def test_matlab_range():
"""
Tests the Matlab range command.
"""
np.testing.assert_array_equal(utils.matlab_range(0, 5, 1), np.arange(6))
np.testing.assert_array_equal(utils.matlab_range(0, 5.5, 1), np.arange(6))
np.testing.assert_array_equal(utils.matlab_range(0, 4.9, 1), np.arange(5))
def test_matlab_range():
"""
Tests the Matlab range command.
"""
np.testing.assert_array_equal(utils.matlab_range(0, 5, 1), np.arange(6))
np.testing.assert_array_equal(utils.matlab_range(0, 5.5, 1), np.arange(6))
np.testing.assert_array_equal(utils.matlab_range(0, 4.9, 1), np.arange(5))
def time_frequency_cc_difference(t, s1, s2, dt_new, width, threshold):
"""
Straight port of tfa_cc_new.m
:param t: discrete time
:param s1: discrete signal 1
:param s2: discrete signal 2
:param dt_new: time increment in the tf domain
:param width: width of the Gaussian window
:param threshold: fraction of the absolute signal below which the Fourier
transform is set to zero in order to reduce computation time
"""
# New time axis
ti = utils.matlab_range(t[0], t[-1], dt_new)
# Interpolate both signals to the new time axis
si1 = interp1d(t, s1, kind=1)(ti)
si2 = interp1d(t, s2, kind=1)(ti)
# Extend the time axis, required for the correlation
N = len(ti)
t_cc = utils.matlab_range(t[0], (2 * N - 2) * dt_new, dt_new)
# Rename some variables
s1 = si1
s2 = si2
t_min = t_cc[0]
# Initialize the meshgrid
N = len(t_cc)
dnu = 1.0 / (N * dt_new)
nu = utils.matlab_range(0, float(N - 1) / (N * dt_new), dnu)
tau = t_cc
TAU, NU = np.meshgrid(tau, nu)
# Compute the time frequency representation
tfs = np.zeros(NU.shape, dtype="complex128")
for k in xrange(len(tau)):
# Window the signals
w = utils.gaussian_window(ti - tau[k], width)
f1 = w * s1
f2 = w * s2
if np.abs(f1).max() > (threshold * np.abs(s1).max()):
cc = utils.cross_correlation(f2, f1)
tfs[k, :] = np.fft.fft(cc) / np.sqrt(2.0 * np.pi) * dt_new
tfs[k, :] = tfs[k, :] * np.exp(-2.0 * np.pi * 1j * t_min * nu)
else:
tfs[k, :] = 0.0
return TAU, NU, tfs
def time_frequency_cc_difference(t, s1, s2, dt_new, width, threshold):
"""
Straight port of tfa_cc_new.m
:param t: discrete time
:param s1: discrete signal 1
:param s2: discrete signal 2
:param dt_new: time increment in the tf domain
:param width: width of the Gaussian window
:param threshold: fraction of the absolute signal below which the Fourier
transform is set to zero in order to reduce computation time
"""
# New time axis
ti = utils.matlab_range(t[0], t[-1], dt_new)
# Interpolate both signals to the new time axis
si1 = interp1d(t, s1, kind=1)(ti)
si2 = interp1d(t, s2, kind=1)(ti)
# Extend the time axis, required for the correlation
N = len(ti)
t_cc = utils.matlab_range(t[0], (2 * N - 2) * dt_new, dt_new)
# Rename some variables
s1 = si1
s2 = si2
t_min = t_cc[0]
# Initialize the meshgrid
N = len(t_cc)
dnu = 1.0 / (N * dt_new)
nu = utils.matlab_range(0, float(N - 1) / (N * dt_new), dnu)
tau = t_cc
TAU, NU = np.meshgrid(tau, nu)
# Compute the time frequency representation
tfs = np.zeros(NU.shape, dtype="complex128")
