def spectralWhitening(data, sr=None, smoothi=None, freq_domain=False, apply_filter=None):
"""
Apply spectral whitening to data.
sr: sampling rate (only needed for smoothing)
smoothi: None or int
Data is divided by its smoothed (Default: None) amplitude spectrum.
"""
if freq_domain:
mask = False
spec = data
else:
mask = np.ma.getmask(data)
N = len(data)
nfft = nextpow2(N)
spec = fft(data, nfft)
#df = sr/N
spec_ampl = np.sqrt(np.abs(np.multiply(spec, np.conjugate(spec))))
if isinstance(smoothi, basestring) and isnumber(smoothi) and smoothi > 0:
smoothi = int(smoothi * N / sr)
spec /= ifftshift(smooth(fftshift(spec_ampl), smoothi))
else:
spec /= spec_ampl
if apply_filter is not None:
spec *= filterResp(*apply_filter, sr=sr, N=len(spec), whole=True)[1]
if freq_domain:
return spec
else:
ret = np.real(ifft(spec, nfft)[:N])
if USE_FFTW3:
ret = ret.copy()
return fillArray(ret, mask=mask, fill_value=0.)
def spectralWhitening(data,
sr=None,
smoothi=None,
freq_domain=False,
apply_filter=None):
"""
Apply spectral whitening to data.
sr: sampling rate (only needed for smoothing)
smoothi: None or int
Data is divided by its smoothed (Default: None) amplitude spectrum.
"""
if freq_domain:
mask = False
spec = data
else:
mask = np.ma.getmask(data)
N = len(data)
nfft = nextpow2(N)
spec = fft(data, nfft)
#df = sr/N
spec_ampl = np.sqrt(np.abs(np.multiply(spec, np.conjugate(spec))))
if isinstance(smoothi, basestring) and isnumber(smoothi) and smoothi > 0:
smoothi = int(smoothi * N / sr)
spec /= ifftshift(smooth(fftshift(spec_ampl), smoothi))
else:
spec /= spec_ampl
if apply_filter is not None:
spec *= filterResp(*apply_filter, sr=sr, N=len(spec), whole=True)[1]
if freq_domain:
return spec
else:
ret = np.real(ifft(spec, nfft)[:N])
if USE_FFTW3:
ret = ret.copy()
return fillArray(ret, mask=mask, fill_value=0.)
def timeNorm(data, method=None, param=None, recursive=0):
"""
Calculates normalized data. See Bensen et al.(2007)
Method is a string. There are the following methods:
1bit: reduce data to +1 if >0 and -1 if <0
clip: clip data to the root mean square (rms)
eventremoval: automatic event detection and removal - if an value is bigger
than the threshold, the following values are set to zero.
param: (threshold, number of samples (eg. 30min) to set to zero)
stalta: automatic event removing with recursive sta/lta trigger
runningmean: the data is normalized with the running average
The width of the normalization window determines how much amplitude
information is retained (N=1 -> 1bit normalization, N very big ->
rescaled data). Half of the maximum period of the passband filter_ works
well.
param: width of window (should be odd)
runningmean_over_filtered: the data is normalized with the running average
over the filtered data.
A band pass filter_ between 20s and 100s period can remove local
seismicity.
param: (width of window in seconds, sampling rate, filter_, freq1, freq2)
filter_: in ('band', 'low', high')
if filter_ in ('low', 'high') only on frequency is needed
waterlevel: any amplitude above the waterlevel (multiple of rms) is
down-weighted by a factor. This procedure is repeated all of the
waveform data is under the water-level
param: (water-level factor, reducing factor)
"""
mask = np.ma.getmask(data)
if method == '1bit':
data = np.sign(data)
elif method == 'clip':
std = np.std(data)
data[data > std] = std
data[data < -std] = -std
elif method == 'eventremoval':
if param == None:
# remove 30 min (at 10Hz) after events if data is bigger than 2000
param = (2000, 30 * 60 * 10)
clip = np.nonzero(abs(data) >= param[0])[0]
if len(clip) > 0:
clip = clip[0]
index = min(clip + param[1], len(data))
data[clip:index] = 0
if index < len(data):
data[index:] = timeNorm(data[index:],
method=method,
param=param)
elif method == 'stalta':
if param is None:
# STA: 3s at 100Hz, LTA: 10s, trigger on: 1.2, trigger off:1.0
param = (100 * 3, 100 * 10, 1.2, 1.0)
cft = obspy.signal.trigger.recSTALTA(data, param[0], param[1])
trg = obspy.signal.trigger.triggerOnset(cft, param[2], param[3])
for on, off in trg:
data[on:off] = 0
elif method == 'runningmean':
if param == None:
# smooth over 20s at 10Hz
param = 10 * 10
smoothed = smooth(np.abs(data), param)
data /= smoothed
elif method == 'runningmean_over_filtered':
if param is None:
# smooth over 20s at 10Hz over bandpassed data
param = (10, 10, 'band', 1 / 50., 1 / 15.)
