def vespagram_backazimuth(st,
s,
bazmin,
bazmax,
bazsteps,
winlen,
stat='power',
n=1):
'''
Calculates the vespagram for a seismic array over a given range of backazimuths, for a single scalar slowness, using the statistic specified.
The chosen statistic is calculated as a function of time (in s) and backazimuth (in deg). This may be:-
* 'amplitude' - the raw amplitude of the linear or nth root stack at each time and slowness step;
* 'power' - the power in the linear or nth root beam calculated over a time window (length winlen) around each time step for each slowness;
* 'F' - the F-statistic of the beam calculated over a time window (length winlen) around each time step for each slowness.
Parameters
----------
st : ObsPy Stream object
Stream of SAC format seismograms for the seismic array, length K = no. of stations in array
s : float
Magnitude of the slowness vector, in s/km
bazmin : float
Minimum backazimuth, in degrees
bazmax : float
Maximum backazimuth, in degrees
bazsteps : int
Integer number of steps between bazmin and bazmax for which to calculate the vespagram
winlen : int
Length of Hann window over which to calculate the power.
stat : string
Statistic to use for plotting the vespagram, either 'amplitude', 'power', or 'F'
Returns
-------
vespagram_data : NumPy array
Array of values for the chosen statistic at each backazimuth and time step. Dimensions: bazsteps*len(tr) for traces tr in st.
'''
if stat == 'amplitude':
vespagram_data = np.array([
nth_root_stack(st, s, baz, n)
for baz in np.linspace(bazmin, bazmax, bazsteps)
])
elif stat == 'power':
vespagram_data = np.array([
n_power_vespa(st, s, baz, n, winlen)
for baz in np.linspace(bazmin, bazmax, bazsteps)
])
elif stat == 'F':
vespagram_data = np.array([
f_vespa(st, s, baz, winlen)
for baz in np.linspace(bazmin, bazmax, bazsteps)
])
else:
raise AssertionError(
"'stat' argument must be one of 'amplitude', 'power' or 'F'")
return vespagram_data
def vespagram(st, smin, smax, ssteps, baz, winlen, stat='power', n=1):
'''
Calculates the vespagram for a seismic array over a given slowness range, for a single backazimuth, using the statistic specified.
The chosen statistic is calculated as a function of time (in s) and slowness (in s/km). This may be:-
* 'amplitude' - the raw amplitude of the linear or nth root stack at each time and slowness step;
* 'power' - the power in the linear or nth root beam calculated over a time window (length winlen) around each time step for each slowness;
* 'F' - the F-statistic of the beam calculated over a time window (length winlen) around each time step for each slowness.
Parameters
----------
st : ObsPy Stream object
Stream of SAC format seismograms for the seismic array, length K = no. of stations in array
smin : float
Minimum magnitude of slowness vector, in s / km
smax : float
Maximum magnitude of slowness vector, in s / km
ssteps : int
Integer number of steps between smin and smax for which to calculate the vespagram
baz : float
Backazimuth of slowness vector, (i.e. angle from North back to epicentre of event)
winlen : int
Length of Hann window over which to calculate the power.
stat : string
Statistic to use for plotting the vespagram, either 'amplitude', 'power', or 'F'
Returns
-------
vespagram_data : NumPy array
Array of values for the chosen statistic at each slowness and time step. Dimensions: ssteps*len(tr) for traces tr in st.
'''
assert stat == 'amplitude' or stat == 'power' or stat == 'F', "'stat' argument must be one of 'amplitude', 'power' or 'F'"
vespagram_data = np.array([])
try:
if stat == 'amplitude':
vespagram_data = np.array([
nth_root_stack(st, s, baz, n)
for s in np.linspace(smin, smax, ssteps)
])
elif stat == 'power':
vespagram_data = np.array([
n_power_vespa(st, s, baz, n, winlen)
for s in np.linspace(smin, smax, ssteps)
])
elif stat == 'F':
vespagram_data = np.array([
f_vespa(st, s, baz, winlen)
for s in np.linspace(smin, smax, ssteps)
])
except AssertionError as err:
raise err
return vespagram_data
def vespagram(st, smin, smax, ssteps, baz, winlen, stat='power', n=1):
'''
Calculates the vespagram for a seismic array over a given slowness range, for a single backazimuth, using the statistic specified.
The chosen statistic is calculated as a function of time (in s) and slowness (in s/km). This may be:-
* 'amplitude' - the raw amplitude of the linear or nth root stack at each time and slowness step;
* 'power' - the power in the linear or nth root beam calculated over a time window (length winlen) around each time step for each slowness;
* 'F' - the F-statistic of the beam calculated over a time window (length winlen) around each time step for each slowness.