for k in xrange(len(tau)):
# Window the signals
w = utils.gaussian_window(ti - tau[k], width)
f1 = w * s1
f2 = w * s2
if np.abs(f1).max() > (threshold * np.abs(s1).max()):
cc = utils.cross_correlation(f2, f1)
tfs[k, :] = np.fft.fft(cc) / np.sqrt(2.0 * np.pi) * dt_new
tfs[k, :] = tfs[k, :] * np.exp(-2.0 * np.pi * 1j * t_min * nu)
else:
tfs[k, :] = 0.0
return TAU, NU, tfs
def time_frequency_transform(t, s, dt_new, width, threshold):
"""
:param t: discrete time
:param s: discrete signal
:param dt_new: time increment in the tf domain
:param width: width of the Gaussian window
:param threshold: fraction of the absolute signal below which the Fourier
transform is set to zero in order to reduce computation time
"""
# New time axis
ti = utils.matlab_range(t[0], t[-1], dt_new)
# Interpolate both signals to the new time axis
si = interp1d(t, s, kind=1)(ti)
# Rename some variables
t = ti
s = si
t_min = t[0]
# Initialize the meshgrid
N = len(t)
nu = np.linspace(0, float(N - 1) / (N * dt_new), len(t))
tau = t
TAU, NU = np.meshgrid(tau, nu)
# Compute the time frequency representation
tfs = np.zeros(NU.shape, dtype="complex128")
for k in xrange(len(tau)):
# Window the signals
w = utils.gaussian_window(t - tau[k], width)
f = w * s
if np.abs(f).max() > (threshold * np.abs(s).max()):
tfs[k, :] = np.fft.fft(f) / np.sqrt(2.0 * np.pi) * dt_new
tfs[k, :] = tfs[k, :] * np.exp(-2.0 * np.pi * 1j * t_min * nu)
else:
tfs[k, :] = 0.0
return TAU, NU, tfs
def time_frequency_transform(t, s, dt_new, width, threshold):
"""
:param t: discrete time
:param s: discrete signal
:param dt_new: time increment in the tf domain
:param width: width of the Gaussian window
:param threshold: fraction of the absolute signal below which the Fourier
transform is set to zero in order to reduce computation time
"""
# New time axis
ti = utils.matlab_range(t[0], t[-1], dt_new)
# Interpolate both signals to the new time axis
si = interp1d(t, s, kind=1)(ti)
# Rename some variables
t = ti
s = si
t_min = t[0]
# Initialize the meshgrid
N = len(t)
nu = np.linspace(0, float(N - 1) / (N * dt_new), len(t))
tau = t
TAU, NU = np.meshgrid(tau, nu)
# Compute the time frequency representation
tfs = np.zeros(NU.shape, dtype="complex128")
for k in xrange(len(tau)):
# Window the signals
w = utils.gaussian_window(t - tau[k], width)
f = w * s
if np.abs(f).max() > (threshold * np.abs(s).max()):
tfs[k, :] = np.fft.fft(f) / np.sqrt(2.0 * np.pi) * dt_new
tfs[k, :] = tfs[k, :] * np.exp(-2.0 * np.pi * 1j * t_min * nu)
else:
tfs[k, :] = 0.0
return TAU, NU, tfs
def adsrc_tf_phase_misfit(t, data, synthetic, min_period, max_period,
plot=False):
"""
:rtype: dictionary
:returns: Return a dictionary with three keys:
* adjoint_source: The calculated adjoint source as a numpy array
* misfit: The misfit value
* messages: A list of strings giving additional hints to what happened
in the calculation.
"""
# Assumes that t starts at 0. Pad your data if that is not the case -
# Parts with zeros are essentially skipped making it fairly efficient.
assert t[0] == 0
messages = []
