def make_steering_vectors(geometry, stream, freqs, xSlowness, ySlowness = 0):
if isinstance(geometry, list):
geometry = np.array(geometry).transpose()
## define the frequency axis
fs = stream[0].stats.sampling_rate
deltaf = freqs[1] - freqs[0]
nlow = 1
nf = len(freqs)
nhigh = freqs.max() / deltaf
## code adapted from get_timeshift
mx = np.outer(geometry[:, 0], xSlowness)
my = np.outer(geometry[:, 1], ySlowness)
timeShiftTable = np.require(mx[:, :, np.newaxis].repeat(len(ySlowness), axis=2) +
my[:, np.newaxis, :].repeat(len(xSlowness), axis=1), dtype=np.float32)
## code adapted from array_processing
steeringVectors = np.empty((nf, len(xSlowness), len(ySlowness), len(stream)), dtype=np.complex128)
clibsignal.calcSteer(len(stream), len(xSlowness), len(ySlowness), nf, nlow, deltaf, timeShiftTable, steeringVectors)
return steeringVectors
def array_processing(stream, win_len, win_frac, sll_x, slm_x, sll_y, slm_y,
sl_s, semb_thres, vel_thres, frqlow, frqhigh, stime,
etime, prewhiten, verbose=False, coordsys='lonlat',
timestamp='mlabday', method=0, store=None):
"""
Method for Seismic-Array-Beamforming/FK-Analysis/Capon
:param stream: Stream object, the trace.stats dict like class must
contain an :class:`~obspy.core.util.attribdict.AttribDict` with
'latitude', 'longitude' (in degrees) and 'elevation' (in km), or 'x',
'y', 'elevation' (in km) items/attributes. See param ``coordsys``.
:type win_len: float
:param win_len: Sliding window length in seconds
:type win_frac: float
:param win_frac: Fraction of sliding window to use for step
:type sll_x: float
:param sll_x: slowness x min (lower)
:type slm_x: float
:param slm_x: slowness x max
:type sll_y: float
:param sll_y: slowness y min (lower)
:type slm_y: float
:param slm_y: slowness y max
:type sl_s: float
:param sl_s: slowness step
:type semb_thres: float
:param semb_thres: Threshold for semblance
:type vel_thres: float
:param vel_thres: Threshold for velocity
:type frqlow: float
:param frqlow: lower frequency for fk/capon
:type frqhigh: float
:param frqhigh: higher frequency for fk/capon
:type stime: :class:`~obspy.core.utcdatetime.UTCDateTime`
:param stime: Start time of interest
:type etime: :class:`~obspy.core.utcdatetime.UTCDateTime`
:param etime: End time of interest
:type prewhiten: int
:param prewhiten: Do prewhitening, values: 1 or 0
:param coordsys: valid values: 'lonlat' and 'xy', choose which stream
attributes to use for coordinates
:type timestamp: str
:param timestamp: valid values: 'julsec' and 'mlabday'; 'julsec' returns
the timestamp in seconds since 1970-01-01T00:00:00, 'mlabday'
returns the timestamp in days (decimals represent hours, minutes
and seconds) since '0001-01-01T00:00:00' as needed for matplotlib
date plotting (see e.g. matplotlib's num2date)
:type method: int
:param method: the method to use 0 == bf, 1 == capon
:type store: function
:param store: A custom function which gets called on each iteration. It is
called with the relative power map and the time offset as first and
second arguments and the iteration number as third argument. Useful for
storing or plotting the map for each iteration. For this purpose the
dump function of this module can be used.
