def _plot_radiation_pattern_quiver(ax3d, ned_mt, type):
"""
Private routine that plots the wave farfield into an
:class:`~mpl_toolkits.mplot3d.axes3d.Axes3D` object
:type ax3d: :class:`mpl_toolkits.mplot3d.axes3d.Axes3D`
:param ax3d: matplotlib Axes3D object
:param ned_mt: the 6 comp moment tensor in NED orientation
:type type: str
:param type: 'P' or 'S' (P or S wave).
"""
import matplotlib.pyplot as plt
if MATPLOTLIB_VERSION < [1, 4]:
msg = ("Matplotlib 3D quiver plot needs matplotlib version >= 1.4.")
raise ImportError(msg)
type = type.upper()
if type not in ("P", "S"):
msg = ("type must be 'P' or 'S'")
raise ValueError(msg)
is_p_wave = type == "P"
# precompute even spherical grid and directional cosine array
points = _equalarea_spherical_grid(nlat=14)
if is_p_wave:
# get radiation pattern
disp = farfield(ned_mt, points, type="P")
# normalized magnitude:
magn = np.sum(disp * points, axis=0)
magn /= np.max(np.abs(magn))
cmap = get_cmap('bwr')
else:
# get radiation pattern
disp = farfield(ned_mt, points, type="S")
# normalized magnitude (positive only):
magn = np.sqrt(np.sum(disp * disp, axis=0))
magn /= np.max(np.abs(magn))
cmap = get_cmap('Greens')
# plot
# there is a mlab3d bug that quiver vector colors and lengths
# can only be changed if we plot each arrow independently
for loc, vec, mag in zip(points.T, disp.T, magn.T):
norm = plt.Normalize(-1., 1.)
color = cmap(norm(mag))
if is_p_wave:
loc *= (1. + mag / 2.)
length = abs(mag) / 2.0
else:
length = abs(mag) / 5.0
ax3d.quiver(loc[0], loc[1], loc[2], vec[0], vec[1], vec[2],
length=length, color=color)
ax3d.set(xlim=(-1.5, 1.5), ylim=(-1.5, 1.5), zlim=(-1.5, 1.5),
xticks=[-1, 1], yticks=[-1, 1], zticks=[-1, 1],
xticklabels=['South', 'North'],
yticklabels=['West', 'East'],
zticklabels=['Up', 'Down'],
title='{} wave farfield'.format(type))
ax3d.view_init(elev=-110., azim=0.)
def _plot_radiation_pattern_quiver(ax3d, ned_mt, type):
"""
Private routine that plots the wave farfield into an
:class:`~mpl_toolkits.mplot3d.axes3d.Axes3D` object
:type ax3d: :class:`mpl_toolkits.mplot3d.axes3d.Axes3D`
:param ax3d: matplotlib Axes3D object
:param ned_mt: the 6 comp moment tensor in NED orientation
:type type: str
:param type: 'P' or 'S' (P or S wave).
"""
import matplotlib.pyplot as plt
if MATPLOTLIB_VERSION < [1, 4]:
msg = ("Matplotlib 3D quiver plot needs matplotlib version >= 1.4.")
raise ImportError(msg)
type = type.upper()
if type not in ("P", "S"):
msg = ("type must be 'P' or 'S'")
raise ValueError(msg)
is_p_wave = type == "P"
# precompute even spherical grid and directional cosine array
points = _equalarea_spherical_grid(nlat=14)
if is_p_wave:
# get radiation pattern
disp = farfield(ned_mt, points, type="P")
# normalized magnitude:
magn = np.sum(disp * points, axis=0)
magn /= np.max(np.abs(magn))
cmap = get_cmap('bwr')
else:
# get radiation pattern
disp = farfield(ned_mt, points, type="S")
# normalized magnitude (positive only):
magn = np.sqrt(np.sum(disp * disp, axis=0))
magn /= np.max(np.abs(magn))
cmap = get_cmap('Greens')
# plot
# there is a mlab3d bug that quiver vector colors and lengths
# can only be changed if we plot each arrow independently
for loc, vec, mag in zip(points.T, disp.T, magn.T):
norm = plt.Normalize(-1., 1.)
color = cmap(norm(mag))
if is_p_wave:
loc *= (1. + mag/2.)