# Internal sampling interval. Some explanations for this "magic" number.
# LASIF's preprocessing allows no frequency content with smaller periods
# than min_period / 2.2 (see function_templates/preprocesssing_function.py
# for details). Assuming most users don't change this, this is equal to
# the Nyquist frequency and the largest possible sampling interval to
# catch everything is min_period / 4.4.
#
# The current choice is historic as changing does (very slightly) chance
# the calculated misfit and we don't want to disturb inversions in
# progress. The difference is likely minimal in any case. We might have
# same aliasing into the lower frequencies but the filters coupled with
# the TF-domain weighting will get rid of them in essentially all
# realistically occurring cases.
dt_new = max(float(int(min_period / 3.0)), t[1] - t[0])
# New time axis
ti = utils.matlab_range(t[0], t[-1], dt_new)
# Make sure its odd - that avoid having to deal with some issues
# regarding frequency bin interpolation. Now positive and negative
# frequencies will always be all symmetric. Data is assumed to be
# tapered in any case so no problem are to be expected.
if not len(ti) % 2:
ti = ti[:-1]
# Interpolate both signals to the new time axis - this massively speeds
# up the whole procedure as most signals are highly oversampled. The
# adjoint source at the end is re-interpolated to the original sampling
# points.
original_data = data
original_synthetic = synthetic
data = lanczos_interpolation(
data=data, old_start=t[0], old_dt=t[1] - t[0], new_start=t[0],
new_dt=dt_new, new_npts=len(ti), a=8, window="blackmann")
synthetic = lanczos_interpolation(
data=synthetic, old_start=t[0], old_dt=t[1] - t[0], new_start=t[0],
new_dt=dt_new, new_npts=len(ti), a=8, window="blackmann")
original_time = t
t = ti
# -------------------------------------------------------------------------
# Compute time-frequency representations
# Window width is twice the minimal period.
width = 2.0 * min_period
# Compute time-frequency representation of the cross-correlation
_, _, tf_cc = time_frequency.time_frequency_cc_difference(
t, data, synthetic, width)
# Compute the time-frequency representation of the synthetic
tau, nu, tf_synth = time_frequency.time_frequency_transform(t, synthetic,
width)
# -------------------------------------------------------------------------
# compute tf window and weighting function
# noise taper: down-weight tf amplitudes that are very low
tf_cc_abs = np.abs(tf_cc)
m = tf_cc_abs.max() / 10.0 # NOQA
weight = ne.evaluate("1.0 - exp(-(tf_cc_abs ** 2) / (m ** 2))")
nu_t = nu.T
# highpass filter (periods longer than max_period are suppressed
# exponentially)
weight *= (1.0 - np.exp(-(nu_t * max_period) ** 2))
# lowpass filter (periods shorter than min_period are suppressed
# exponentially)
nu_t_large = np.zeros(nu_t.shape)
nu_t_small = np.zeros(nu_t.shape)
thres = (nu_t <= 1.0 / min_period)
nu_t_large[np.invert(thres)] = 1.0
nu_t_small[thres] = 1.0
weight *= (np.exp(-10.0 * np.abs(nu_t * min_period - 1.0)) * nu_t_large +
nu_t_small)
# normalisation
weight /= weight.max()
# computation of phase difference, make quality checks and misfit ---------
# Compute the phase difference.
# DP = np.imag(np.log(m + tf_cc / (2 * m + np.abs(tf_cc))))
DP = np.angle(tf_cc)
# Attempt to detect phase jumps by taking the derivatives in time and
# frequency direction. 0.7 is an emperical value.
abs_weighted_DP = np.abs(weight * DP)
_x = abs_weighted_DP.max() # NOQA
test_field = ne.evaluate("weight * DP / _x")
criterion_1 = np.sum([np.abs(np.diff(test_field, axis=0)) > 0.7])
criterion_2 = np.sum([np.abs(np.diff(test_field, axis=1)) > 0.7])
criterion = np.sum([criterion_1, criterion_2])
if criterion > 7.0:
warning = ("Possible phase jump detected. Misfit included. No "
"adjoint source computed.")
warnings.warn(warning)
messages.append(warning)
# Compute the phase misfit
dnu = nu[1] - nu[0]
i = ne.evaluate("sum(weight ** 2 * DP ** 2)")
phase_misfit = np.sqrt(i * dt_new * dnu)
# Sanity check. Should not occur.
if np.isnan(phase_misfit):
msg = "The phase misfit is NaN."
