Forsyth and Uyeda’s slab pull (1975)

Donald Forsyth and Seiya Uyeda compared the forces on each plate and found that plates attached to sinking slabs move fastest. Per metre of trench, the excess weight of a cold slab exceeds ridge push by about an order of magnitude. Ridge push uses the half-space formula of Turcotte and Schubert.

import matplotlib.pyplot as plt
import numpy as np

from earthsciencekit.constants import GRAVITY
from earthsciencekit.plate_tectonics import slab_pull_force
from earthsciencekit.units import convert

mantle, water, expansivity, excess_temperature, diffusivity = 3300.0, 1000.0, 3e-5, 1280.0, 1e-6
age = convert(100e6, "year", "s")
buoyancy = 2 * mantle * expansivity * excess_temperature / (np.pi * (mantle - water))
ridge_push = GRAVITY * mantle * expansivity * excess_temperature * diffusivity * age * (1 + buoyancy)
density_excess = mantle * expansivity * excess_temperature / 2
length = np.linspace(0, 700e3, 71)
pull = slab_pull_force(density_excess, 100e3 * length, GRAVITY)
assert float(slab_pull_force(density_excess, 100e3 * 600e3, GRAVITY)) > 5 * ridge_push

fig, ax = plt.subplots()
ax.plot(length / 1e3, pull / 1e12, label="slab pull, 100 km thick slab")
ax.axhline(ridge_push / 1e12, color="tab:red", ls="--", label="ridge push, 100 million year plate")
ax.set(xlabel="slab length [km]", ylabel="force per trench length [10^12 N/m]", title="Slabs pull harder than ridges push")
ax.legend()

plt.show()