"""
Early development functions to do **very** basic simulations of seismograms \
to be used as general matched-filter templates and see how well a simple \
model would fit with real data. Mostly used in EQcorrscan for testing.
:copyright:
Calum Chamberlain, Chet Hopp.
:license:
GNU Lesser General Public License, Version 3
(https://www.gnu.org/copyleft/lesser.html)
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals
import numpy as np
[docs]def seis_sim(SP, amp_ratio=1.5, flength=False, phaseout='all'):
"""
Generate a simulated seismogram from a given S-P time. \
Will generate spikes separated by a given S-P time, which are then \
convolved with a decaying sine function. The P-phase is simulated by a \
positive spike of value 1, the S-arrival is simulated by a decaying \
boxcar of maximum amplitude 1.5. These ampitude ratios can be altered by \
changing the amp_ratio, which is the ratio S amplitude:P amplitude.
.. note:: In testing this can achieve 0.3 or greater cross-correlations \
with data.
:type SP: int
:param SP: S-P time in samples
:type amp_ratio: float
:param amp_ratio: S:P amplitude ratio
:type flength: int
:param flength: Fixed length in samples, defaults to False
:type phaseout: str
:param phaseout: Either 'P', 'S' or 'all', controls which phases to cut \
around, defaults to 'all'. Can only be used with 'P' or 'S' options \
if flength is set.
:returns: np.ndarray
"""
if flength and 2.5 * SP < flength and 100 < flength:
additional_length = flength
elif 2.5 * SP < 100.0:
additional_length = 100
else:
additional_length = 2.5 * SP
synth = np.zeros(int(SP + 10 + additional_length))
# Make the array begin 10 samples before the P
# and at least 2.5 times the S-P samples after the S arrival
synth[10] = 1.0 # P-spike fixed at 10 samples from start of window
# The length of the decaying S-phase should depend on the SP time,\
# Some basic estimations suggest this should be atleast 10 samples\
# and that the coda should be about 1/10 of the SP time
S_length = 10 + int(SP // 3)
S_spikes = np.arange(amp_ratio, 0, -(amp_ratio / S_length))
# What we actually want, or what appears better is to have a series of\
# individual spikes, of alternating polarity...
for i in range(len(S_spikes)):
if i in np.arange(1, len(S_spikes), 2):
S_spikes[i] = 0
if i in np.arange(2, len(S_spikes), 4):
S_spikes[i] *= -1
# Put these spikes into the synthetic
synth[10 + SP:10 + SP + len(S_spikes)] = S_spikes
# Generate a rough damped sine wave to convolve with the model spikes
sine_x = np.arange(0, 10.0, 0.5)
damped_sine = np.exp(-sine_x) * np.sin(2 * np.pi * sine_x)
# Convolve the spike model with the damped sine!
synth = np.convolve(synth, damped_sine)
# Normalize snyth
synth = synth / np.max(np.abs(synth))
if not flength:
return synth
else:
if phaseout in ['all', 'P']:
synth = synth[0:flength]
elif phaseout == 'S':
synth = synth[SP:]
if len(synth) < flength:
# If this is too short, pad
synth = np.append(synth, np.zeros(flength - len(synth)))
else:
synth = synth[0:flength]
return synth
[docs]def SVD_sim(SP, lowcut, highcut, samp_rate,
amp_range=np.arange(-10, 10, 0.01)):
"""
Generate basis vectors of a set of simulated seismograms.
Inputs should have a range of S-P amplitude ratios, in theory to simulate \
a range of focal mechanisms.
:type SP: int
:param SP: S-P time in seconds - will be converted to samples according \
to samp_rate.
:type lowcut: float
:param lowcut: Low-cut for bandpass filter in Hz
:type highcut: float
:param highcut: High-cut for bandpass filter in Hz
:type samp_rate: float
:param samp_rate: Sampling rate in Hz
:type amp_range: np.ndarray
:param amp_range: Amplitude ratio range to generate synthetics for.
:returns: nd.ndarray, set of output basis vectors
"""
from obspy import Stream, Trace
# Convert SP to samples
SP = int(SP * samp_rate)
# Scan through a range of amplitude ratios
synthetics = [Stream(Trace(seis_sim(SP, a))) for a in amp_range]
for st in synthetics:
for tr in st:
tr.stats.station = 'SYNTH'
tr.stats.channel = 'SH1'
tr.stats.sampling_rate = samp_rate
tr.filter('bandpass', freqmin=lowcut, freqmax=highcut)
# We have a list of obspy Trace objects, we can pass this to EQcorrscan's\
# SVD functions
from utils import clustering
V, s, U, stachans = clustering.SVD(synthetics)
return V, s, U, stachans
[docs]def template_grid(stations, nodes, travel_times, phase, PS_ratio=1.68,
samp_rate=100, flength=False, phaseout='all'):
"""
Generate a group of synthetic seismograms for a grid of sources.
