import numpy as np
from obspy.core import Trace, UTCDateTime
x = np.zeros(200)
x[100] = 1
tr = Trace(x)
tr.stats.network = "XX"
tr.stats.station = "SDFD1"
print tr
print "showing original trace"
tr.plot()
tr.stats.sampling_rate = 20
tr.stats.starttime = UTCDateTime(2011, 2, 21, 8)
print tr
tr.plot()
tr.filter("lowpass", freq=1)
print "showing filtered trace"
tr.plot()
tr.trim(tr.stats.starttime + 4.5, tr.stats.endtime - 2)
print "showing trimmed trace"
tr.plot()
tr.data = tr.data * 500
tr2 = tr.copy()
tr2.data = tr2.data + np.random.randn(len(tr2))
tr2.stats.station = "SDFD2"
print tr2
print "showing trace with gaussian noise added"
tr2.plot()
def nowhiten(data, Nfft, delta, freqmin, freqmax, plot=False):
"""This function takes 1-dimensional *data* timeseries array
and returns the fft between *freqmin* and *freqmax*.
:type data: :class:`numpy.ndarray`
:param data: Contains the 1D time series to whiten
:type Nfft: int
:para Nfft: The number of points to compute the FFT
:type delta: float
:param delta: The sampling frequency of the `data`
:type freqmin: float
:param freqmin: The lower frequency bound
:type freqmax: float
:param freqmax: The upper frequency bound
:type plot: bool
:param plot: Whether to show a raw plot of the action (default: False)
:rtype: :class:`numpy.ndarray`
:returns: The FFT of the input trace between the frequency bounds
"""
if plot:
plt.subplot(211)
plt.plot(np.arange(len(data)) * delta, data)
plt.xlim(0, len(data) * delta)
plt.title('Input trace')
stats = {'sampling_rate': 20.}
trdata=Trace(data, header=stats)
# Napod = 100
# Nfft = int(Nfft)
# freqVec = scipy.fftpack.fftfreq(Nfft,d=delta)[:Nfft/2]
#
# J = np.where((freqVec >= freqmin) & (freqVec <= freqmax))[0]
# low = J[0] - Napod
# if low <= 0:
# low = 1
#
# porte1 = J[0]
# porte2 = J[-1]
# high = J[-1] + Napod
# if high > Nfft / 2:
# high = Nfft // 2
trdata.filter("bandpass",freqmin=freqmin,freqmax=freqmax,zerophase=True)
FFTRawSign = scipy.fftpack.fft(trdata, Nfft)
if plot:
plt.subplot(212)
axis = np.arange(len(FFTRawSign))
plt.plot(axis[1:], np.abs(FFTRawSign[1:]))
plt.xlim(0, max(axis))
plt.title('FFTRawSign')
# # Left tapering:
# FFTRawSign[0:low] *= 0
# FFTRawSign[low:porte1] = np.cos(np.linspace(np.pi / 2., np.pi, porte1 - low)) ** 2 * FFTRawSign[low:porte1]
# # Pass band:
# FFTRawSign[porte1:porte2] = FFTRawSign[porte1:porte2]
# # Right tapering:
# FFTRawSign[porte2:high] = np.cos(np.linspace(0., np.pi / 2., high - porte2)) ** 2 * FFTRawSign[porte2:high]
# FFTRawSign[high:Nfft+1] *= 0
# Hermitian symmetry (because the input is real)
#FFTRawSign[-Nfft/2+1:] = FFTRawSign[1:Nfft/2].conjugate()[::-1]
# if plot:
# plt.subplot(413)
# axis = np.arange(len(FFTRawSign))
# plt.axvline(low, c='g')
# plt.axvline(porte1, c='g')
# plt.axvline(porte2, c='r')
# plt.axvline(high, c='r')
#
# plt.axvline(Nfft - high, c='r')
# plt.axvline(Nfft - porte2, c='r')
# plt.axvline(Nfft - porte1, c='g')
# plt.axvline(Nfft - low, c='g')
#
# plt.plot(axis, np.abs(FFTRawSign))
# plt.xlim(0, max(axis))
#
# wdata = np.real(scipy.fftpack.ifft(FFTRawSign))
# plt.subplot(414)
# plt.plot(np.arange(len(wdata)) * delta, wdata)
# plt.xlim(0, len(wdata) * delta)
# plt.show()
return FFTRawSign
def test_sonic(self):
# for i in xrange(100):
np.random.seed(2348)
geometry = np.array([[0.0, 0.0, 0.0],
[-5.0, 7.0, 0.0],
[5.0, 7.0, 0.0],
[10.0, 0.0, 0.0],
[5.0, -7.0, 0.0],
[-5.0, -7.0, 0.0],
[-10.0, 0.0, 0.0]])
geometry /= 100 # in km
slowness = 1.3 # in s/km
baz_degree = 20.0 # 0.0 > source in x direction
baz = baz_degree * np.pi / 180.