length = abs(mag) / 2.0
else:
length = abs(mag) / 5.0
ax3d.quiver(loc[0], loc[1], loc[2], vec[0], vec[1], vec[2],
length=length, color=color)
ax3d.set(xlim=(-1.5, 1.5), ylim=(-1.5, 1.5), zlim=(-1.5, 1.5),
xticks=[-1, 1], yticks=[-1, 1], zticks=[-1, 1],
xticklabels=['South', 'North'],
yticklabels=['West', 'East'],
zticklabels=['Up', 'Down'],
title='{} wave farfield'.format(type))
ax3d.view_init(elev=-110., azim=0.)
def test_farfield_2xn_input(self):
"""
Tests to compute P/S wave farfield radiation pattern using (theta,phi)
pairs as input
"""
# Peru 2001/6/23 20:34:23:
# RTP system: [2.245, -0.547, -1.698, 1.339, -3.728, 1.444]
# NED system: [-0.547, -1.698, 2.245, -1.444, 1.339, 3.728]
mt = [-0.547, -1.698, 2.245, -1.444, 1.339, 3.728]
theta = np.arange(0, 360, 60)
phi = np.zeros(len(theta))
rays = np.array([theta, phi]) * np.pi / 180.0
result = farfield(mt, rays, 'P')
ref = np.array([[0., 1.13501984, -0.873480164, 2.749332e-16,
-1.13501984, 0.873480164], [0, 0, -0, 0, -0, 0],
[2.245, 0.655304008, 0.504304008, -2.245,
-0.655304008, -0.504304008]])
np.testing.assert_allclose(result, ref, rtol=1e-5, atol=1e-8)
def test_farfield_2xn_input(self):
"""
Tests to compute P/S wave farfield radiation pattern using (theta,phi)
pairs as input
"""
# Peru 2001/6/23 20:34:23:
# RTP system: [2.245, -0.547, -1.698, 1.339, -3.728, 1.444]
# NED system: [-0.547, -1.698, 2.245, -1.444, 1.339, 3.728]
mt = [-0.547, -1.698, 2.245, -1.444, 1.339, 3.728]
theta = np.arange(0, 360, 60)
phi = np.zeros(len(theta))
rays = np.array([theta, phi]) * np.pi / 180.0
result = farfield(mt, rays, 'P')
ref = np.array([[0., 1.13501984, -0.873480164, 2.749332e-16,
-1.13501984, 0.873480164], [0, 0, -0, 0, -0, 0],
[2.245, 0.655304008, 0.504304008, -2.245,
-0.655304008, -0.504304008]])
np.testing.assert_allclose(result, ref, rtol=1e-5, atol=1e-8)
def test_farfield_2xn_input(self):
"""
Tests to compute P/S wave farfield radiation pattern using (theta,phi)
pairs as input
"""
# Peru 2001/6/23 20:34:23:
mt = [2.245, -0.547, -1.698, 1.339, -3.728, 1.444]
theta = np.arange(0, 360, 60)
phi = np.zeros(len(theta))
rays = np.array([theta, phi])
result = farfield(mt, rays, 'P')
ref = np.array([[
-0., 1.06567166, -2.26055006, 2.19679324, -0.44435406, -2.07785517
], [-0., 0., -0., 0., -0., -0.],
[
-1.698, 3.32980367, -3.16993006, 1.64100194,
-0.15311543, -0.04592479
]])
np.testing.assert_allclose(result, ref)
def test_farfield_2xn_input(self):
"""
Tests to compute P/S wave farfield radiation pattern using (theta,phi)
pairs as input
"""
# Peru 2001/6/23 20:34:23:
mt = [2.245, -0.547, -1.698, 1.339, -3.728, 1.444]
theta = np.arange(0, 360, 60)
phi = np.zeros(len(theta))
rays = np.array([theta, phi])
result = farfield(mt, rays, "P")
ref = np.array(
[
[-0.0, 1.06567166, -2.26055006, 2.19679324, -0.44435406, -2.07785517],
[-0.0, 0.0, -0.0, 0.0, -0.0, -0.0],
[-1.698, 3.32980367, -3.16993006, 1.64100194, -0.15311543, -0.04592479],
]
)