raise LASIFAdjointSourceCalculationError(msg)
# compute the adjoint source when no phase jump detected ------------------
if criterion <= 7.0:
# Make kernel for the inverse tf transform
idp = ne.evaluate(
"weight ** 2 * DP * tf_synth / (m + abs(tf_synth) ** 2)")
# Invert tf transform and make adjoint source
ad_src, it, I = time_frequency.itfa(tau, idp, width)
# Interpolate both signals to the new time axis
ad_src = lanczos_interpolation(
# Pad with a couple of zeros in case some where lost in all
# these resampling operations. The first sample should not
# change the time.
data=np.concatenate([ad_src.imag, np.zeros(100)]),
old_start=tau[0],
old_dt=tau[1] - tau[0],
new_start=original_time[0],
new_dt=original_time[1] - original_time[0],
new_npts=len(original_time), a=8, window="blackmann")
# Divide by the misfit and change sign.
ad_src /= (phase_misfit + eps)
ad_src = -1.0 * np.diff(ad_src) / (t[1] - t[0])
# Taper at both ends. Exploit ObsPy to not have to deal with all the
# nasty things.
ad_src = \
obspy.Trace(ad_src).taper(max_percentage=0.05, type="hann").data
# Reverse time and add a leading zero so the adjoint source has the
# same length as the input time series.
ad_src = ad_src[::-1]
ad_src = np.concatenate([[0.0], ad_src])
else:
# Criterion failed, no misfit and adjoint source calculated.
raise LASIFAdjointSourceCalculationError(
"Criterion failed, no misfit has been calculated.")
# Plot if requested. ------------------------------------------------------
if plot:
import matplotlib as mpl
import matplotlib.pyplot as plt
plt.style.use("seaborn-whitegrid")
from lasif.colors import get_colormap
if isinstance(plot, mpl.figure.Figure):
fig = plot
else:
fig = plt.gcf()
# Manually set-up the axes for full control.
l, b, w, h = 0.1, 0.05, 0.80, 0.22
rect = l, b + 3 * h, w, h
waveforms_axis = fig.add_axes(rect)
rect = l, b + h, w, 2 * h
tf_axis = fig.add_axes(rect)
rect = l, b, w, h
adj_src_axis = fig.add_axes(rect)
rect = l + w + 0.02, b, 1.0 - (l + w + 0.02) - 0.05, 4 * h
cm_axis = fig.add_axes(rect)
# Plot the weighted phase difference.
weighted_phase_difference = (DP * weight).transpose()
mappable = tf_axis.pcolormesh(
tau, nu, weighted_phase_difference, vmin=-1.0, vmax=1.0,
cmap=get_colormap("tomo_full_scale_linear_lightness_r"),
shading="gouraud", zorder=-10)
tf_axis.grid(True)
tf_axis.grid(True, which='minor', axis='both', linestyle='-',
color='k')
cm = fig.colorbar(mappable, cax=cm_axis)
cm.set_label("Phase difference in radian", fontsize="large")
# Various texts on the time frequency domain plot.
text = "Misfit: %.4f" % phase_misfit
tf_axis.text(x=0.99, y=0.02, s=text, transform=tf_axis.transAxes,
fontsize="large", color="#C25734", fontweight=900,
verticalalignment="bottom",
horizontalalignment="right")
txt = "Weighted Phase Difference - red is a phase advance of the " \
"synthetics"
tf_axis.text(x=0.99, y=0.95, s=txt,
fontsize="large", color="0.1",
transform=tf_axis.transAxes,
verticalalignment="top",
horizontalalignment="right")
if messages:
message = "\n".join(messages)
tf_axis.text(x=0.99, y=0.98, s=message,
transform=tf_axis.transAxes,
bbox=dict(facecolor='red', alpha=0.8),
verticalalignment="top",
horizontalalignment="right")
# Adjoint source.
adj_src_axis.plot(original_time, ad_src[::-1], color="0.1", lw=2,
label="Adjoint source (non-time-reversed)")
adj_src_axis.legend()
# Waveforms.
waveforms_axis.plot(original_time, original_data, color="0.1", lw=2,
label="Observed")
waveforms_axis.plot(original_time, original_synthetic,
color="#C11E11", lw=2, label="Synthetic")
waveforms_axis.legend()
