Defining a Plate

Understanding Plate Boundaries and Definitions

The lecture discusses the complexities of defining a tectonic plate, particularly focusing on the base of the plate and the various methods used to determine it.

Thermal Definition of a Plate

Convective Theory

In a convecting medium, thermal boundary layers form at the top and bottom. The Earth's cooling at the surface creates a thick, rigid outer boundary layer that behaves rigidly. This is due to high viscosities (e.g., $10^{21}$ - $10^{22}$ pascal seconds), making it much stiffer than the material below.

Composition of Tectonic Plates

Tectonic plates are composed of the lithosphere, including both the crust and a portion of the upper mantle. Thickness varies:

• Mid-Ocean Ridges: Plates have 2-3km thickness where they are newly formed.

• Old Oceanic Crust: Can reach up to 180 km in thickness, commonly at the far edges of the Pacific.

• Beneath Continents: Varies from thin to over 300 km thick, especially in continental cratons, sometimes referred to as the 'tectosphere'.

Seismological Methods

Seismology helps to image plate structures using seismic velocities. Higher velocities indicate rigid, solid media, while lower velocities indicate viscous, warm areas.

• Active Areas (e.g., Western North America): High velocities at the top, followed by a low-velocity region.

• Canadian Shield: High velocities extending to depths of nearly 200 km.

• Old Ocean Part of Western North America: Thinner, well-defined plate.

Plate Thickness and Age

Plate thickness increases with age, following a square root relationship, which becomes apparent when moving away from a mid-ocean ridge.

The relationship between plate thickness and age is described as following a square root function.

Methods to Define the Base of the Plate

1. Thermal Description: Using an isotherm (a line of constant temperature) to define the base.

2. Mechanical Definition: Identifying the transition from rigid to ductile behavior.

3. Seismic Definition: Observing the reduction in seismic velocities.

4. Experimental Research: Recent research suggests the base of the plate might be sharper than previously thought.

Isotherms and Seismicity

Seismicity moving away from mid-ocean ridges typically doesn't go deeper than the 600-degree isotherm. However, the low-velocity zone corresponds more closely to the 1000-degree isotherm, creating ambiguity in defining the plate boundary.

East Pacific Rise

Velocity structure images under the East Pacific Rise show asymmetrical plate production, with one side differing from the other.

Forces Driving Plate Tectonics

Primary Forces

1. Slab Pull: The force exerted by a dense, descending plate sinking into the mantle drives the movement. This is considered the dominant force.

2. Ridge Push: Upwelling mantle at mid-ocean ridges creates increased topography, and gravity causes the ridge to push the plate towards an equipotential surface.

3. Trench Suction: Coupling between overriding and downgoing plates at trenches creates suction, pulling plates.

4. Shear Tractions: Convection in the mantle exerts shear forces on the base of the lithosphere.

Local Tectonic Forces

• Island Loading: Large islands (e.g., Hawaii) deform the plate, creating a moat around the island. The degree of depression indicates plate strength.

• Glacial Rebound: Removal of heavy ice loads (e.g., from Antarctica) causes the plate to rebound. The rate of rebound relates to plate strength, viscosity, and thickness. Haskell's work in the 1930s estimated mantle viscosity from plate rebound.

• Subduction Zone Bending: The amount of bending at a subduction zone indicates plate strength.

Examples of Isostatic Rebound:

• Scottish islands and Hudson Bay are rebounding upwards.

• First Nations communities have had to relocate due to coastal rebound.

Thames River Tidal Barrage:

Built primarily due to London's rising, exacerbated by sea-level rise from climate change.

Mathematical Descriptions

Factors Influencing Plate Response

Key parameters determining how plates respond to forces include:

• Temperature as a function of depth and time, $T(z,t)$

• Pressure as a function of depth, $P(z)$

• Density as a function of depth, $\rho(z)$

• Composition (felsic vs. mafic rocks)

• Rheology (how rocks deform)

• Strain rate

Contrasting Lithosphere

There is a significant contrast between oceanic and continental lithosphere.

Oceanic Lithosphere:

• Thin crust that thickens quickly away from the ridge.

• Mantle component thickening to about 125 km.

Continental Lithosphere:

• Thick crustal roots under mountains.

• Lithospheric roots below.

• Generally thicker and more irregular than oceanic lithosphere.

Heat Flow Equation

To understand plate thickening, we examine how temperature varies with distance from where the plate forms. This involves the heat flow equation, which includes factors like thermal diffusivity, thermal conductivity, density, and specific heat constant.

Solution Form:

The solution to the heat equation involves the error function:

$T(z,t)=\left(T_{m}\right)\cdot erf(\frac{z}{2\sqrt{\kappa t}})$

Where:

• $T(z, t)$: Temperature as a function of depth and time

• $T_m$: Mantle temperature

• $z$: Depth

• $\kappa$: Thermal diffusivity

• $t$: Time

With a surface temperature of 0 degrees, the equation simplifies. By converting $t$ to $x/V$, where $x$ is distance and $V$ is velocity, we can plot the isotherm's progression over time.

