# http://pyrocko.org - GPLv3
#
# The Pyrocko Developers, 21st Century
# ---|P------/S----------~Lg----------
import numpy as num
from pyrocko import moment_tensor as pmt
[docs]def project(mt):
'''
Calculate Hudson's (u, v) coordinates for a given moment tensor.
The moment tensor can be given as a
:py:class:`pyrocko.moment_tensor.MomentTensor` object, or by anything that
can be converted to a 3x3 NumPy matrix, or as the six independent moment
tensor entries as ``(mnn, mee, mdd, mne, mnd, med)``.
'''
mt = pmt.values_to_matrix(mt)
eig_m = pmt.eigh_check(mt)[0]
m3, m2, m1 = eig_m / num.max(num.abs(eig_m))
u = -2./3. * (m1 + m3 - 2.0*m2)
v = 1./3. * (m1 + m2 + m3)
return u, v
[docs]def draw_axes(axes, color='black', fontsize=12, linewidth=1.5):
'''
Plot axes and annotations of Hudson's MT decomposition diagram.
'''
axes.set_axis_off()
axes.set_aspect(1.0)
axes.set_xlim(-4./3.-0.1, 4./3.+0.1)
axes.set_ylim(-1.1, 1.1)
axes.plot(
[-4./3., 0., 4./3., 0., -4/3.],
[-1./3., -1., 1./3., 1., -1./3.],
zorder=-1,
linewidth=linewidth,
color=color)
axes.plot(
[-1.0, 1.0],
[0., 0.],
zorder=-1,
linewidth=linewidth,
color=color)
axes.plot(
[0., 0.],
[-1., 1.],
zorder=-1,
linewidth=linewidth,
color=color)
d = fontsize/3.
for txt, pos, off, va, ha in [
('+Isotropic', (0., 1.), (-d, d), 'bottom', 'right'),
('-Isotropic', (0., -1.), (d, -d), 'top', 'left'),
('-CLVD', (+1.0, 0.), (d, -d), 'top', 'left'),
('+CLVD', (-1.0, 0.), (-d, d), 'bottom', 'right')]:
axes.plot(
pos[0], pos[1], 'o',
color=color,
markersize=fontsize/2.)
axes.annotate(
txt,
xy=pos,
xycoords='data',
xytext=off,
textcoords='offset points',
verticalalignment=va,
horizontalalignment=ha,
rotation=0.)
for txt, pos, off, va, ha in [
('-Dipole', (2./3., -1./3.), (d, -d), 'top', 'left'),
('+Dipole', (-2./3., 1./3.), (-d, d), 'bottom', 'right'),
('-Crack', (4./9., -5./9.), (d, -d), 'top', 'left'),
('+Crack', (-4./9., 5./9.), (-d, d), 'bottom', 'right')]:
axes.plot(
pos[0], pos[1], 'o',
color=color,
markersize=fontsize/2.)
axes.annotate(
txt,
xy=pos,
xycoords='data',
xytext=off,
textcoords='offset points',
verticalalignment=va,
horizontalalignment=ha,
rotation=0.)
