Resolve plate motion in a common reference frame

1. Define the evidence and frame

A plate boundary is a relationship between moving bodies, not a speed attached to one plate. In a local east–north frame, subtract velocity of plate A from plate B. Then project that relative vector onto a boundary normal directed from A toward B and a perpendicular tangent. Positive normal motion increases separation; negative normal motion closes it.

2. Connect mechanism and model

The fictional velocities are A=(10,0) and B=(a,20) mm/yr. With the normal at angle θ north of east, opening is (a−10)cosθ+20sinθ and tangential motion is −(a−10)sinθ+20cosθ. An oblique boundary can have opening or convergence plus sideways slip. A common frame translation cancels in the subtraction; rotating the boundary changes the projections.

Divergent boundaries create new oceanic lithosphere through upwelling and decompression melting. Convergent oceanic lithosphere can descend at subduction zones; buoyant continental collision instead commonly thickens crust. Transform boundaries accommodate lateral relative motion. These mechanisms require rock and structural evidence as well as the local vector: positive opening alone does not establish that an observed continental rift already contains oceanic crust.

Plate kinematics are not a force balance. Cooling lithosphere can become negatively buoyant and exert slab pull; elevated ridges create gravitational potential gradients, while mantle flow and resistance interact with moving plates. The mostly solid mantle deforms over long timescales. A conveyor-belt sketch is not evidence that every plate simply follows a prescribed underlying circulation cell.

3. Reconstruct the worked packet

At a=40 and θ=30°, relative motion is (30,20) mm/yr. Opening is 35.9808 mm/yr, tangent 2.3205 mm/yr and speed √1300=36.0555 mm/yr. Components depend on boundary orientation, while speed does not.

4. Predict and investigate

Predict first: Can a boundary have a large relative speed but little opening?

Rotate the normal while holding the two plate velocities fixed. Reconstruct both projections, mark positive directions and compare their squared sum with relative speed squared. Explain what observations distinguish rifting, subduction and transform accommodation.

5. Test a changed case

Apply the evidence to a changed case

Set B east velocity −20 and the normal due east. What are the normal and tangential components? Does adding (100,−50) mm/yr to both plate velocities change them?

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Relative motion is (−30,20), so convergence is 30 mm/yr and tangent +20 mm/yr. A shared frame translation cancels; it does not change either relative component.

6. Retain a defensible evidence notebook

Preserve first predictions, full units, geometry, source provenance, assumptions and rejected alternatives. Synthetic models are not field measurements. The explicitly labeled USGS packet is actual catalog evidence, but working through a public example is not independent practical competence or an operational hazard assessment.

Mechanism and data reference, checked 30 October 2026. Original teaching prose, diagrams and exercises; actual USGS rows retain their agency and provenance.