np.testing.assert_allclose(result, ref)
def _write_radiation_pattern_vtk(ned_mt,
fname_rpattern='rpattern.vtk',
fname_beachlines='beachlines.vtk'):
# output a vtkfile that can for exampled be displayed by ParaView
mtensor = MomentTensor(ned_mt, system='NED')
bb = BeachBall(mtensor, npoints=200)
bb._setup_BB(unit_circle=False)
# extract the coordinates of the nodal lines
neg_nodalline = bb._nodalline_negative
pos_nodalline = bb._nodalline_positive
# plot radiation pattern and nodal lines
points = _equalarea_spherical_grid()
ndim, npoints = points.shape
dispp = farfield(ned_mt, points, type="P")
disps = farfield(ned_mt, points, type="S")
# write vector field
with open(fname_rpattern, 'w') as vtk_file:
vtk_header = '# vtk DataFile Version 2.0\n' + \
'radiation pattern vector field\n' + \
'ASCII\n' + \
'DATASET UNSTRUCTURED_GRID\n' + \
'POINTS {:d} float\n'.format(npoints)
vtk_file.write(vtk_header)
# write point locations
for x, y, z in np.transpose(points):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
# write vector field
vtk_file.write('POINT_DATA {:d}\n'.format(npoints))
vtk_file.write('VECTORS s_radiation float\n')
for x, y, z in np.transpose(disps):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
vtk_file.write('VECTORS p_radiation float\n'.format(npoints))
for x, y, z in np.transpose(dispp):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
# write nodal lines
with open(fname_beachlines, 'w') as vtk_file:
npts_neg = neg_nodalline.shape[1]
npts_pos = pos_nodalline.shape[1]
npts_tot = npts_neg + npts_pos
vtk_header = '# vtk DataFile Version 2.0\n' + \
'beachball nodal lines\n' + \
'ASCII\n' + \
'DATASET UNSTRUCTURED_GRID\n' + \
'POINTS {:d} float\n'.format(npts_tot)
vtk_file.write(vtk_header)
# write point locations
for x, y, z in np.transpose(neg_nodalline):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
for x, y, z in np.transpose(pos_nodalline):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
# write line segments
vtk_file.write('\nCELLS 2 {:d}\n'.format(npts_tot + 4))
ipoints = list(range(0, npts_neg)) + [0]
vtk_file.write('{:d} '.format(npts_neg + 1))
for ipoint in ipoints:
if ipoint % 30 == 29:
vtk_file.write('\n')
vtk_file.write('{:d} '.format(ipoint))
vtk_file.write('\n')
ipoints = list(range(0, npts_pos)) + [0]
vtk_file.write('{:d} '.format(npts_pos + 1))
for ipoint in ipoints:
if ipoint % 30 == 29:
vtk_file.write('\n')
vtk_file.write('{:d} '.format(ipoint + npts_neg))
vtk_file.write('\n')
# cell types. 4 means cell type is a poly_line
vtk_file.write('\nCELL_TYPES 2\n')
vtk_file.write('4\n4')
def _plot_radiation_pattern_mayavi(ned_mt):
"""
Plot the radiation pattern using MayaVi.
This private function uses the mayavi (vtk) library to plot the radiation
pattern to screen. Note that you might have to set the QT_API environmental
variable to e.g. export QT_API=pyqt that mayavi works properly.
:param ned_mt: moment tensor in NED convention
"""