df = 100 # samplerate
# SNR = 100. # signal to noise ratio
amp = .00001 # amplitude of coherent wave
length = 500 # signal length in samples
coherent_wave = amp * np.random.randn(length)
# time offsets in samples
dt = df * slowness * (np.cos(baz) * geometry[:, 1] + np.sin(baz) *
geometry[:, 0])
dt = np.round(dt)
dt = dt.astype('int32')
max_dt = np.max(dt) + 1
min_dt = np.min(dt) - 1
trl = list()
for i in xrange(len(geometry)):
tr = Trace(coherent_wave[-min_dt + dt[i]:-max_dt + dt[i]].copy())
# + amp / SNR * \
# np.random.randn(length - abs(min_dt) - abs(max_dt)))
tr.stats.sampling_rate = df
tr.stats.coordinates = AttribDict()
tr.stats.coordinates.x = geometry[i, 0]
tr.stats.coordinates.y = geometry[i, 1]
tr.stats.coordinates.elevation = geometry[i, 2]
# lowpass random signal to f_nyquist / 2
tr.filter("lowpass", freq=df / 4.)
trl.append(tr)
st = Stream(trl)
stime = UTCDateTime(1970, 1, 1, 0, 0)
etime = UTCDateTime(1970, 1, 1, 0, 0) + \
(length - abs(min_dt) - abs(max_dt)) / df
win_len = 2.
step_frac = 0.2
sll_x = -3.0
slm_x = 3.0
sll_y = -3.0
slm_y = 3.0
sl_s = 0.1
frqlow = 1.0
frqhigh = 8.0
prewhiten = 0
semb_thres = -1e99
vel_thres = -1e99
# out returns: rel. power, abs. power, backazimuth, slowness
out = sonic(st, win_len, step_frac, sll_x, slm_x, sll_y, slm_y, sl_s,
semb_thres, vel_thres, frqlow, frqhigh, stime, etime,
prewhiten, coordsys='xy', verbose=False)
# returns baz
np.testing.assert_almost_equal(out[:, 3].mean(), 18.434948822922024)
# slowness ~= 1.3
np.testing.assert_almost_equal(out[:, 4].mean(), 1.26491106407)
def nowhiten(data, Nfft, delta, freqmin, freqmax, plot=False):
"""This function takes 1-dimensional *data* timeseries array
and returns the fft between *freqmin* and *freqmax*.
:type data: :class:`numpy.ndarray`
:param data: Contains the 1D time series to whiten
:type Nfft: int
:para Nfft: The number of points to compute the FFT
:type delta: float
:param delta: The sampling frequency of the `data`
:type freqmin: float
:param freqmin: The lower frequency bound
:type freqmax: float
:param freqmax: The upper frequency bound
:type plot: bool
:param plot: Whether to show a raw plot of the action (default: False)
:rtype: :class:`numpy.ndarray`
:returns: The FFT of the input trace between the frequency bounds
"""
if plot:
plt.subplot(211)
plt.plot(np.arange(len(data)) * delta, data)
plt.xlim(0, len(data) * delta)
plt.title('Input trace')
stats = {'sampling_rate': 20.}
trdata = Trace(data, header=stats)
# Napod = 100
# Nfft = int(Nfft)
# freqVec = scipy.fftpack.fftfreq(Nfft,d=delta)[:Nfft/2]
#
# J = np.where((freqVec >= freqmin) & (freqVec <= freqmax))[0]
# low = J[0] - Napod
# if low <= 0:
# low = 1
#
# porte1 = J[0]
# porte2 = J[-1]
# high = J[-1] + Napod
# if high > Nfft / 2:
# high = Nfft // 2
trdata.filter("bandpass",
freqmin=freqmin,
freqmax=freqmax,
corners=4,
zerophase=True)
#Raph FFTRawSign = scipy.fftpack.fft(trdata, Nfft)
if plot:
plt.subplot(212)
axis = np.arange(len(FFTRawSign))
plt.plot(axis[1:], np.abs(FFTRawSign[1:]))
plt.xlim(0, max(axis))