:return: :class:`numpy.ndarray` of timestamp, relative relpow, absolute
relpow, backazimuth, slowness
"""
res = []
eotr = True
# check that sampling rates do not vary
fs = stream[0].stats.sampling_rate
if len(stream) != len(stream.select(sampling_rate=fs)):
msg = 'in sonic sampling rates of traces in stream are not equal'
raise ValueError(msg)
grdpts_x = int(((slm_x - sll_x) / sl_s + 0.5) + 1)
grdpts_y = int(((slm_y - sll_y) / sl_s + 0.5) + 1)
geometry = get_geometry(stream, coordsys=coordsys, verbose=verbose)
if verbose:
print("geometry:")
print(geometry)
print("stream contains following traces:")
print(stream)
print("stime = " + str(stime) + ", etime = " + str(etime))
time_shift_table = get_timeshift(geometry, sll_x, sll_y,
sl_s, grdpts_x, grdpts_y)
# offset of arrays
spoint, _epoint = get_spoint(stream, stime, etime)
#
# loop with a sliding window over the dat trace array and apply bbfk
#
nstat = len(stream)
fs = stream[0].stats.sampling_rate
nsamp = int(win_len * fs)
nstep = int(nsamp * win_frac)
# generate plan for rfftr
nfft = next_pow_2(nsamp)
deltaf = fs / float(nfft)
nlow = int(frqlow / float(deltaf) + 0.5)
nhigh = int(frqhigh / float(deltaf) + 0.5)
nlow = max(1, nlow) # avoid using the offset
nhigh = min(nfft // 2 - 1, nhigh) # avoid using nyquist
nf = nhigh - nlow + 1 # include upper and lower frequency
# to speed up the routine a bit we estimate all steering vectors in advance
steer = np.empty((nf, grdpts_x, grdpts_y, nstat), dtype=np.complex128)
clibsignal.calcSteer(nstat, grdpts_x, grdpts_y, nf, nlow,
deltaf, time_shift_table, steer)
_r = np.empty((nf, nstat, nstat), dtype=np.complex128)
ft = np.empty((nstat, nf), dtype=np.complex128)
newstart = stime
# 0.22 matches 0.2 of historical C bbfk.c
tap = cosine_taper(nsamp, p=0.22)
offset = 0
relpow_map = np.empty((grdpts_x, grdpts_y), dtype=np.float64)
abspow_map = np.empty((grdpts_x, grdpts_y), dtype=np.float64)
while eotr:
try:
for i, tr in enumerate(stream):
dat = tr.data[spoint[i] + offset:
spoint[i] + offset + nsamp]
dat = (dat - dat.mean()) * tap
ft[i, :] = np.fft.rfft(dat, nfft)[nlow:nlow + nf]
except IndexError:
break
ft = np.ascontiguousarray(ft, np.complex128)
relpow_map.fill(0.)
abspow_map.fill(0.)
# computing the covariances of the signal at different receivers
dpow = 0.
for i in range(nstat):
for j in range(i, nstat):
_r[:, i, j] = ft[i, :] * ft[j, :].conj()
if method == 1:
_r[:, i, j] /= np.abs(_r[:, i, j].sum())
if i != j:
_r[:, j, i] = _r[:, i, j].conjugate()
else:
dpow += np.abs(_r[:, i, j].sum())
dpow *= nstat
if method == 1:
# P(f) = 1/(e.H R(f)^-1 e)
for n in range(nf):
_r[n, :, :] = np.linalg.pinv(_r[n, :, :], rcond=1e-6)
errcode = clibsignal.generalizedBeamformer(
relpow_map, abspow_map, steer, _r, nstat, prewhiten,
grdpts_x, grdpts_y, nf, dpow, method)
if errcode != 0:
msg = 'generalizedBeamforming exited with error %d'
raise Exception(msg % errcode)
ix, iy = np.unravel_index(relpow_map.argmax(), relpow_map.shape)
relpow, abspow = relpow_map[ix, iy], abspow_map[ix, iy]
if store is not None:
store(relpow_map, abspow_map, offset)
# here we compute baz, slow
slow_x = sll_x + ix * sl_s
slow_y = sll_y + iy * sl_s
slow = np.sqrt(slow_x ** 2 + slow_y ** 2)
if slow < 1e-8:
slow = 1e-8
azimut = 180 * math.atan2(slow_x, slow_y) / math.pi
baz = azimut % -360 + 180
if relpow > semb_thres and 1. / slow > vel_thres:
res.append(np.array([newstart.timestamp, relpow, abspow, baz,
slow]))
if verbose:
print(newstart, (newstart + (nsamp / fs)), res[-1][1:])
if (newstart + (nsamp + nstep) / fs) > etime:
eotr = False
offset += nstep
newstart += nstep / fs
res = np.array(res)
if timestamp == 'julsec':
pass
elif timestamp == 'mlabday':
# 719163 == days between 1970 and 0001 + 1
res[:, 0] = res[:, 0] / (24. * 3600) + 719163
else:
msg = "Option timestamp must be one of 'julsec', or 'mlabday'"
raise ValueError(msg)
return np.array(res)
def array_processing(stream, win_len, win_frac, sll_x, slm_x, sll_y, slm_y,
sl_s, semb_thres, vel_thres, frqlow, frqhigh, stime,
etime, prewhiten, verbose=False, coordsys='lonlat',
timestamp='mlabday', method=0, store=None):
"""
Method for Seismic-Array-Beamforming/FK-Analysis/Capon
:param stream: Stream object, the trace.stats dict like class must
contain an :class:`~obspy.core.util.attribdict.AttribDict` with
'latitude', 'longitude' (in degrees) and 'elevation' (in km), or 'x',
'y', 'elevation' (in km) items/attributes. See param ``coordsys``.
