"""
Gutenberg's core shadow (1914)
==============================

Beno Gutenberg placed the core-mantle boundary at a depth of about 2900 km.
A slower core bends rays towards the centre, so in the real Earth direct P
waves fade near 103 degrees from the source and refracted core waves return
only beyond about 143 degrees. In between is a shadow. The ray parameter,
which is conserved along a ray, connects the two. This toy Earth has a uniform
13 km/s mantle over an 8 km/s core, so its rays are straight within each
shell and its shadow starts later, at about 114 degrees.
"""

import matplotlib.pyplot as plt
import numpy as np

from earthsciencekit.seismology import ray_parameter

R, rc = 6371e3, 3480e3
vm, vc = 13e3, 8e3
takeoff = np.linspace(1e-4, np.pi / 2 - 1e-4, 4000)
p = ray_parameter(R, vm, takeoff)
direct = p * vm >= rc
distance = np.empty_like(p)
# Center angle of a straight chord between radii r1 > r2 with r sin(i) = b is arccos(b/r1) - arccos(b/r2).
distance[direct] = 2 * np.arccos(p[direct] * vm / R)
core = ~direct
at_cmb = np.arcsin(p[core] * vm / rc)
in_core = np.arcsin(p[core] * vc / rc)
assert np.allclose(ray_parameter(rc, vm, at_cmb), ray_parameter(rc, vc, in_core))
swept = 2 * (np.arccos(p[core] * vm / R) - np.arccos(p[core] * vm / rc)) + np.pi - 2 * in_core
distance[core] = np.where(swept > np.pi, 2 * np.pi - swept, swept)

edge, far = np.degrees(distance[direct].max()), np.degrees(distance[core].min())
assert 110 < edge < 120 and 140 < far < 146
print(f"shadow zone from {edge:.1f} to {far:.1f} degrees")

fig, ax = plt.subplots()
ax.plot(np.degrees(takeoff[direct]), np.degrees(distance[direct]), label="P through the mantle")
ax.plot(np.degrees(takeoff[core]), np.degrees(distance[core]), label="PKP through the core")
ax.axhspan(edge, far, color="0.85", label="shadow zone")
ax.set(xlabel="takeoff angle from vertical [deg]", ylabel="epicentral distance [deg]", title="A slow core casts a shadow")
ax.legend()

plt.show()