Isacks, Oliver and Sykes’s subducting slabs (1968)

Bryan Isacks, Jack Oliver and Lynn Sykes traced deep earthquakes down inclined zones beneath trenches and read them as cold lithosphere sinking into the mantle. A shallower dip lengthens the path to a given depth; only the part of the relative motion normal to the trench is convergence.

import matplotlib.pyplot as plt
import numpy as np

from earthsciencekit.plate_tectonics import convergence_rate, subduction_travel_time
from earthsciencekit.units import convert

relative = convert(9.0, "cm/year", "m/s")
speed = convergence_rate(relative, np.deg2rad(25.0))
depth = np.linspace(0, 660e3, 67)
fig, (left, right) = plt.subplots(1, 2, figsize=(9, 4))
for dip in [30, 45, 60, 90]:
    time = subduction_travel_time(depth, speed, np.deg2rad(dip))
    right.plot(convert(time, "s", "year") / 1e6, depth / 1e3, label=f"dip {dip} degree")
    left.plot(depth / np.tan(np.deg2rad(dip)) / 1e3 if dip < 90 else 0 * depth, depth / 1e3)
assert np.isclose(float(subduction_travel_time(660e3, speed, np.pi / 2)), 660e3 / speed)
assert np.isclose(float(subduction_travel_time(660e3, speed, np.pi / 6)), 2 * 660e3 / speed)
for ax in (left, right):
    ax.invert_yaxis()
left.set(xlabel="distance from trench [km]", ylabel="depth [km]", title="Slab geometry")
right.set(xlabel="time since entering trench [million years]", title="Time to reach depth")
right.legend()
fig.tight_layout()

plt.show()