sr = param[1]
over = int(param[0] * sr)
filter_ = param[2]
if filter_ == 'band':
data2 = obspy.signal.bandpass(data, param[3], param[4], sr)
elif filter_ == 'low':
data2 = obspy.signal.lowpass(data, param[3], sr)
elif filter_ == 'high':
data2 = obspy.signal.highpass(data, param[3], sr)
else:
raise ValueError("filter_ should be in ('band', 'high', 'low')")
data /= smooth(np.abs(data2), over)
elif method == 'waterlevel':
if param == None:
# data above 6*rms is recursively reduced by a factor of 10
param = (6., 10.)
waterlevel = param[0] * np.std(data)
indices = np.abs(data) > waterlevel
if np.any(indices):
if param[1] == 0:
data[indices] = 0
else:
data[indices] /= param[1]
data = timeNorm(data,
method=method,
param=param,
recursive=recursive + 1)
elif method == 'waterlevel_rm':
if param == None:
# running mean over 5s at 10Hz data
# data above 4*rms is recursively reduced by a factor of 10
param = (5 * 10, 4., 10.)
running_mean = smooth(np.abs(data), param[0])
waterlevel = param[1] * np.std(running_mean)
indices = (running_mean > waterlevel) + (np.abs(data) > waterlevel)
if np.any(indices):
param = list(param)
frac_zeros = 1. * np.count_nonzero(indices) / len(data)
if param[2] == 0:
data[indices] = 0
param[1] *= (1 + frac_zeros)
else:
data[indices] /= param[2]
param[1] *= (1 + frac_zeros * (1 - 1 / param[2]))
print recursive, frac_zeros, waterlevel
data = timeNorm(data,
method=method,
param=param,
recursive=recursive + 1)
elif method == 'waterlevel_env':
if param == None:
# data above 4*rms is recursively reduced by a factor of 10
param = (4., 10.)
param = list(param)
if len(param) == 2:
param.append(0)
param.append(0)
env = obspy.signal.cpxtrace.envelope(data)[1][:len(data)]
# correct std because of zeros
waterlevel = param[0] * np.std(env) / (1 - param[2])
# import pylab as plt
# from imaging import plotTrace
# from sito import Trace
# trace = Trace(data=data)
# trace2 = Trace(data=env)
# plotTrace(trace)
# plotTrace(trace2)
# plt.figure()
# plt.plot(data)
# plt.plot(env)
# plt.hlines(waterlevel, 0, len(data))
# plt.show()
indices = env > waterlevel
frac_zeros = 1. * np.count_nonzero(indices) / len(data)
if np.any(indices) and frac_zeros > 0.0005 and param[3] < 20:
if param[1] == 0:
data[indices] = 0
#param[0] *= (1 + frac_zeros)
else:
data[indices] /= param[2]
#param[0] *= (1 + frac_zeros * (1 - 1 / param[1]))
print param[3], frac_zeros, param[2], waterlevel
param[2] += frac_zeros
param[3] += 1
data = timeNorm(data, method=method, param=param)
elif method == 'waterlevel_env2':
if param == None:
# data above 4*rms is recursively reduced by a factor of 10
param = (4., 10.)