# Set limits for all axes.
tf_axis.set_ylim(0, 2.0 / min_period)
tf_axis.set_xlim(0, tau[-1])
adj_src_axis.set_xlim(0, tau[-1])
waveforms_axis.set_xlim(0, tau[-1])
waveforms_axis.set_ylabel("Velocity [m/s]", fontsize="large")
tf_axis.set_ylabel("Period [s]", fontsize="large")
adj_src_axis.set_xlabel("Seconds since event", fontsize="large")
# Hack to keep ticklines but remove the ticks - there is probably a
# better way to do this.
waveforms_axis.set_xticklabels([
"" for _i in waveforms_axis.get_xticks()])
tf_axis.set_xticklabels(["" for _i in tf_axis.get_xticks()])
_l = tf_axis.get_ylim()
_r = _l[1] - _l[0]
_t = tf_axis.get_yticks()
_t = _t[(_l[0] + 0.1 * _r < _t) & (_t < _l[1] - 0.1 * _r)]
tf_axis.set_yticks(_t)
tf_axis.set_yticklabels(["%.1fs" % (1.0 / _i) for _i in _t])
waveforms_axis.get_yaxis().set_label_coords(-0.08, 0.5)
tf_axis.get_yaxis().set_label_coords(-0.08, 0.5)
fig.suptitle("Time Frequency Phase Misfit and Adjoint Source",
fontsize="xx-large")
ret_dict = {
"adjoint_source": ad_src,
"misfit_value": phase_misfit,
"details": {"messages": messages}
}
return ret_dict
def adsrc_tf_phase_misfit(t,
data,
synthetic,
min_period,
max_period,
plot=False,
max_criterion=7.0):
"""
:rtype: dictionary
:returns: Return a dictionary with three keys:
* adjoint_source: The calculated adjoint source as a numpy array
* misfit: The misfit value
* messages: A list of strings giving additional hints to what happened
in the calculation.
"""
# Assumes that t starts at 0. Pad your data if that is not the case -
# Parts with zeros are essentially skipped making it fairly efficient.
assert t[0] == 0
messages = []
# Internal sampling interval. Some explanations for this "magic" number.
# LASIF's preprocessing allows no frequency content with smaller periods
# than min_period / 2.2 (see function_templates/preprocesssing_function.py
# for details). Assuming most users don't change this, this is equal to
# the Nyquist frequency and the largest possible sampling interval to
# catch everything is min_period / 4.4.
#
# The current choice is historic as changing does (very slightly) chance
# the calculated misfit and we don't want to disturb inversions in
# progress. The difference is likely minimal in any case. We might have
# same aliasing into the lower frequencies but the filters coupled with
# the TF-domain weighting will get rid of them in essentially all
# realistically occurring cases.
dt_new = max(float(int(min_period / 3.0)), t[1] - t[0])
# New time axis
ti = utils.matlab_range(t[0], t[-1], dt_new)
# Make sure its odd - that avoid having to deal with some issues
# regarding frequency bin interpolation. Now positive and negative
# frequencies will always be all symmetric. Data is assumed to be
# tapered in any case so no problem are to be expected.
if not len(ti) % 2:
ti = ti[:-1]
# Interpolate both signals to the new time axis - this massively speeds
# up the whole procedure as most signals are highly oversampled. The
# adjoint source at the end is re-interpolated to the original sampling
# points.
original_data = data
original_synthetic = synthetic
data = lanczos_interpolation(data=data,
old_start=t[0],
old_dt=t[1] - t[0],
new_start=t[0],
new_dt=dt_new,
new_npts=len(ti),
a=8,
window="blackmann")
synthetic = lanczos_interpolation(data=synthetic,
old_start=t[0],
old_dt=t[1] - t[0],
new_start=t[0],
new_dt=dt_new,
new_npts=len(ti),
a=8,
window="blackmann")