# use mayavi if possible.
try:
from mayavi import mlab
except Exception as err:
print(err)
msg = ("ObsPy failed to import MayaVi. "
"You need to install the mayavi module "
"(e.g. 'conda install mayavi', 'pip install mayavi'). "
"If it is installed and still doesn't work, "
"try setting the environmental variable QT_API to "
"pyqt (e.g. export QT_API=pyqt) before running the "
"code. Another option is to avoid mayavi and "
"directly use kind='vtk' for vtk file output of the "
"radiation pattern that can be used by external "
"software like ParaView")
raise ImportError(msg)
# get mopad moment tensor
mopad_mt = MomentTensor(ned_mt, system='NED')
bb = BeachBall(mopad_mt, npoints=200)
bb._setup_BB(unit_circle=False)
# extract the coordinates of the nodal lines
neg_nodalline = bb._nodalline_negative
pos_nodalline = bb._nodalline_positive
# add the first point to the end to close the nodal line
neg_nodalline = np.hstack((neg_nodalline, neg_nodalline[:, 0][:, None]))
pos_nodalline = np.hstack((pos_nodalline, pos_nodalline[:, 0][:, None]))
# plot radiation pattern and nodal lines
points = _equalarea_spherical_grid(nlat=20)
dispp = farfield(ned_mt, points, type="P")
disps = farfield(ned_mt, points, type="S")
# get vector lengths
normp = np.sum(dispp * points, axis=0)
normp /= np.max(np.abs(normp))
norms = np.sqrt(np.sum(disps * disps, axis=0))
norms /= np.max(np.abs(norms))
# make sphere to block view to the other side of the beachball
rad = 0.8
pi = np.pi
cos = np.cos
sin = np.sin
phi, theta = np.mgrid[0:pi:101j, 0:2 * pi:101j]
x = rad * sin(phi) * cos(theta)
y = rad * sin(phi) * sin(theta)
z = rad * cos(phi)
# p wave radiation pattern
mlab.figure(size=(800, 800), bgcolor=(0, 0, 0))
pts1 = mlab.quiver3d(points[0],
points[1],
points[2],
dispp[0],
dispp[1],
dispp[2],
scalars=normp,
vmin=-1.,
vmax=1.)
pts1.glyph.color_mode = 'color_by_scalar'
mlab.plot3d(*neg_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.plot3d(*pos_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.mesh(x, y, z, color=(0, 0, 0))
# s wave radiation pattern
mlab.figure(size=(800, 800), bgcolor=(0, 0, 0))
pts2 = mlab.quiver3d(points[0],
points[1],
points[2],
disps[0],
disps[1],
disps[2],
scalars=norms,
vmin=-0.,
vmax=1.)
pts2.glyph.color_mode = 'color_by_scalar'
mlab.plot3d(*neg_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.plot3d(*pos_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.mesh(x, y, z, color=(0, 0, 0))
mlab.show()
def _plot_radiation_pattern_sphere(ax3d,
ned_mt,
type,
p_sphere_direction='inwards'):
"""
Private function that plots a radiation pattern sphere into an
:class:`~mpl_toolkits.mplot3d.axes3d.Axes3D`.
:type ax3d: :class:`mpl_toolkits.mplot3d.axes3d.Axes3D`
:param ax3d: matplotlib Axes3D object
:param ned_mt: moment tensor in NED convention
:param p_sphere_direction: If this is 'inwards', the tension regions of the
beachball deform the radiation sphere inwards. If 'outwards' it deforms
outwards.
:param type: 'P' or 'S' (P or S wave).
"""
import matplotlib.pyplot as plt
type = type.upper()
if type not in ("P", "S"):
msg = ("type must be 'P' or 'S'")
raise ValueError(msg)
is_p_wave = type == "P"
# generate spherical mesh that is aligned with the moment tensor null
# axis. MOPAD should use NED coordinate system to avoid internal
# coordinate transformations
mtensor = MomentTensor(ned_mt, system='NED')
# use the most isolated eigenvector as axis of symmetry
evecs = mtensor.get_eigvecs()
evals = np.abs(mtensor.get_eigvals())**2
evals_dev = np.abs(evals - np.mean(evals))
if is_p_wave:
if p_sphere_direction == 'outwards':
evec_max = evecs[np.argmax(evals_dev)]
elif p_sphere_direction == 'inwards':
evec_max = evecs[np.argmax(evals)]
else:
evec_max = evecs[np.argmax(evals_dev)]
orientation = np.ravel(evec_max)
# get a uv sphere that is oriented along the moment tensor axes
ntheta, nphi = 100, 100
points = _oriented_uv_sphere(ntheta=ntheta,
nphi=nphi,
orientation=orientation)
sshape = (ntheta, nphi)
# get radiation pattern
if is_p_wave:
disp = farfield(ned_mt, points, type="P")
magn = np.sum(disp * points, axis=0)
cmap = get_cmap('bwr')
norm = plt.Normalize(-1, 1)
else:
disp = farfield(ned_mt, points, type="S")
magn = np.sqrt(np.sum(disp * disp, axis=0))
cmap = get_cmap('Greens')
norm = plt.Normalize(0, 1)
magn /= np.max(np.abs(magn))
# compute colours and displace points along normal
if is_p_wave:
if p_sphere_direction == 'outwards':
points *= (1. + np.abs(magn) / 2.)