Parameters
----------
st : ObsPy Stream object
Stream of SAC format seismograms for the seismic array, length K = no. of stations in array
smin : float
Minimum magnitude of slowness vector, in s / km
smax : float
Maximum magnitude of slowness vector, in s / km
ssteps : int
Integer number of steps between smin and smax for which to calculate the vespagram
baz : float
Backazimuth of slowness vector, (i.e. angle from North back to epicentre of event)
winlen : int
Length of Hann window over which to calculate the power.
stat : string
Statistic to use for plotting the vespagram, either 'amplitude', 'power', or 'F'
Returns
-------
vespagram_data : NumPy array
Array of values for the chosen statistic at each slowness and time step. Dimensions: ssteps*len(tr) for traces tr in st.
'''
assert stat == 'amplitude' or stat == 'power' or stat == 'F', "'stat' argument must be one of 'amplitude', 'power' or 'F'"
vespagram_data = np.array([])
try:
if stat == 'amplitude':
vespagram_data = np.array([nth_root_stack(st, s, baz, n) for s in np.linspace(smin, smax, ssteps)])
elif stat == 'power':
vespagram_data = np.array([n_power_vespa(st, s, baz, n, winlen) for s in np.linspace(smin, smax, ssteps)])
elif stat == 'F':
vespagram_data = np.array([f_vespa(st, s, baz, winlen) for s in np.linspace(smin, smax, ssteps)])
except AssertionError as err:
raise err
return vespagram_data
def vespagram_backazimuth(st, s, bazmin, bazmax, bazsteps, winlen, stat='power', n=1):
'''
Calculates the vespagram for a seismic array over a given range of backazimuths, for a single scalar slowness, using the statistic specified.
The chosen statistic is calculated as a function of time (in s) and backazimuth (in deg). This may be:-
* 'amplitude' - the raw amplitude of the linear or nth root stack at each time and slowness step;
* 'power' - the power in the linear or nth root beam calculated over a time window (length winlen) around each time step for each slowness;
* 'F' - the F-statistic of the beam calculated over a time window (length winlen) around each time step for each slowness.
Parameters
----------
st : ObsPy Stream object
Stream of SAC format seismograms for the seismic array, length K = no. of stations in array
s : float
Magnitude of the slowness vector, in s/km
bazmin : float
Minimum backazimuth, in degrees
bazmax : float
Maximum backazimuth, in degrees
bazsteps : int
Integer number of steps between bazmin and bazmax for which to calculate the vespagram
winlen : int
Length of Hann window over which to calculate the power.
stat : string
Statistic to use for plotting the vespagram, either 'amplitude', 'power', or 'F'
Returns
-------
vespagram_data : NumPy array
Array of values for the chosen statistic at each backazimuth and time step. Dimensions: bazsteps*len(tr) for traces tr in st.
'''
if stat == 'amplitude':
vespagram_data = np.array([nth_root_stack(st, s, baz, n) for baz in np.linspace(bazmin, bazmax, bazsteps)])
elif stat == 'power':
vespagram_data = np.array([n_power_vespa(st, s, baz, n, winlen) for baz in np.linspace(bazmin, bazmax, bazsteps)])
elif stat == 'F':
vespagram_data = np.array([f_vespa(st, s, baz, winlen) for baz in np.linspace(bazmin, bazmax,bazsteps)])
else:
raise AssertionError("'stat' argument must be one of 'amplitude', 'power' or 'F'")
return vespagram_data
def f_vespagram_theoretical_arrivals(st, origin, smin, smax, ssteps, baz,
winlen):
'''
Plots the F-stat vespagram for a seismic array over a given slowness range, for a single backazimuth, using the statistic specified. Also plots theoretical arrival times and slownesses for each phase.
The chosen statistic is plotted as a function of time (in s) and slowness (in s/km). This may be:-
* 'amplitude' - the raw amplitude of the linear or nth root stack at each time and slowness step;
* 'power' - the power in the linear or nth root beam calculated over a time window (length winlen) around each time step for each slowness;
* 'F' - the F-statistic of the beam calculated over a time window (length winlen) around each time step for each slowness.
Parameters
----------
st : ObsPy Stream object
Stream of SAC format seismograms for the seismic array, length K = no. of stations in array
origin : ObsPy Origin object
Origin of the event in question. Should contain the origin time of the earthquake and if necessary the depth and location.
smin : float
Minimum magnitude of slowness vector, in s / km
smax : float
Maximum magnitude of slowness vector, in s / km
ssteps : int
Integer number of steps between smin and smax for which to calculate the vespagram
baz : float
Backazimuth of slowness vector, (i.e. angle from North back to epicentre of event)
winlen : int
Length of Hann window over which to calculate the power.
stat : string
Statistic to use for plotting the vespagram, either 'amplitude', 'power', or 'F'
display: string
Option for plotting: either 'contourf' for filled contour plot, or 'contour' for contour plot. See matplotlib documentation for more details.