N = len(data)
env = obspy.signal.cpxtrace.envelope(data)[1][:N]
if mask is not False:
env[mask] = 0.
num_stds = 96 # 24*4 =^ every 15min
if N < 86400: # 24*3600
num_stds = N // 900
len_parts = N // num_stds # N//96 = N//24//4 =^ 15min
len_stds = len_parts // 15 # len_parts//15 =^ 1min
stds = np.array([
np.std(env[i:i + len_stds])
for i in np.arange(num_stds) * len_parts
])
if np.min(stds) == 0:
stds = stds[stds != 0.]
num_stds = len(stds)
stds = np.sort(stds)[num_stds // 15:-num_stds // 15]
stds = stds[stds < np.min(stds) * 2.]
waterlevel = param[0] * np.mean(stds)
# import pylab as plt
# from imaging import plotTrace
# from sito import Trace
# trace = Trace(data=data)
# trace2 = Trace(data=env)
# plotTrace(trace)
# plotTrace(trace2)
# plt.figure()
# plt.plot(data)
# plt.plot(env)
# plt.hlines(waterlevel, 0, len(data))
# plt.show()
indices = env > waterlevel
#frac_zeros = 1. * np.count_nonzero(indices) / len(data)
if np.any(indices):
if param[1] == 0:
# not setting values to zero but masking them
# -> they will stay zero after spectral whitening
# and 1bit normalization
mask = np.ma.mask_or(mask, indices)
#data[indices] = 0
else:
data[indices] /= param[2]
elif method is not None:
raise ValueError('The method passed to timeNorm() is not known.')
return fillArray(data, mask=mask, fill_value=0.)
def plotPSD(self,
ax=None,
x_time=True,
scale_by_freq=True,
Nfft=256 * 16 * 16,
pad_to=None,
xscale='log',
yscale='log',
grid=True,
xlabel='time (s)',
ylabel=None,
figtitle='PSD station component date',
title_in_axis=False,
smooth=True,
just_calculate=False,
**kwargs):
"""
Plot PSD of first trace.
Doc matplotlib.mlab.psd:
"""
if self.stats.is_fft:
pxx = self.data
if 'freq_min' in self.stats:
freqs = np.linspace(self.stats.freq_min, self.stats.freq_max,
self.stats.npts)
else:
freqs = self.fftfreq()
else:
pxx, freqs = psd(self.data,
NFFT=Nfft,
Fs=self.stats.sampling_rate,
scale_by_freq=scale_by_freq,
pad_to=pad_to)
if just_calculate:
return pxx, freqs
if x_time:
pxx = pxx[::-1]
freqs = 1. / freqs[::-1]
elif 'time' in xlabel:
xlabel = 'freq (Hz)'
if smooth:
pxx = util.smooth(pxx, smooth)
if ax is None:
fig = plt.figure()
ax = fig.add_subplot(111)
else:
fig = ax.get_figure()
# ## print title
if figtitle is not None:
figtitle = figtitle.replace('station', self.stats.station)
figtitle = figtitle.replace('component', self.stats.channel[-1])
try:
starttime = self.stats.starttime + 0.5
figtitle = figtitle.replace('time', '%s' % starttime)
figtitle = figtitle.replace('date', '%s' % starttime.date)
figtitle = figtitle.replace('year', '%d' % starttime.year)
figtitle = figtitle.replace('nfft', '%d' % Nfft)
except:
pass
if not title_in_axis:
fig.suptitle(figtitle, x=0.5, horizontalalignment='center')
# fig.text(title, 0., 0.95, horizontalalignment = 'left' )
else:
ax.text(0.1,
1,
figtitle,
verticalalignment='top',
transform=ax.transAxes)
if xlabel is not None:
ax.set_xlabel(xlabel)
if ylabel is not None:
ax.set_ylabel(ylabel)
ax.set_xscale(xscale)
ax.set_yscale(yscale)
ax.grid(grid)
ax.plot(freqs, pxx, **kwargs)
return ax
def plotPSD(self, ax=None, x_time=True, scale_by_freq=True, Nfft=256 * 16 * 16,
pad_to=None,
xscale='log', yscale='log', grid=True,
xlabel='time (s)', ylabel=None,
figtitle='PSD station component date',
title_in_axis=False, smooth=True,
just_calculate=False, ** kwargs):
"""
Plot PSD of first trace.
