def test_projections(self):
n = 1000
points = num.zeros((n, 3))
phi = num.random.random(n) * math.pi * 2.0
theta = num.random.random(n) * math.pi / 2.0
points[:, 0] = num.cos(phi) * num.sin(theta)
points[:, 1] = num.sin(phi) * num.sin(theta)
points[:, 2] = num.cos(theta)
for projection in ['lambert', 'stereographic', 'orthographic']:
projection = 'stereographic'
points2 = beachball.project(points, projection=projection)
points_new = beachball.inverse_project(points2,
projection=projection)
assert num.all(num.abs(points - points_new) < 1e-5)
def test_projections(self):
n = 1000
points = num.zeros((n, 3))
phi = num.random.random(n) * math.pi * 2.0
theta = num.random.random(n) * math.pi / 2.0
points[:, 0] = num.cos(phi) * num.sin(theta)
points[:, 1] = num.sin(phi) * num.sin(theta)
points[:, 2] = num.cos(theta)
for projection in ['lambert', 'stereographic', 'orthographic']:
projection = 'stereographic'
points2 = beachball.project(points, projection=projection)
points_new = beachball.inverse_project(
points2, projection=projection)
assert num.all(num.abs(points - points_new) < 1e-5)
def plot_directivity(engine,
source,
store_id,
distance=300 * km,
azi_begin=0.,
azi_end=360.,
dazi=1.,
phase_begin='first{stored:any_P}-10%',
phase_end='last{stored:any_S}+50',
quantity='displacement',
envelope=False,
component='R',
fmin=0.01,
fmax=0.1,
hillshade=True,
cmap=None,
plot_mt='full',
show_phases=True,
show_description=True,
reverse_time=False,
show_nucleations=True,
axes=None,
nthreads=0):
'''Plot the directivity and radiation characteristics of source models
Synthetic seismic traces (R, T or Z) are forward-modelled at a defined
radius, covering the full or partial azimuthal range and projected on a
polar plot. Difference in the amplitude are enhanced by hillshading
the data.
:param engine: Forward modelling engine
:type engine: :py:class:`~pyrocko.gf.seismosizer.Engine`
:param source: Parametrized source model
:type source: :py:class:`~pyrocko.gf.seismosizer.Source`
:param store_id: Store ID used for forward modelling
:type store_id: str
:param distance: Distance in [m]
:type distance: float
:param azi_begin: Begin azimuth in [deg]
:type azi_begin: float
:param azi_end: End azimuth in [deg]
:type azi_end: float
:param dazi: Delta azimuth, bin size [deg]
:type dazi: float
:param phase_begin: Start time of the window
:type phase_begin: :py:class:`~pyrocko.gf.meta.Timing`
:param phase_end: End time of the window
:type phase_end: :py:class:`~pyrocko.gf.meta.Timing`
:param quantity: Seismogram quantity, default ``displacement``
:type quantity: str
:param envelope: Plot envelop instead of seismic trace
:type envelope: bool
:param component: Forward modelled component, default ``R``. Choose from
`RTZ`
:type component: str
:param fmin: Bandpass lower frequency [Hz], default ``0.01``
:type fmin: float
:param fmax: Bandpass upper frequency [Hz], default ``0.1``
:type fmax: float
:param hillshade: Enable hillshading, default ``True``
:type hillshade: bool
:param cmap: Matplotlit colormap to use, default ``seismic``.
When ``envelope`` is ``True`` the default colormap will be ``Reds``.
:type cmap: str
:param plot_mt: Plot a centered moment tensor, default ``full``.