plt.title('FFTRawSign')
# # Left tapering:
# FFTRawSign[0:low] *= 0
# FFTRawSign[low:porte1] = np.cos(np.linspace(np.pi / 2., np.pi, porte1 - low)) ** 2 * FFTRawSign[low:porte1]
# # Pass band:
# FFTRawSign[porte1:porte2] = FFTRawSign[porte1:porte2]
# # Right tapering:
# FFTRawSign[porte2:high] = np.cos(np.linspace(0., np.pi / 2., high - porte2)) ** 2 * FFTRawSign[porte2:high]
# FFTRawSign[high:Nfft+1] *= 0
# Hermitian symmetry (because the input is real)
#FFTRawSign[-Nfft/2+1:] = FFTRawSign[1:Nfft/2].conjugate()[::-1]
# if plot:
# plt.subplot(413)
# axis = np.arange(len(FFTRawSign))
# plt.axvline(low, c='g')
# plt.axvline(porte1, c='g')
# plt.axvline(porte2, c='r')
# plt.axvline(high, c='r')
#
# plt.axvline(Nfft - high, c='r')
# plt.axvline(Nfft - porte2, c='r')
# plt.axvline(Nfft - porte1, c='g')
# plt.axvline(Nfft - low, c='g')
#
# plt.plot(axis, np.abs(FFTRawSign))
# plt.xlim(0, max(axis))
#
# wdata = np.real(scipy.fftpack.ifft(FFTRawSign))
# plt.subplot(414)
# plt.plot(np.arange(len(wdata)) * delta, wdata)
# plt.xlim(0, len(wdata) * delta)
# plt.show()
#Raph return FFTRawSign
return trdata
def test_sonic(self):
# for i in xrange(100):
np.random.seed(2348)
geometry = np.array(
[
[0.0, 0.0, 0.0],
[-5.0, 7.0, 0.0],
[5.0, 7.0, 0.0],
[10.0, 0.0, 0.0],
[5.0, -7.0, 0.0],
[-5.0, -7.0, 0.0],
[-10.0, 0.0, 0.0],
]
)
geometry /= 100 # in km
slowness = 1.3 # in s/km
baz_degree = 20.0 # 0.0 > source in x direction
baz = baz_degree * np.pi / 180.0
df = 100 # samplerate
# SNR = 100. # signal to noise ratio
amp = 0.00001 # amplitude of coherent wave
length = 500 # signal length in samples
coherent_wave = amp * np.random.randn(length)
# time offsets in samples
dt = df * slowness * (np.cos(baz) * geometry[:, 1] + np.sin(baz) * geometry[:, 0])
dt = np.round(dt)
dt = dt.astype("int32")
max_dt = np.max(dt) + 1
min_dt = np.min(dt) - 1
trl = list()
for i in xrange(len(geometry)):
tr = Trace(coherent_wave[-min_dt + dt[i] : -max_dt + dt[i]].copy())
# + amp / SNR * \
# np.random.randn(length - abs(min_dt) - abs(max_dt)))
tr.stats.sampling_rate = df
tr.stats.coordinates = AttribDict()
tr.stats.coordinates.x = geometry[i, 0]
tr.stats.coordinates.y = geometry[i, 1]
tr.stats.coordinates.elevation = geometry[i, 2]
# lowpass random signal to f_nyquist / 2
tr.filter("lowpass", freq=df / 4.0)
trl.append(tr)
st = Stream(trl)
stime = UTCDateTime(1970, 1, 1, 0, 0)
etime = UTCDateTime(1970, 1, 1, 0, 0) + (length - abs(min_dt) - abs(max_dt)) / df
win_len = 2.0
step_frac = 0.2
sll_x = -3.0
slm_x = 3.0
sll_y = -3.0
slm_y = 3.0
sl_s = 0.1
frqlow = 1.0
frqhigh = 8.0
prewhiten = 0
semb_thres = -1e99
vel_thres = -1e99
# out returns: rel. power, abs. power, backazimuth, slowness
out = sonic(
st,
win_len,
step_frac,
sll_x,
slm_x,
sll_y,
slm_y,
sl_s,
semb_thres,
vel_thres,
frqlow,
frqhigh,
stime,
etime,
prewhiten,
coordsys="xy",
verbose=False,
)
# returns baz
np.testing.assert_almost_equal(out[:, 3].mean(), 18.434948822922024)
# slowness ~= 1.3
np.testing.assert_almost_equal(out[:, 4].mean(), 1.26491106407)
