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# - GPLv3
# The Pyrocko Developers, 21st Century
# ---|P------/S----------~Lg----------
import logging
import numpy as num
import matplotlib.pyplot as plt
from import ScalarMappable
from matplotlib.ticker import FuncFormatter
from pyrocko.plot import beachball
from import Timing
from import LocalEngine, Target, RectangularSource, map_anchor
from pyrocko.util import num_full_like
km = 1e3
r2d = 180. / num.pi
d2r = num.pi / 180.
logger = logging.getLogger(__name__)
'displacement': 'Displacement [m]',
'velocity': 'Velocity [m/s]',
'acceleration': 'Acceleration [m/s²]'
def get_azimuthal_targets(
store_id, source, radius,
azi_begin=0., azi_end=360., dazi=1.,
components='RTZ', quantity='displacement'):
assert dazi > 0.
assert azi_begin < azi_end
nstations = int((azi_end - azi_begin) // dazi)
assert nstations > 0
azimuths = num.linspace(azi_begin, azi_end, nstations)
coords = num.zeros((2, nstations))
coords[0, :] = num.cos(azimuths*d2r)
coords[1, :] = num.sin(azimuths*d2r)
coords *= radius
dips = {'R': 0., 'T': 0., 'Z': -90.}
for comp in components:
assert comp in dips.keys()
target_kwargs = dict(
targets = [
north_shift=coords[0, iazi] + source.north_shift,
east_shift=coords[1, iazi] + source.east_shift,
'R': azi,
'T': azi+90.,
'Z': 0.
codes=('', 'S%01d' % iazi, '', channel),
for iazi, azi in enumerate(azimuths)
for channel in components]
for target, azi in zip(targets, azimuths):
target.azimuth = azi
target.dazi = dazi
return targets, azimuths
def get_seismogram_array(
response, fmin=None, fmax=None,
component='R', envelope=False):
resp = response
assert len(resp.request.sources) == 1, 'more than one source in response'
tmin = None
tmax = None
traces = []
for _, target, tr in response.iter_results():
if[-1] != component:
assert hasattr(target, 'azimuth')
assert target.dazi
if fmin is not None:
tr.highpass(4, fmin, demean=False)
if fmax is not None:
tr.lowpass(4, fmax, demean=False)
tmin = min(tmin, tr.tmin) if tmin else tr.tmin
tmax = max(tmax, tr.tmax) if tmax else tr.tmax
for tr in traces:
tr.extend(tmin, tmax, fillmethod='repeat')
if envelope:
data = num.array([tr.get_ydata() for tr in traces])
nsamples = data.shape[1]
return data, num.linspace(tmin, tmax, nsamples)
def hillshade(array, azimuth, angle_altitude):
azimuth = 360.0 - azimuth
azi = azimuth * r2d
alt = angle_altitude * r2d
x, y = num.gradient(array)
slope = num.pi/2. - num.arctan(num.sqrt(x*x + y*y))
aspect = num.arctan2(-x, y)
shaded = num.sin(alt)*num.sin(slope) \
+ num.cos(alt)*num.cos(slope)*num.cos((azi - num.pi/2.) - aspect)
return (shaded + 1.)/2.
def hillshade_seismogram_array(
seismogram_array, rgba_map,
shad_lim=(.4, .98), contrast=1., blend_mode='multiply'):
assert blend_mode in ('multiply', 'screen'), 'unknown blend mode'
assert shad_lim[0] < shad_lim[1], 'bad shading limits'
from scipy.ndimage import convolve as im_conv
# Light source from somewhere above - psychologically the best choice
# from upper left
ramp = num.array([[1., 0.], [0., -1.]]) * contrast
# convolution of two 2D arrays
shad = im_conv(seismogram_array, ramp.T).ravel()
shad *= -1.
# if there are strong artifical edges in the data, shades get
# dominated by them. Cutting off the largest and smallest 2% of
# # shades helps
percentile2 = num.percentile(shad, 2.0)
percentile98 = num.percentile(shad, 98.0)
shad[shad > percentile98] = percentile98
shad[shad < percentile2] = percentile2
# # normalize shading
shad -= num.nanmin(shad)
shad /= num.nanmax(shad)
# # reduce range to balance gray color
shad *= shad_lim[1] - shad_lim[0]
shad += shad_lim[0]
if blend_mode == 'screen':
rgba_map[:, :3] = 1. - ((1. - rgba_map[:, :3])*(shad[:, num.newaxis]))
elif blend_mode == 'multiply':
rgba_map[:, :3] *= shad[:, num.newaxis]
return rgba_map
def plot_directivity(
engine, source, store_id,
distance=300*km, azi_begin=0., azi_end=360., dazi=1.,
phases={'P': 'first{stored:any_P}-10%',
'S': '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:``
:param source: Parametrized source model
:type source: :py:class:``
: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 phases: Phases to define start and end of time window
:type phases: :py:class:`dict` with :py:class:`str` keys and
:py:class:`` values
:param quantity: Seismogram quantity, default ``displacement``
:type quantity: str
:param envelope: Plot envelope instead of seismic trace
:type envelope: bool
:param component: Forward modelled component, default ``R``. Choose from
: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: Matplotlib 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 description, 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)
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)
ref_target = targets[0]
store = engine.get_store(store_id)
mt = source.pyrocko_moment_tensor(store=store, target=ref_target)
resp = engine.process(source, targets, nthreads=nthreads)
data, times = get_seismogram_array(
resp, fmin, fmax,
component=component, envelope=envelope)
nucl_depth = source.depth
nucl_distance = distance
if hasattr(source, 'nucleation_x') and hasattr(source, 'nucleation_y'):
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.
timings = [Timing(p) for p in phases.values()]
phase_times = [store.t(t, source, ref_target) for t in timings]
tbegin = min(phase_times)
tend = max(phase_times)
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_clim(-vmax, vmax)
if envelope:
cmw.set_clim(0., vmax)
strike_label = mt.strike1
if hasattr(source, 'strike'):
strike_label = source.strike
ax.set_rlabel_position(strike_label % 180. - 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
if reverse_time:
ax.set_rlim(times[0] - .3*duration, times[-1])
ax.set_rlim(times[-1] + .3*duration, times[0])
if isinstance(plot_mt, str):
mt_size = .15
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:
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, norm=cmw.norm, shading='gouraud', zorder=0)
if hillshade:
color = mesh.get_facecolor()
color = hillshade_seismogram_array(
data, color, shad_lim=(.85, 1.), blend_mode='multiply')
if show_phases:
label_theta = 270.
theta = num.linspace(0, 2*num.pi, 360)
for label, phase_str in phases.items():
phase = Timing(phase_str)
phase.offset = 0.
phase.offset_is_slowness = False
phase.offset_is_percent = False
time = store.t(phase, source, ref_target)
times = num_full_like(theta, time)
ax.plot(theta, times, color='k', alpha=.3, lw=1., ls='--')
label_theta*d2r, time, label,
ha='left', color='k', fontsize='small')
label_theta += 30.
if show_description:
description = (
'Component {component:s}\n'
'Distance {distance:g} km').format(
component=component, distance=distance / km)
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)
-.05, -.05, description,
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)
if axes is None:
return resp
__all__ = ['plot_directivity']
if __name__ == '__main__':
engine = LocalEngine(store_superdirs=['.'], use_config=True)
rect_source = RectangularSource(
resp = plot_directivity(
engine, rect_source, 'crust2_ib',
dazi=5, component='R', quantity='displacement', envelope=True)