Doc matplotlib.mlab.psd:
"""
if self.stats.is_fft:
pxx = self.data
if 'freq_min' in self.stats:
freqs = np.linspace(self.stats.freq_min, self.stats.freq_max, self.stats.npts)
else:
freqs = self.fftfreq()
else:
pxx, freqs = psd(self.data, NFFT=Nfft, Fs=self.stats.sampling_rate,
scale_by_freq=scale_by_freq, pad_to=pad_to)
if just_calculate:
return pxx, freqs
if x_time:
pxx = pxx[::-1]
freqs = 1. / freqs[::-1]
elif 'time' in xlabel:
xlabel = 'freq (Hz)'
if smooth:
pxx = util.smooth(pxx, smooth)
if ax is None:
fig = plt.figure()
ax = fig.add_subplot(111)
else:
fig = ax.get_figure()
# ## print title
if figtitle is not None:
figtitle = figtitle.replace('station', self.stats.station)
figtitle = figtitle.replace('component', self.stats.channel[-1])
try:
starttime = self.stats.starttime + 0.5
figtitle = figtitle.replace('time', '%s' % starttime)
figtitle = figtitle.replace('date', '%s' % starttime.date)
figtitle = figtitle.replace('year', '%d' % starttime.year)
figtitle = figtitle.replace('nfft', '%d' % Nfft)
except:
pass
if not title_in_axis:
fig.suptitle(figtitle, x=0.5,
horizontalalignment='center')
# fig.text(title, 0., 0.95, horizontalalignment = 'left' )
else:
ax.text(0.1, 1, figtitle, verticalalignment='top',
transform=ax.transAxes)
if xlabel is not None:
ax.set_xlabel(xlabel)
if ylabel is not None:
ax.set_ylabel(ylabel)
ax.set_xscale(xscale)
ax.set_yscale(yscale)
ax.grid(grid)
ax.plot(freqs, pxx, **kwargs)
return ax
def timeNorm(data, method=None, param=None, recursive=0):
"""
Calculates normalized data. See Bensen et al.(2007)
Method is a string. There are the following methods:
1bit: reduce data to +1 if >0 and -1 if <0
clip: clip data to the root mean square (rms)
eventremoval: automatic event detection and removal - if an value is bigger
than the threshold, the following values are set to zero.
param: (threshold, number of samples (eg. 30min) to set to zero)
stalta: automatic event removing with recursive sta/lta trigger
runningmean: the data is normalized with the running average
The width of the normalization window determines how much amplitude
information is retained (N=1 -> 1bit normalization, N very big ->
rescaled data). Half of the maximum period of the passband filter_ works
well.
param: width of window (should be odd)
runningmean_over_filtered: the data is normalized with the running average
over the filtered data.
A band pass filter_ between 20s and 100s period can remove local
seismicity.
param: (width of window in seconds, sampling rate, filter_, freq1, freq2)
filter_: in ('band', 'low', high')
if filter_ in ('low', 'high') only on frequency is needed
waterlevel: any amplitude above the waterlevel (multiple of rms) is
down-weighted by a factor. This procedure is repeated all of the
waveform data is under the water-level
param: (water-level factor, reducing factor)
"""
mask = np.ma.getmask(data)
if method == '1bit':
data = np.sign(data)
elif method == 'clip':
std = np.std(data)
data[data > std] = std
data[data < -std] = -std
elif method == 'eventremoval':
if param == None:
# remove 30 min (at 10Hz) after events if data is bigger than 2000
param = (2000, 30 * 60 * 10)
clip = np.nonzero(abs(data) >= param[0])[0]
if len(clip) > 0:
clip = clip[0]
index = min(clip + param[1], len(data))
data[clip:index] = 0
if index < len(data):
data[index:] = timeNorm(data[index:], method=method, param=param)
elif method == 'stalta':
if param is None:
# STA: 3s at 100Hz, LTA: 10s, trigger on: 1.2, trigger off:1.0
param = (100 * 3, 100 * 10, 1.2, 1.0)
cft = obspy.signal.trigger.recSTALTA(data, param[0], param[1])
trg = obspy.signal.trigger.triggerOnset(cft, param[2], param[3])
for on, off in trg:
data[on:off] = 0
elif method == 'runningmean':
if param == None:
# smooth over 20s at 10Hz
param = 10 * 10
smoothed = smooth(np.abs(data), param)
data /= smoothed
elif method == 'runningmean_over_filtered':
if param is None:
# smooth over 20s at 10Hz over bandpassed data
param = (10, 10, 'band', 1 / 50., 1 / 15.)
sr = param[1]
over = int(param[0] * sr)
filter_ = param[2]
if filter_ == 'band':
data2 = obspy.signal.bandpass(data, param[3], param[4], sr)
elif filter_ == 'low':
data2 = obspy.signal.lowpass(data, param[3], sr)
elif filter_ == 'high':
data2 = obspy.signal.highpass(data, param[3], sr)
else:
raise ValueError("filter_ should be in ('band', 'high', 'low')")
data /= smooth(np.abs(data2), over)
elif method == 'waterlevel':
if param == None:
# data above 6*rms is recursively reduced by a factor of 10
param = (6., 10.)