Result:

Depth or plate thickening increases as the square root of the lithospheric age. Described in the paper by Parsons and Slater.

Limitations of the Simple Thermal Model

Reality is more complex than the simple thermal boundary layer model. Observations of heat flow show less heat flow near the ridge due to hydrothermal circulation. Further away, heat flow is slightly higher than predicted, suggesting warming effects from the mantle that flatten the isotherms beyond 70 million years.

Plate Model vs. Half-Space Model:

The plate model considers the insulating effect of the lithosphere, leading to heat build-up in the mantle and a flattening of isotherms in older plates.

Mechanical Definition: Seismicity and Plate Strength

Earthquake Distribution

We define plates seismically as strong enough to have brittle failure and earthquakes.

Oceanic Intraplate Earthquakes

Compilations show limited earthquake depths, typically not exceeding the 600-degree isotherm. Slower spreading rates correlate with deeper seismicity, while faster rates have shallower events.

Challenges in Depth Calculation

Accurately calculating earthquake depths, especially for shallow events, is challenging.

Alex Copley's Work:

Data from the Atlantic shows earthquakes generally not deeper than 600 degrees, aligning with the strength of the plate.

Seismic Velocity Definitions

Seismic Waves

Seismic waves travel faster in rigid plates and slower in ductile mantle. Surface waves are used to image velocity structures.

Types of Seismic Waves:

• Body Waves: Propagate through the Earth's interior.

• Surface Waves: Cling to the Earth's surface and decay exponentially with depth. These include Love waves (transverse polarization) and Rayleigh waves (vertical polarization).

Surface waves exhibit dispersive behavior, with low-frequency parts arriving before high-frequency parts. Low-frequency waves are sensitive to deeper, faster parts of the Earth.

Dispersion Patterns

Plots of velocity vs. frequency/period show that young lithosphere has lower velocities than old lithosphere at short periods, but they converge at long periods, reflecting plate thickness variations.

Seismic Velocity Profiles

Profiles of depth vs. shear wave velocity show steep drops in velocity for young lithosphere and more gradual changes for older plates.

Forsyth's Work

Forsyth et al. used surface waves to calculate dispersion curves and invert them for seismic velocity as a function of depth, mapping plate thickening with age.

Receiver Functions and Plate Boundaries

Receiver Functions

Exploits conversions of seismic energy from P-waves to S-waves (and vice versa) at boundaries with contrasting material properties. This method helps identify the Moho and the Lithosphere-Asthenosphere Boundary (LAB).

Lithosphere-Asthenosphere Boundary (LAB)

Signals from seismic stations across a wide area are used to isolate conversions and map the thickness of the crust and LAB.

Ocean Bottom Seismometer Experiment

Experiment by Kate Reichert et al. used ocean bottom seismometers near the Mid-Atlantic Ridge to image the plate structure. The instruments were deployed for a year and picked up. It was used to try and image what the Atlantic plate looks like as it thickens and grows away from the Mid Atlantic Ridge.

Results

Images revealed a more complicated lithosphere, with the base of the lithosphere varying significantly. Tomographic images showed low-velocity zones, possibly due to convective instabilities.

Magnetotellurics (MT)

Uses electromagnetic induction to map conductive and resistive parts of the mantle by measuring variations in magnetic fields induced by solar winds. In the Pacific, the MT data shows a consistent picture of plate formation and thickening. In the Atlantic, MT data reveals a more complex picture, with a thin melt layer at the base. Conductive areas indicate mantle convection and instabilities.

Plate Response to Loads

Flexural Rigidity

• Island or Mountain Loading: The plate bends under the weight of islands or mountains, creating a foreland basin.

• Glacial Rebound: After ice melts, the plate rebounds; the rate indicates plate strength.

• Elastic Thickness: The elastic thickness of the lithosphere can be determined by analyzing how it bends under loads. The elastic thickness is related to flexural rigidity and elastic parameters (Young's modulus and Poisson's ratio).

• Hudson Bay Example: Raised beaches show ongoing rebound.

Effective Elastic Thickness

The effective elastic thickness, related to flexural rigidity, quantifies how hard it is to bend the plate. It is smaller than the true lithospheric thickness and ranges from 3 to 80f km, although up to 120 km in some regions.

It depends on Young's modulus (ratio of pressure to deformation) and Poisson's Ratio (lateral expansion vs. contraction).

Effective Elastic Thickness and Age

Correlates with age, showing that older plates are thicker. Consistent with plate cooling models, surface wave imaging, and mechanical thickness estimates from earthquakes.

Conclusion: Defining the Base of a Plate Is Complex

There are several ways to define plates:

• Seismic lithosphere

• Elastic lithosphere

• Thermal lithosphere

Each definition yields slightly different results. The low-velocity zone generally begins at the 1000-degree isotherm. Seismic phase conversions at the base of the asthenosphere suggest a more complex picture than simple thickening. The most important thing is to be specific about how you're defining it and what you're using it for.