def n_power_vespa(st, s, baz, n, winlen):
'''
Returns the nth root power vespa (i.e. the power in the nth root stack) for a seismic array, for a beam of given slowness and backazimuth.
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 slowness vector, in s / km
baz : float
Backazimuth of slowness vector, (i.e. angle from North back to epicentre of event)
n : int
Order of the nth root process
winlen : int
Length of Hann window over which to calculate the power.
Returns
-------
power : NumPy array
The power of the nth root stack at the given slowness and backazimuth, as a time series.
'''
amplitude = nth_root_stack(st, s, baz, n)
power = np.convolve(amplitude**2, np.hanning(winlen), mode='same')
return power
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 n_power_vespa(st, s, baz, n, winlen):
"""
Returns the nth root power vespa (i.e. the power in the nth root stack) for a seismic array, for a beam of given slowness and backazimuth.
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 slowness vector, in s / km
baz : float
Backazimuth of slowness vector, (i.e. angle from North back to epicentre of event)
n : int
Order of the nth root process
winlen : int
Length of Hann window over which to calculate the power.
Returns
-------
power : NumPy array
The power of the nth root stack at the given slowness and backazimuth, as a time series.
"""
amplitude = nth_root_stack(st, s, baz, n)
power = np.convolve(amplitude ** 2, np.hanning(winlen), mode="same")
return power
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