elif p_sphere_direction == 'inwards':
points *= (1. + magn / 2.)
else:
points *= (1. + magn / 2.)
colors = np.array([cmap(norm(val)) for val in magn])
colors = colors.reshape(ntheta, nphi, 4)
x = points[0].reshape(sshape)
y = points[1].reshape(sshape)
z = points[2].reshape(sshape)
# plot 3d radiation pattern
ax3d.plot_surface(x, y, z, rstride=4, cstride=4, facecolors=colors)
ax3d.set(xlim=(-1.5, 1.5),
ylim=(-1.5, 1.5),
zlim=(-1.5, 1.5),
xticks=[-1, 1],
yticks=[-1, 1],
zticks=[-1, 1],
xticklabels=['South', 'North'],
yticklabels=['West', 'East'],
zticklabels=['Up', 'Down'],
title='{} wave farfield'.format(type))
ax3d.view_init(elev=-110., azim=0.)
def _write_radiation_pattern_vtk(
ned_mt, fname_rpattern='rpattern.vtk',
fname_beachlines='beachlines.vtk'):
# output a vtkfile that can for exampled be displayed by ParaView
mtensor = MomentTensor(ned_mt, system='NED')
bb = BeachBall(mtensor, npoints=200)
bb._setup_BB(unit_circle=False)
# extract the coordinates of the nodal lines
neg_nodalline = bb._nodalline_negative
pos_nodalline = bb._nodalline_positive
# plot radiation pattern and nodal lines
points = _equalarea_spherical_grid()
ndim, npoints = points.shape
dispp = farfield(ned_mt, points, type="P")
disps = farfield(ned_mt, points, type="S")
# write vector field
with open(fname_rpattern, 'w') as vtk_file:
vtk_header = '# vtk DataFile Version 2.0\n' + \
'radiation pattern vector field\n' + \
'ASCII\n' + \
'DATASET UNSTRUCTURED_GRID\n' + \
'POINTS {:d} float\n'.format(npoints)
vtk_file.write(vtk_header)
# write point locations
for x, y, z in np.transpose(points):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
# write vector field
vtk_file.write('POINT_DATA {:d}\n'.format(npoints))
vtk_file.write('VECTORS s_radiation float\n')
for x, y, z in np.transpose(disps):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
vtk_file.write('VECTORS p_radiation float\n'.format(npoints))
for x, y, z in np.transpose(dispp):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
# write nodal lines
with open(fname_beachlines, 'w') as vtk_file:
npts_neg = neg_nodalline.shape[1]
npts_pos = pos_nodalline.shape[1]
npts_tot = npts_neg + npts_pos
vtk_header = '# vtk DataFile Version 2.0\n' + \
'beachball nodal lines\n' + \
'ASCII\n' + \
'DATASET UNSTRUCTURED_GRID\n' + \
'POINTS {:d} float\n'.format(npts_tot)
vtk_file.write(vtk_header)
# write point locations
for x, y, z in np.transpose(neg_nodalline):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
for x, y, z in np.transpose(pos_nodalline):
vtk_file.write('{:.3e} {:.3e} {:.3e}\n'.format(x, y, z))
# write line segments
vtk_file.write('\nCELLS 2 {:d}\n'.format(npts_tot + 4))
ipoints = list(range(0, npts_neg)) + [0]
vtk_file.write('{:d} '.format(npts_neg + 1))
for ipoint in ipoints:
if ipoint % 30 == 29:
vtk_file.write('\n')
vtk_file.write('{:d} '.format(ipoint))
vtk_file.write('\n')
ipoints = list(range(0, npts_pos)) + [0]
vtk_file.write('{:d} '.format(npts_pos + 1))
for ipoint in ipoints:
if ipoint % 30 == 29:
vtk_file.write('\n')
vtk_file.write('{:d} '.format(ipoint + npts_neg))
vtk_file.write('\n')
# cell types. 4 means cell type is a poly_line
vtk_file.write('\nCELL_TYPES 2\n')
vtk_file.write('4\n4')
def _plot_radiation_pattern_mayavi(ned_mt):
"""
Plot the radiation pattern using MayaVi.
This private function uses the mayavi (vtk) library to plot the radiation
pattern to screen. Note that you might have to set the QT_API environmental
variable to e.g. export QT_API=pyqt that mayavi works properly.