waterlevel = param[0] * np.std(data)
indices = np.abs(data) > waterlevel
if np.any(indices):
if param[1] == 0:
data[indices] = 0
else:
data[indices] /= param[1]
data = timeNorm(data, method=method, param=param, recursive=recursive + 1)
elif method == 'waterlevel_rm':
if param == None:
# running mean over 5s at 10Hz data
# data above 4*rms is recursively reduced by a factor of 10
param = (5 * 10, 4., 10.)
running_mean = smooth(np.abs(data), param[0])
waterlevel = param[1] * np.std(running_mean)
indices = (running_mean > waterlevel) + (np.abs(data) > waterlevel)
if np.any(indices):
param = list(param)
frac_zeros = 1. * np.count_nonzero(indices) / len(data)
if param[2] == 0:
data[indices] = 0
param[1] *= (1 + frac_zeros)
else:
data[indices] /= param[2]
param[1] *= (1 + frac_zeros * (1 - 1 / param[2]))
print recursive, frac_zeros, waterlevel
data = timeNorm(data, method=method, param=param, recursive=recursive + 1)
elif method == 'waterlevel_env':
if param == None:
# data above 4*rms is recursively reduced by a factor of 10
param = (4., 10.)
param = list(param)
if len(param) == 2:
param.append(0)
param.append(0)
env = obspy.signal.cpxtrace.envelope(data)[1][:len(data)]
# correct std because of zeros
waterlevel = param[0] * np.std(env) / (1 - param[2])
# import pylab as plt
# from imaging import plotTrace
# from sito import Trace
# trace = Trace(data=data)
# trace2 = Trace(data=env)
# plotTrace(trace)
# plotTrace(trace2)
# plt.figure()
# plt.plot(data)
# plt.plot(env)
# plt.hlines(waterlevel, 0, len(data))
# plt.show()
indices = env > waterlevel
frac_zeros = 1. * np.count_nonzero(indices) / len(data)
if np.any(indices) and frac_zeros > 0.0005 and param[3] < 20:
if param[1] == 0:
data[indices] = 0
#param[0] *= (1 + frac_zeros)
else:
data[indices] /= param[2]
#param[0] *= (1 + frac_zeros * (1 - 1 / param[1]))
print param[3], frac_zeros, param[2], waterlevel
param[2] += frac_zeros
param[3] += 1
data = timeNorm(data, method=method, param=param)
elif method == 'waterlevel_env2':
if param == None:
# data above 4*rms is recursively reduced by a factor of 10
param = (4., 10.)
N = len(data)
env = obspy.signal.cpxtrace.envelope(data)[1][:N]
if mask is not False:
env[mask] = 0.
num_stds = 96 # 24*4 =^ every 15min
if N < 86400: # 24*3600
num_stds = N // 900
len_parts = N // num_stds # N//96 = N//24//4 =^ 15min
len_stds = len_parts // 15 # len_parts//15 =^ 1min
stds = np.array([np.std(env[i:i + len_stds]) for i in np.arange(num_stds) * len_parts])
if np.min(stds) == 0:
stds = stds[stds != 0.]
num_stds = len(stds)
stds = np.sort(stds)[num_stds // 15:-num_stds // 15]
stds = stds[stds < np.min(stds) * 2.]
waterlevel = param[0] * np.mean(stds)
# import pylab as plt
# from imaging import plotTrace
# from sito import Trace
# trace = Trace(data=data)
# trace2 = Trace(data=env)
# plotTrace(trace)
# plotTrace(trace2)
# plt.figure()
# plt.plot(data)
# plt.plot(env)
# plt.hlines(waterlevel, 0, len(data))
# plt.show()
indices = env > waterlevel
#frac_zeros = 1. * np.count_nonzero(indices) / len(data)
if np.any(indices):
if param[1] == 0:
# not setting values to zero but masking them
# -> they will stay zero after spectral whitening
# and 1bit normalization
mask = np.ma.mask_or(mask, indices)
#data[indices] = 0
else:
data[indices] /= param[2]
elif method is not None:
raise ValueError('The method passed to timeNorm() is not known.')
return fillArray(data, mask=mask, fill_value=0.)