Used to simulate phase \
arrivals from a grid of known sources in a three-dimensional model. Lags \
must be known and supplied, these can be generated from the bright_lights \
function: read_tt, and resampled to fit the desired grid dimensions and \
spacing using other functions therein. These synthetic seismograms are \
very simple models of seismograms using the seis_sim function herein. \
These approximate body-wave P and S first arrivals as spikes convolved \
with damped sine waves.
:type stations: list
:param stations: List of the station names
:type nodes: list
:param nodes: List of node locations in (lon,lat,depth)
:type travel_times: numpy.ndarray
:param travel_times: Array of travel times where travel_times[i][:] \
refers to the travel times for station=stations[i], and \
travel_times[i][j] refers to stations[i] for nodes[j]
:type phase: str
:param phase: Can be either 'P' or 'S'
:type PS_ratio: float
:param PS_ratio: P/S velocity ratio, defaults to 1.68
:type samp_rate: float
:param samp_rate: Desired sample rate in Hz, defaults to 100.0
:type flength: int
:param flength: Length of template in samples, defaults to False
:type phaseout: str
:param phaseout: Either 'S', 'P', 'all' or 'both', determines which \
phases to clip around. 'all' Encompasses both phases in one channel, \
but will return nothing if the flength is not long enough, 'both' \
will return two channels for each stations, one SYN_Z with the \
synthetic P-phase, and one SYN_H with the synthetic S-phase.
:returns: List of :class: obspy.core.stream.Stream
"""
import warnings
if phase not in ['S', 'P']:
raise IOError('Phase is neither P nor S')
from obspy import Stream, Trace
# Initialize empty list for templates
templates = []
# Loop through the nodes, for every node generate a template!
for i, node in enumerate(nodes):
st = [] # Empty list to be filled with synthetics
# Loop through stations
for j, station in enumerate(stations):
tr = Trace()
tr.stats.sampling_rate = samp_rate
tr.stats.station = station
tr.stats.channel = 'SYN'
tt = travel_times[j][i]
if phase == 'P':
# If the input travel-time is the P-wave travel-time
SP_time = (tt * PS_ratio) - tt
if phaseout == 'S':
tr.stats.starttime += tt + SP_time
else:
tr.stats.starttime += tt
elif phase == 'S':
# If the input travel-time is the S-wave travel-time
SP_time = tt - (tt / PS_ratio)
if phaseout == 'S':
tr.stats.starttime += tt
else:
tr.stats.starttime += tt - SP_time
else:
raise IOError('Input grid is not P or S')
# Set start-time of trace to be travel-time for P-wave
# Check that the template length is long enough to include the SP
if flength and SP_time * samp_rate < flength - 11 \
and phaseout == 'all':
tr.data = seis_sim(SP=int(SP_time * samp_rate), amp_ratio=1.5,
flength=flength, phaseout=phaseout)
st.append(tr)
elif flength and phaseout == 'all':
warnings.warn('Cannot make a bulk synthetic with this fixed ' +
'length for station ' + station)
elif phaseout == 'all':
tr.data = seis_sim(SP=int(SP_time * samp_rate), amp_ratio=1.5,
flength=flength, phaseout=phaseout)
st.append(tr)
elif phaseout in ['P', 'S']:
tr.data = seis_sim(SP=int(SP_time * samp_rate), amp_ratio=1.5,
flength=flength, phaseout=phaseout)
st.append(tr)
elif phaseout == 'both':
for _phaseout in ['P', 'S']:
_tr = tr.copy()
_tr.data = seis_sim(SP=int(SP_time * samp_rate),
amp_ratio=1.5, flength=flength,
phaseout=_phaseout)
if _phaseout == 'P':
_tr.stats.channel = 'SYN_Z'
# starttime defaults to S-time
_tr.stats.starttime = _tr.stats.starttime - SP_time
elif _phaseout == 'S':
_tr.stats.channel = 'SYN_H'
st.append(_tr)
templates.append(Stream(st))
# Stream(st).plot(size=(800,600))
return templates
[docs]def generate_synth_data(nsta=5, ntemplates=3, nseeds=100, samp_rate=20.0,
t_length=3.0, max_amp=10.0, max_lag=20, debug=0):
"""
Generate a synthetic dataset to be used for testing.