Choose from ``full, deviatoric, dc or False``
:type plot_mt: str, bool
:param show_phases: Show annotations, default ``True``
:type show_phases: bool
:param show_description: Show desciption, default ``True``
:type show_description: bool
:param reverse_time: Reverse time axis. First phases arrive at the center,
default ``False``
:type reverse_time: bool
:param show_nucleations: Show nucleation piercing points on the moment
tensor, default ``True``
:type show_nucleations: bool
:param axes: Give axes to plot into
:type axes: :py:class:`matplotlib.axes.Axes`
:param nthreads: Number of threads used for forward modelling,
default ``0`` - all available cores
:type nthreads: int
'''
if axes is None:
fig = plt.figure()
ax = fig.add_subplot(111, polar=True)
else:
fig = axes.figure
ax = axes
if envelope and cmap is None:
cmap = 'Reds'
elif cmap is None:
cmap = 'seismic'
targets, azimuths = get_azimuthal_targets(store_id,
source,
distance,
azi_begin,
azi_end,
dazi,
components='R',
quantity=quantity)
store = engine.get_store(store_id)
mt = source.pyrocko_moment_tensor(store=store, target=targets[0])
resp = engine.process(source, targets, nthreads=nthreads)
data, times = get_seismogram_array(resp,
fmin,
fmax,
component=component,
envelope=envelope)
timing_begin = Timing(phase_begin)
timing_end = Timing(phase_end)
nucl_depth = source.depth
nucl_distance = distance
if hasattr(source, 'nucleation_x') and hasattr(source, 'nucleation_y'):
try:
iter(source.nucleation_x)
nx = float(source.nucleation_x[0])
ny = float(source.nucleation_y[0])
except TypeError:
nx = source.nucleation_x
ny = source.nucleation_y
nucl_distance += nx * source.length / 2.
nucl_depth += ny * num.sin(source.dip * d2r) * source.width / 2.
if hasattr(source, 'anchor'):
anch_x, anch_y = map_anchor[source.anchor]
nucl_distance -= anch_x * source.length / 2.
nucl_depth -= anch_y * num.sin(source.dip * d2r) * source.width / 2.
tbegin = store.t(timing_begin, (nucl_depth, nucl_distance))
tend = store.t(timing_end, (nucl_depth, nucl_distance))
tsel = num.logical_and(times >= tbegin, times <= tend)
data = data[:, tsel].T
times = times[tsel]
duration = times[-1] - times[0]
vmax = num.abs(data).max()
cmw = ScalarMappable(cmap=cmap)
cmw.set_array(data)
cmw.set_clim(-vmax, vmax)
if envelope:
cmw.set_clim(0., vmax)
ax.set_theta_zero_location("N")
ax.set_theta_direction(-1)
strike_label = mt.strike1
if hasattr(source, 'strike'):
strike_label = source.strike
try:
ax.set_rlabel_position(strike_label % 180.)
except AttributeError:
logger.warn('Old matplotlib version: cannot set label positions')
def r_fmt(v, p):
if v < tbegin or v > tend:
return ''
return '%g s' % v
ax.yaxis.set_major_formatter(FuncFormatter(r_fmt))
if reverse_time:
ax.set_rlim(times[0] - .3 * duration, times[-1])
else:
ax.set_rlim(times[-1] + .3 * duration, times[0])
ax.grid(zorder=20)
if isinstance(plot_mt, str):
mt_size = .15
beachball.plot_beachball_mpl(mt,
ax,
beachball_type=plot_mt,
size=mt_size,
size_units='axes',
color_t=(0.7, 0.4, 0.4),
position=(.5, .5),
linewidth=1.)
if hasattr(source, 'nucleation_x') and hasattr(source, 'nucleation_y')\
and show_nucleations:
try:
iter(source.nucleation_x)
nucleation_x = source.nucleation_x
nucleation_y = source.nucleation_y
except TypeError:
nucleation_x = [source.nucleation_x]
nucleation_y = [source.nucleation_y]
for nx, ny in zip(nucleation_x, nucleation_y):
angle = float(num.arctan2(ny, nx))
rtp = num.array([[1., angle, (90. - source.strike) * d2r]])
points = beachball.numpy_rtp2xyz(rtp)
x, y = beachball.project(points, projection='lambert').T
norm = num.sqrt(x**2 + y**2)
x = x / norm * mt_size / 2.
y = y / norm * mt_size / 2.
ax.plot(x + .5,
y + .5,
'x',
ms=6,
mew=2,
mec='darkred',
mfc='red',
transform=ax.transAxes,
zorder=10)
mesh = ax.pcolormesh(azimuths * d2r,
times,
data,
cmap=cmw.cmap,
shading='gouraud',
zorder=0)
if hillshade:
mesh.update_scalarmappable()
color = mesh.get_facecolor()
color = hillshade_seismogram_array(data,
color,
shad_lim=(.85, 1.),
blend_mode='multiply')
mesh.set_facecolor(color)
if show_phases:
_phase_begin = Timing(phase_begin)
_phase_end = Timing(phase_end)
for p in (_phase_begin, _phase_end):
p.offset = 0.
