Plate Tectonics World Map: Euler Poles, Boundaries and Drift

Presets

Live readouts

Graphs

Selected point

click to inspect

Process graphs

process

speed

drift

Numerical checks

running...

How to use

Pick a real place under Presets (each uses the opening/closing rate stored for that boundary in PB2002), then click the map to inspect any point: plate, speed in the chosen frame, nearest boundary type and rate. Switch the reference frame to see how the same plates look from Africa, Eurasia or the mantle. Drag the time offset or tick Animate drift to watch the plates move at today's speed. Try: (1) Pacific plate fixed - everything else moves away; (2) show Euler poles and check that speed is zero at the pole; (3) India fixed vs Eurasia fixed at the Himalaya; (4) the Transform preset with a small slip at failure to get frequent smaller quakes; (5) the Hotspot preset and compare the model track with the dated volcanoes. Space pauses, R resets.

The science

Rigid plates on a sphere. Euler's theorem: any motion of a rigid plate on a sphere is a rotation about an axis through the centre, the Euler pole. A point at position r (unit vector) moves with the velocity

v = R (ω × r), speed = R ω sin(d), R = 6371 km

where ω is the plate's angular velocity (deg/Myr) and d the angular distance to the pole. 1 deg/Myr at 90 degrees from the pole is 111 mm/yr, so the speed grows from zero at the pole to a maximum on the great circle 90 degrees away. The poles used here are the 52-plate table of Bird (2003, PB2002), given relative to the Pacific plate. The relative velocity of plate A with respect to B is (ω_A - ω_B) × r, so choosing a different reference frame just subtracts that frame's rotation vector from every plate.

Reference frames. The "no-net-rotation" frame is the one in which the area-weighted total rotation of the lithosphere vanishes: ∑_i (A_i I - M_i)(ω_i - ω₀) = 0, with A_i = ∫ dA and M_i = ∫ r r^T dA over plate i. It is solved here from the 0.25 degree plate raster. It is only a stand-in for the true mantle (hotspot) frame, which differs by a few mm/yr.

Boundary types. Each of the 5 824 boundary steps carries Bird's class: spreading ridge (OSR), transform (OTF, CTF), subduction (SUB), oceanic and continental convergence (OCB, CCB) and continental rift (CRB). The map colours them by kinematic family: divergent (blue), transform (green), convergent (orange). The opening rate is the boundary-normal component of the relative velocity, the shear rate the boundary-parallel one.

Drift in time. The time slider rotates every plate about its pole by ω t, an exact spherical rotation (Rodrigues formula), using today's rates. Real rates changed over tens of millions of years (India slowed from about 18 cm/yr to 5 cm/yr), so beyond a few tens of Myr this is an illustration of the mechanism, not a plate reconstruction. A few fast microplates (Easter, Juan Fernandez, Manus, Tonga ...) follow a neighbouring large plate when drifting.

Process models (cross-section panel). Ridge: half-space cooling gives seafloor depth d = 2.5 + 0.35 √age km and lithosphere thickness 2.32 √(κ t) = 13 √age km (κ = 10^-6 m²/s); stripes are random polarity chrons. Subduction: the slab is a conveyor at the plate speed; the arc sits where the slab surface is about 110 km deep, and quakes along the Wadati-Benioff zone follow the Gutenberg-Richter law log N = a - b M with b = 1. Collision: crustal area is conserved, T = T₀ W / (W - shortening), and Airy isostasy lifts the surface by ΔT (1 - ρ_c/ρ_m) with ρ_c = 2800 and ρ_m = 3300 kg/m³. Transform: a stick-slip spring-slider accumulates slip deficit at the plate rate and releases it at failure; the moment is M₀ = μ A D (μ = 30 GPa, 100 km x 15 km fault) and M_w = 2/3 (log₁₀ M₀ - 9.1). Hotspot: the plume is fixed, the plate carries volcanoes away, age = distance / speed.

Honest simplifications. Plates are perfectly rigid (real boundaries are broad deformation zones); cross-sections are schematic, with the relief vertically exaggerated and slab geometry straight; model earthquakes are random draws weighted by boundary type and rate, not a seismic catalogue; the hotspot track from constant Pacific motion cannot reproduce the 47 Ma Hawaii-Emperor bend (the plate or the plume changed course). Ages of the Hawaiian-Emperor volcanoes are rounded literature values.

Data and credits. Plate polygons, boundary steps and Euler poles: Bird, P. (2003), An updated digital model of plate boundaries, Geochem. Geophys. Geosyst. 4(3), 1027 (Open Data Commons Attribution). Shaded-relief and bathymetry base map and coastlines: Natural Earth (public domain). Literature rates used in the checks: DeMets et al. (1994, NUVEL-1A) and GPS studies.