:param ned_mt: moment tensor in NED convention
"""
# use mayavi if possible.
try:
from mayavi import mlab
except Exception as err:
print(err)
msg = ("ObsPy failed to import MayaVi. "
"You need to install the mayavi module "
"(e.g. 'conda install mayavi', 'pip install mayavi'). "
"If it is installed and still doesn't work, "
"try setting the environmental variable QT_API to "
"pyqt (e.g. export QT_API=pyqt) before running the "
"code. Another option is to avoid mayavi and "
"directly use kind='vtk' for vtk file output of the "
"radiation pattern that can be used by external "
"software like ParaView")
raise ImportError(msg)
# get mopad moment tensor
mopad_mt = MomentTensor(ned_mt, system='NED')
bb = BeachBall(mopad_mt, npoints=200)
bb._setup_BB(unit_circle=False)
# extract the coordinates of the nodal lines
neg_nodalline = bb._nodalline_negative
pos_nodalline = bb._nodalline_positive
# add the first point to the end to close the nodal line
neg_nodalline = np.hstack((neg_nodalline, neg_nodalline[:, 0][:, None]))
pos_nodalline = np.hstack((pos_nodalline, pos_nodalline[:, 0][:, None]))
# plot radiation pattern and nodal lines
points = _equalarea_spherical_grid(nlat=20)
dispp = farfield(ned_mt, points, type="P")
disps = farfield(ned_mt, points, type="S")
# get vector lengths
normp = np.sum(dispp * points, axis=0)
normp /= np.max(np.abs(normp))
norms = np.sqrt(np.sum(disps * disps, axis=0))
norms /= np.max(np.abs(norms))
# make sphere to block view to the other side of the beachball
rad = 0.8
pi = np.pi
cos = np.cos
sin = np.sin
phi, theta = np.mgrid[0:pi:101j, 0:2 * pi:101j]
x = rad * sin(phi) * cos(theta)
y = rad * sin(phi) * sin(theta)
z = rad * cos(phi)
# p wave radiation pattern
mlab.figure(size=(800, 800), bgcolor=(0, 0, 0))
pts1 = mlab.quiver3d(points[0], points[1], points[2],
dispp[0], dispp[1], dispp[2],
scalars=normp, vmin=-1., vmax=1.)
pts1.glyph.color_mode = 'color_by_scalar'
mlab.plot3d(*neg_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.plot3d(*pos_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.mesh(x, y, z, color=(0, 0, 0))
# s wave radiation pattern
mlab.figure(size=(800, 800), bgcolor=(0, 0, 0))
pts2 = mlab.quiver3d(points[0], points[1], points[2],
disps[0], disps[1], disps[2], scalars=norms,
vmin=-0., vmax=1.)
pts2.glyph.color_mode = 'color_by_scalar'
mlab.plot3d(*neg_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.plot3d(*pos_nodalline, color=(0, 0.5, 0), tube_radius=0.01)
mlab.mesh(x, y, z, color=(0, 0, 0))
mlab.show()
def _plot_radiation_pattern_sphere(
ax3d, ned_mt, type, p_sphere_direction='inwards'):
"""
Private function that plots a radiation pattern sphere into an
:class:`~mpl_toolkits.mplot3d.axes3d.Axes3D`.
:type ax3d: :class:`mpl_toolkits.mplot3d.axes3d.Axes3D`
:param ax3d: matplotlib Axes3D object
:param ned_mt: moment tensor in NED convention
:param p_sphere_direction: If this is 'inwards', the tension regions of the
beachball deform the radiation sphere inwards. If 'outwards' it deforms
outwards.
:param type: 'P' or 'S' (P or S wave).