p.offset_is_slowness = False
p.offset_is_percent = False
tphase_first = store.t(_phase_begin, (nucl_depth, nucl_distance))
tphase_last = store.t(_phase_end, (nucl_depth, nucl_distance))
theta = num.linspace(0, 2 * num.pi, 360)
tfirst = num_full_like(theta, tphase_first)
tlast = num_full_like(theta, tphase_last)
ax.plot(theta, tfirst, color='k', alpha=.3, lw=1.)
ax.plot(theta, tlast, color='k', alpha=.3, lw=1.)
ax.text(num.pi * 7 / 5,
tphase_first,
'|'.join(_phase_begin.phase_defs),
ha='left',
color='k',
fontsize='small')
ax.text(num.pi * 6 / 5,
tphase_last,
'|'.join(_phase_end.phase_defs),
ha='left',
color='k',
fontsize='small')
description = ('Component {component:s}\n'
'Distance {distance:g} km').format(component=component,
distance=distance / km)
if show_description:
if fmin and fmax:
description += '\nBandpass {fmin:g} - {fmax:g} Hz'.format(
fmin=fmin, fmax=fmax)
elif fmin:
description += '\nHighpass {fmin:g} Hz'.format(fmin=fmin)
elif fmax:
description += '\nLowpass {fmax:g} Hz'.format(fmax=fmax)
ax.text(-.05,
-.05,
description,
fontsize='small',
ha='left',
va='bottom',
transform=ax.transAxes)
cbar_label = QUANTITY_LABEL[quantity]
if envelope:
cbar_label = 'Envelope ' + cbar_label
cb = fig.colorbar(cmw, ax=ax, orientation='vertical', shrink=.8, pad=0.11)
cb.set_label(cbar_label)
if axes is None:
plt.show()
return resp
color_t=(0.3, 0.3, 0.8),
projection=projection,
size_units='data')
for rlat, rlon in rlatlons:
distance = orthodrome.distance_accurate50m(slat, slon, rlat, rlon)
rays = mod.arrivals(phases=cake.PhaseDef('P'),
zstart=sdepth,
zstop=rdepth,
distances=[distance * cake.m2d])
if not rays:
continue
takeoff = rays[0].takeoff_angle()
azi = orthodrome.azimuth(slat, slon, rlat, rlon)
# to spherical coordinates, r, theta, phi in radians
rtp = num.array([[1., num.deg2rad(takeoff), num.deg2rad(90. - azi)]])
# to 3D coordinates (x, y, z)
points = beachball.numpy_rtp2xyz(rtp)
# project to 2D with same projection as used in beachball
x, y = beachball.project(points, projection=projection).T
axes.plot(x, y, '+', ms=10., mew=2.0, mec='black', mfc='none')
#fig.savefig('beachball-example04.png')
plt.show()
position=(0., 0.),
size=2.0,
color_t=(0.7, 0.4, 0.4),
projection=projection,
size_units='data')
for rlat, rlon in rlatlons:
distance = orthodrome.distance_accurate50m(slat, slon, rlat, rlon)
rays = mod.arrivals(
phases=cake.PhaseDef('P'),
zstart=sdepth, zstop=rdepth, distances=[distance*cake.m2d])
if not rays:
continue
takeoff = rays[0].takeoff_angle()
azi = orthodrome.azimuth(slat, slon, rlat, rlon)
# to spherical coordinates, r, theta, phi in radians
rtp = num.array([[1., num.deg2rad(takeoff), num.deg2rad(90.-azi)]])
# to 3D coordinates (x, y, z)
points = beachball.numpy_rtp2xyz(rtp)
# project to 2D with same projection as used in beachball
x, y = beachball.project(points, projection=projection).T
axes.plot(x, y, '+', ms=10., mew=2.0, mec='black', mfc='none')
fig.savefig('beachball-example04.png')