original_time = t
t = ti
# -------------------------------------------------------------------------
# Compute time-frequency representations
# Window width is twice the minimal period.
width = 2.0 * min_period
# Compute time-frequency representation of the cross-correlation
_, _, tf_cc = time_frequency.time_frequency_cc_difference(
t, data, synthetic, width)
# Compute the time-frequency representation of the synthetic
tau, nu, tf_synth = time_frequency.time_frequency_transform(
t, synthetic, width)
# -------------------------------------------------------------------------
# compute tf window and weighting function
# noise taper: down-weight tf amplitudes that are very low
tf_cc_abs = np.abs(tf_cc)
m = tf_cc_abs.max() / 10.0 # NOQA
weight = ne.evaluate("1.0 - exp(-(tf_cc_abs ** 2) / (m ** 2))")
nu_t = nu.T
# highpass filter (periods longer than max_period are suppressed
# exponentially)
weight *= (1.0 - np.exp(-(nu_t * max_period)**2))
# lowpass filter (periods shorter than min_period are suppressed
# exponentially)
nu_t_large = np.zeros(nu_t.shape)
nu_t_small = np.zeros(nu_t.shape)
thres = (nu_t <= 1.0 / min_period)
nu_t_large[np.invert(thres)] = 1.0
nu_t_small[thres] = 1.0
weight *= (np.exp(-10.0 * np.abs(nu_t * min_period - 1.0)) * nu_t_large +
nu_t_small)
# normalisation
weight /= weight.max()
# computation of phase difference, make quality checks and misfit ---------
# Compute the phase difference.
# DP = np.imag(np.log(m + tf_cc / (2 * m + np.abs(tf_cc))))
DP = np.angle(tf_cc)
# Attempt to detect phase jumps by taking the derivatives in time and
# frequency direction. 0.7 is an emperical value.
abs_weighted_DP = np.abs(weight * DP)
_x = abs_weighted_DP.max() # NOQA
test_field = ne.evaluate("weight * DP / _x")
criterion_1 = np.sum([np.abs(np.diff(test_field, axis=0)) > 0.7])
criterion_2 = np.sum([np.abs(np.diff(test_field, axis=1)) > 0.7])
criterion = np.sum([criterion_1, criterion_2])
# Compute the phase misfit
dnu = nu[1] - nu[0]
i = ne.evaluate("sum(weight ** 2 * DP ** 2)")
phase_misfit = np.sqrt(i * dt_new * dnu)
# Sanity check. Should not occur.
if np.isnan(phase_misfit):
msg = "The phase misfit is NaN."
raise LASIFAdjointSourceCalculationError(msg)
# The misfit can still be computed, even if not adjoint source is
# available.
if criterion > max_criterion:
warning = ("Possible phase jump detected. Misfit included. No "
"adjoint source computed. Criterion: %.1f - Max allowed "
"criterion: %.1f" % (criterion, max_criterion))
warnings.warn(warning)
messages.append(warning)
ret_dict = {
"adjoint_source": None,
"misfit_value": phase_misfit,
"details": {
"messages": messages
}
}
return ret_dict
# Make kernel for the inverse tf transform
idp = ne.evaluate("weight ** 2 * DP * tf_synth / (m + abs(tf_synth) ** 2)")
# Invert tf transform and make adjoint source
ad_src, it, I = time_frequency.itfa(tau, idp, width)
# Interpolate both signals to the new time axis
ad_src = lanczos_interpolation(
# Pad with a couple of zeros in case some where lost in all
# these resampling operations. The first sample should not
# change the time.
data=np.concatenate([ad_src.imag, np.zeros(100)]),
old_start=tau[0],
old_dt=tau[1] - tau[0],
new_start=original_time[0],
new_dt=original_time[1] - original_time[0],
new_npts=len(original_time),
a=8,
window="blackmann")
# Divide by the misfit and change sign.
ad_src /= (phase_misfit + eps)
ad_src = -1.0 * np.diff(ad_src) / (t[1] - t[0])
# Taper at both ends. Exploit ObsPy to not have to deal with all the
# nasty things.
ad_src = \
obspy.Trace(ad_src).taper(max_percentage=0.05, type="hann").data
# Reverse time and add a leading zero so the adjoint source has the
# same length as the input time series.
ad_src = ad_src[::-1]
ad_src = np.concatenate([[0.0], ad_src])
# Plot if requested. ------------------------------------------------------
if plot:
import matplotlib as mpl
import matplotlib.pyplot as plt
plt.style.use("seaborn-whitegrid")
from lasif.colors import get_colormap
if isinstance(plot, mpl.figure.Figure):
fig = plot
else:
fig = plt.gcf()