"""
import matplotlib.pyplot as plt
type = type.upper()
if type not in ("P", "S"):
msg = ("type must be 'P' or 'S'")
raise ValueError(msg)
is_p_wave = type == "P"
# generate spherical mesh that is aligned with the moment tensor null
# axis. MOPAD should use NED coordinate system to avoid internal
# coordinate transformations
mtensor = MomentTensor(ned_mt, system='NED')
# use the most isolated eigenvector as axis of symmetry
evecs = mtensor.get_eigvecs()
evals = np.abs(mtensor.get_eigvals())**2
evals_dev = np.abs(evals - np.mean(evals))
if is_p_wave:
if p_sphere_direction == 'outwards':
evec_max = evecs[np.argmax(evals_dev)]
elif p_sphere_direction == 'inwards':
evec_max = evecs[np.argmax(evals)]
else:
evec_max = evecs[np.argmax(evals_dev)]
orientation = np.ravel(evec_max)
# get a uv sphere that is oriented along the moment tensor axes
ntheta, nphi = 100, 100
points = _oriented_uv_sphere(ntheta=ntheta, nphi=nphi,
orientation=orientation)
sshape = (ntheta, nphi)
# get radiation pattern
if is_p_wave:
disp = farfield(ned_mt, points, type="P")
magn = np.sum(disp * points, axis=0)
cmap = get_cmap('bwr')
norm = plt.Normalize(-1, 1)
else:
disp = farfield(ned_mt, points, type="S")
magn = np.sqrt(np.sum(disp * disp, axis=0))
cmap = get_cmap('Greens')
norm = plt.Normalize(0, 1)
magn /= np.max(np.abs(magn))
# compute colours and displace points along normal
if is_p_wave:
if p_sphere_direction == 'outwards':
points *= (1. + np.abs(magn) / 2.)
elif p_sphere_direction == 'inwards':
points *= (1. + magn / 2.)
else:
points *= (1. + magn / 2.)
colors = np.array([cmap(norm(val)) for val in magn])
colors = colors.reshape(ntheta, nphi, 4)
x = points[0].reshape(sshape)
y = points[1].reshape(sshape)
z = points[2].reshape(sshape)
# plot 3d radiation pattern
ax3d.plot_surface(x, y, z, rstride=4, cstride=4, facecolors=colors)
ax3d.set(xlim=(-1.5, 1.5), ylim=(-1.5, 1.5), zlim=(-1.5, 1.5),
xticks=[-1, 1], yticks=[-1, 1], zticks=[-1, 1],
xticklabels=['South', 'North'],
yticklabels=['West', 'East'],
zticklabels=['Up', 'Down'],
title='{} wave farfield'.format(type))
ax3d.view_init(elev=-110., azim=0.)
def radiation_pattern(mt,
takeoff_angle,
azimuth,
wavetype='P',
system='RTP',
normalize=False):
"""Wrapper of obspy.core.event.source.farfield.
Parameters
----------
mt: list(float)
Six component moment tensor ([Mxx, Myy, Mzz, Mxy, Mxz, Myz])
takeoff_angle: float or list(float)
Takeoff angle of seismic ray (in degree)
azimuth: float or list(float)
Azimuth of seismic ray (in degree)
wavetype: str
Specify wave type, 'P' or 'S'
system: str
Coordinate system of mt, NED|USE|RTP
normalize: bool
Return normalized radiation pattern
Returns
-------
float
Magnitude of radiation pattern
Examples
--------
(1) Explosion source:
>>> mt = [1, 1, 1, 0, 0, 0]
>>> mag = radiation_pattern(mt, 35, 44, wavetype='P', system='RTP')
>>> print(mag)
1.0
(2) Event 2001/6/23 20:34:23
>>> mt = [2.245, -0.547, -1.698, 1.339, -3.728, 1.444]
>>> mag_P = radiation_pattern(mt, 80, 30, wavetype='P', system='RTP')
>>> print(mag_P)
0.92058159502
>>> mag_S = radiation_pattern(mt, 80, 30, wavetype='S', system='RTP')
>>> print(mag_S)
3.66100655525
"""
from obspy import __version__ as obspy_version
if obspy_version == '1.0.2':
msg = ("farfield in ObsPy version {} has known issues."
"(see issue #1499 and PR #1553).").format(obspy_version)
warnings.warn(msg)
if system in ('RTP', 'USE'):
ned_mt = mt_converter(mt, system_in='RTP', system_out='NED')
elif system == 'NED':
ned_mt = mt
else:
raise ValueError("Wrong coordinate system of moment tensor")
ray = np.array([[takeoff_angle], [azimuth]]) / 180.0 * np.pi
# farfield return three component displacement
disp = farfield(ned_mt, ray, wavetype)
mag = np.sqrt(np.sum(disp * disp, axis=0))[0]
if normalize:
mag /= get_scalar_moment(ned_mt)
return mag