'''
starttime = st[0].stats.starttime
tt_model = TauPyModel()
# Arrivals are calculated from the information in origin.
delta = locations2degrees(
origin.latitude, origin.longitude, st[0].stats.sac.stla,
st[0].stats.sac.stlo) # Distance in degrees from source to receiver
arrivals = tt_model.get_travel_times(origin.depth / 1000., delta)
arrival_names = [arrival.name for arrival in arrivals]
arrival_times = [
origin.time + arrival.time - starttime for arrival in arrivals
]
arrival_slowness = [
arrival.ray_param_sec_degree / G_KM_DEG for arrival in arrivals
]
plt.figure(figsize=(16, 8))
vespagram = np.array(
[f_vespa(st, s, baz, winlen) for s in np.linspace(smin, smax, ssteps)])
label = 'F'
timestring = str(st[0].stats.starttime.datetime)
title = timestring + ": " + label + " Vespagram"
plt.contourf(st[0].times(), np.linspace(smin, smax, ssteps),
vespagram[:, :])
cb = plt.colorbar()
cb.set_label(label)
# Plot predicted arrivals
plt.scatter(arrival_times, arrival_slowness, c='cyan', s=200, marker='+')
plt.xlabel("Time (s)")
plt.xlim(min(st[0].times()), max(st[0].times()))
plt.ylim(smin, smax)
# Thanks, Stack Overflow: http://stackoverflow.com/questions/5147112/matplotlib-how-to-put-individual-tags-for-a-scatter-plot
for label, x, y in zip(arrival_names, arrival_times, arrival_slowness):
plt.annotate(label,
xy=(x, y),
xytext=(-20, 20),
textcoords='offset points',
ha='right',
va='bottom',
bbox=dict(boxstyle='round,pad=0.5',
fc='yellow',
alpha=0.5),
arrowprops=dict(arrowstyle='->',
connectionstyle='arc3,rad=0'))
plt.ylabel("Slowness (s / km)")
plt.title(title)
def f_vespagram_theoretical_arrivals(st, origin, smin, smax, ssteps, baz, winlen):
'''
Plots the F-stat vespagram for a seismic array over a given slowness range, for a single backazimuth, using the statistic specified. Also plots theoretical arrival times and slownesses for each phase.
The chosen statistic is plotted as a function of time (in s) and slowness (in s/km). This may be:-
* 'amplitude' - the raw amplitude of the linear or nth root stack at each time and slowness step;
* 'power' - the power in the linear or nth root beam calculated over a time window (length winlen) around each time step for each slowness;
* 'F' - the F-statistic of the beam calculated over a time window (length winlen) around each time step for each slowness.
Parameters
----------
st : ObsPy Stream object
Stream of SAC format seismograms for the seismic array, length K = no. of stations in array
origin : ObsPy Origin object
Origin of the event in question. Should contain the origin time of the earthquake and if necessary the depth and location.
smin : float
Minimum magnitude of slowness vector, in s / km
smax : float
Maximum magnitude of slowness vector, in s / km
ssteps : int
Integer number of steps between smin and smax for which to calculate the vespagram
baz : float
Backazimuth of slowness vector, (i.e. angle from North back to epicentre of event)
winlen : int
Length of Hann window over which to calculate the power.
stat : string
Statistic to use for plotting the vespagram, either 'amplitude', 'power', or 'F'
display: string
Option for plotting: either 'contourf' for filled contour plot, or 'contour' for contour plot. See matplotlib documentation for more details.
'''
starttime = st[0].stats.starttime
tt_model = TauPyModel()
# Arrivals are calculated from the information in origin.
delta = locations2degrees(origin.latitude, origin.longitude, st[0].stats.sac.stla, st[0].stats.sac.stlo) # Distance in degrees from source to receiver
arrivals = tt_model.get_travel_times(origin.depth/1000., delta)
arrival_names = [arrival.name for arrival in arrivals]
arrival_times = [origin.time + arrival.time - starttime for arrival in arrivals]
arrival_slowness = [arrival.ray_param_sec_degree/G_KM_DEG for arrival in arrivals]
plt.figure(figsize=(16, 8))
vespagram = np.array([f_vespa(st, s, baz, winlen) for s in np.linspace(smin, smax, ssteps)])
label = 'F'
timestring = str(st[0].stats.starttime.datetime)
title = timestring + ": " + label + " Vespagram"
plt.contourf(st[0].times(), np.linspace(smin, smax, ssteps), vespagram[:, :])
cb = plt.colorbar()
cb.set_label(label)
# Plot predicted arrivals
plt.scatter(arrival_times, arrival_slowness, c='cyan', s=200, marker='+')
plt.xlabel("Time (s)")
plt.xlim(min(st[0].times()), max(st[0].times()))
plt.ylim(smin, smax)
# Thanks, Stack Overflow: http://stackoverflow.com/questions/5147112/matplotlib-how-to-put-individual-tags-for-a-scatter-plot
for label, x, y in zip(arrival_names, arrival_times, arrival_slowness):
plt.annotate(label, xy=(x, y), xytext=(-20, 20), textcoords='offset points', ha='right', va='bottom',
bbox=dict(boxstyle='round,pad=0.5', fc='yellow', alpha=0.5),
arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0'))
plt.ylabel("Slowness (s / km)")
plt.title(title)