This will generate both templates and data to scan through.
Templates will be generated using the utils.synth_seis functions.
The day of data will be random noise, with random signal-to-noise
ratio copies of the templates randomly seeded throughout the day.
It also returns the seed times and signal-to-noise ratios used.
:type nsta: int
:param nsta: Number of stations to generate data for < 15.
:type ntemplates: int
:param ntemplates: Number of templates to generate, will be generated \
with random arrival times.
:type nseeds: int
:param nseeds: Number of copies of the template to seed within the \
day of noisy data for each template.
:type samp_rate: float
:param samp_rate: Sampling rate to use in Hz
:type t_length: float
:param t_length: Length of templates in seconds.
:type max_amp: float
:param max_amp: Maximum signal-to-noise ratio of seeds.
:type max_lag: Maximum lag time in seconds (randomised).
:param max_lag: float
:type debug: int
:param debug: Debug level, bigger the number, the more plotting/output.
:returns: Templates: List of obspy.Stream, Data: obspy.Stream of \
seeded noisy data, Seeds: dictionary of seed SNR and time with \
time in samples.
"""
from eqcorrscan.utils import synth_seis
import numpy as np
from obspy import UTCDateTime
# Generate random arrival times
t_times = np.abs(np.random.random([nsta, ntemplates])) * max_lag
# Generate random node locations - these do not matter as they are only
# used for naming
lats = np.random.random(ntemplates) * 90.0
lons = np.random.random(ntemplates) * 90.0
depths = np.abs(np.random.random(ntemplates) * 40.0)
nodes = zip(lats, lons, depths)
# Generating a 5x3 array to make 3 templates
stations = ['ALPH', 'BETA', 'GAMM', 'KAPP', 'ZETA', 'BOB', 'MAGG',
'ALF', 'WALR', 'ALBA', 'PENG', 'BANA', 'WIGG', 'SAUS',
'MALC']
if debug > 1:
print(nodes)
print(t_times)
print(stations[0:nsta])
templates = synth_seis.template_grid(stations=stations[0:nsta],
nodes=nodes,
travel_times=t_times, phase='S',
samp_rate=samp_rate,
flength=int(t_length * samp_rate))
if debug > 2:
for template in templates:
print(template)
template.plot(size=(800, 600), equal_scale=False)
# Now we want to create a day of synthetic data
seeds = []
data = templates[0].copy() # Copy a template to get the correct length
# and stats for data, we will overwrite the data on this copy
for tr in data:
tr.data = np.zeros(86400 * int(samp_rate))
# Set all the traces to have a day of zeros
tr.stats.starttime = UTCDateTime(0)
for i, template in enumerate(templates):
impulses = np.zeros(86400 * int(samp_rate))
# Generate a series of impulses for seeding
# Need three seperate impulse traces for each of the three templates,
# all will be convolved within the data though.
impulse_times = np.random.randint(86400 * int(samp_rate),
size=nseeds)
impulse_amplitudes = np.random.randn(nseeds) * max_amp
# Generate amplitudes up to maximum amplitude in a normal distribution
seeds.append({'SNR': impulse_amplitudes,
'time': impulse_times})
for j in range(nseeds):
impulses[impulse_times[j]] = impulse_amplitudes[j]
# We now have one vector of impulses, we need nsta numbers of them,
# shifted with the appropriate lags
mintime = min([template_tr.stats.starttime
for template_tr in template])
for j, template_tr in enumerate(template):
offset = int((template_tr.stats.starttime - mintime) * samp_rate)
pad = np.zeros(offset)
tr_impulses = np.append(pad, impulses)[0:len(impulses)]
# Convolve this with the template trace to give the daylong seeds
data[j].data += np.convolve(tr_impulses,
template_tr.data)[0:len(impulses)]
if debug > 2:
data.plot(starttime=UTCDateTime(0) +
impulse_times[0] / samp_rate - 3,
endtime=UTCDateTime(0) +
impulse_times[0] / samp_rate + 15)
# Add the noise
for tr in data:
noise = np.random.randn(86400 * int(samp_rate))
tr.data += noise / max(noise)
if debug > 2:
tr.plot()
return templates, data, seeds
if __name__ == "__main__":
import doctest
doctest.testmod()