# Manually set-up the axes for full control.
l, b, w, h = 0.1, 0.05, 0.80, 0.22
rect = l, b + 3 * h, w, h
waveforms_axis = fig.add_axes(rect)
rect = l, b + h, w, 2 * h
tf_axis = fig.add_axes(rect)
rect = l, b, w, h
adj_src_axis = fig.add_axes(rect)
rect = l + w + 0.02, b, 1.0 - (l + w + 0.02) - 0.05, 4 * h
cm_axis = fig.add_axes(rect)
# Plot the weighted phase difference.
weighted_phase_difference = (DP * weight).transpose()
mappable = tf_axis.pcolormesh(
tau,
nu,
weighted_phase_difference,
vmin=-1.0,
vmax=1.0,
cmap=get_colormap("tomo_full_scale_linear_lightness_r"),
shading="gouraud",
zorder=-10)
tf_axis.grid(True)
tf_axis.grid(True,
which='minor',
axis='both',
linestyle='-',
color='k')
cm = fig.colorbar(mappable, cax=cm_axis)
cm.set_label("Phase difference in radian", fontsize="large")
# Various texts on the time frequency domain plot.
text = "Misfit: %.4f" % phase_misfit
tf_axis.text(x=0.99,
y=0.02,
s=text,
transform=tf_axis.transAxes,
fontsize="large",
color="#C25734",
fontweight=900,
verticalalignment="bottom",
horizontalalignment="right")
txt = "Weighted Phase Difference - red is a phase advance of the " \
"synthetics"
tf_axis.text(x=0.99,
y=0.95,
s=txt,
fontsize="large",
color="0.1",
transform=tf_axis.transAxes,
verticalalignment="top",
horizontalalignment="right")
if messages:
message = "\n".join(messages)
tf_axis.text(x=0.99,
y=0.98,
s=message,
transform=tf_axis.transAxes,
bbox=dict(facecolor='red', alpha=0.8),
verticalalignment="top",
horizontalalignment="right")
# Adjoint source.
adj_src_axis.plot(original_time,
ad_src[::-1],
color="0.1",
lw=2,
label="Adjoint source (non-time-reversed)")
adj_src_axis.legend()
# Waveforms.
waveforms_axis.plot(original_time,
original_data,
color="0.1",
lw=2,
label="Observed")
waveforms_axis.plot(original_time,
original_synthetic,
color="#C11E11",
lw=2,
label="Synthetic")
waveforms_axis.legend()
# Set limits for all axes.
tf_axis.set_ylim(0, 2.0 / min_period)
tf_axis.set_xlim(0, tau[-1])
adj_src_axis.set_xlim(0, tau[-1])
waveforms_axis.set_xlim(0, tau[-1])
waveforms_axis.set_ylabel("Velocity [m/s]", fontsize="large")
tf_axis.set_ylabel("Period [s]", fontsize="large")
adj_src_axis.set_xlabel("Seconds since event", fontsize="large")
# Hack to keep ticklines but remove the ticks - there is probably a
# better way to do this.
waveforms_axis.set_xticklabels(
["" for _i in waveforms_axis.get_xticks()])
tf_axis.set_xticklabels(["" for _i in tf_axis.get_xticks()])
_l = tf_axis.get_ylim()
_r = _l[1] - _l[0]
_t = tf_axis.get_yticks()
_t = _t[(_l[0] + 0.1 * _r < _t) & (_t < _l[1] - 0.1 * _r)]
tf_axis.set_yticks(_t)
tf_axis.set_yticklabels(["%.1fs" % (1.0 / _i) for _i in _t])
waveforms_axis.get_yaxis().set_label_coords(-0.08, 0.5)
tf_axis.get_yaxis().set_label_coords(-0.08, 0.5)
fig.suptitle("Time Frequency Phase Misfit and Adjoint Source",
fontsize="xx-large")
ret_dict = {
"adjoint_source": ad_src,
"misfit_value": phase_misfit,
"details": {
"messages": messages
}
}
return ret_dict