:type win_len: float
:param win_len: Sliding window length in seconds
:type win_frac: float
:param win_frac: Fraction of sliding window to use for step
:type sll_x: float
:param sll_x: slowness x min (lower)
:type slm_x: float
:param slm_x: slowness x max
:type sll_y: float
:param sll_y: slowness y min (lower)
:type slm_y: float
:param slm_y: slowness y max
:type sl_s: float
:param sl_s: slowness step
:type semb_thres: float
:param semb_thres: Threshold for semblance
:type vel_thres: float
:param vel_thres: Threshold for velocity
:type frqlow: float
:param frqlow: lower frequency for fk/capon
:type frqhigh: float
:param frqhigh: higher frequency for fk/capon
:type stime: :class:`~obspy.core.utcdatetime.UTCDateTime`
:param stime: Start time of interest
:type etime: :class:`~obspy.core.utcdatetime.UTCDateTime`
:param etime: End time of interest
:type prewhiten: int
:param prewhiten: Do prewhitening, values: 1 or 0
:param coordsys: valid values: 'lonlat' and 'xy', choose which stream
attributes to use for coordinates
:type timestamp: str
:param timestamp: valid values: 'julsec' and 'mlabday'; 'julsec' returns
the timestamp in seconds since 1970-01-01T00:00:00, 'mlabday'
returns the timestamp in days (decimals represent hours, minutes
and seconds) since '0001-01-01T00:00:00' as needed for matplotlib
date plotting (see e.g. matplotlib's num2date)
:type method: int
:param method: the method to use 0 == bf, 1 == capon
:type store: function
:param store: A custom function which gets called on each iteration. It is
called with the relative power map and the time offset as first and
second arguments and the iteration number as third argument. Useful for
storing or plotting the map for each iteration. For this purpose the
dump function of this module can be used.
:return: :class:`numpy.ndarray` of timestamp, relative relpow, absolute
relpow, backazimuth, slowness
"""
res = []
eotr = True
# check that sampling rates do not vary
fs = stream[0].stats.sampling_rate
if len(stream) != len(stream.select(sampling_rate=fs)):
msg = 'in sonic sampling rates of traces in stream are not equal'
raise ValueError(msg)
grdpts_x = int(((slm_x - sll_x) / sl_s + 0.5) + 1)
grdpts_y = int(((slm_y - sll_y) / sl_s + 0.5) + 1)
geometry = get_geometry(stream, coordsys=coordsys, verbose=verbose)
if verbose:
print("geometry:")
print(geometry)
print("stream contains following traces:")
print(stream)
print("stime = " + str(stime) + ", etime = " + str(etime))
time_shift_table = get_timeshift(geometry, sll_x, sll_y,
sl_s, grdpts_x, grdpts_y)
# offset of arrays
spoint, _epoint = get_spoint(stream, stime, etime)
#
# loop with a sliding window over the dat trace array and apply bbfk
#
nstat = len(stream)
fs = stream[0].stats.sampling_rate
nsamp = int(win_len * fs)
nstep = int(nsamp * win_frac)
# generate plan for rfftr
nfft = nextpow2(nsamp)
deltaf = fs / float(nfft)
nlow = int(frqlow / float(deltaf) + 0.5)
nhigh = int(frqhigh / float(deltaf) + 0.5)
nlow = max(1, nlow) # avoid using the offset
nhigh = min(nfft // 2 - 1, nhigh) # avoid using nyquist
nf = nhigh - nlow + 1 # include upper and lower frequency
# to speed up the routine a bit we estimate all steering vectors in advance
steer = np.empty((nf, grdpts_x, grdpts_y, nstat), dtype=np.complex128)
clibsignal.calcSteer(nstat, grdpts_x, grdpts_y, nf, nlow,
deltaf, time_shift_table, steer)
R = np.empty((nf, nstat, nstat), dtype=np.complex128)
ft = np.empty((nstat, nf), dtype=np.complex128)
newstart = stime
tap = cosTaper(nsamp, p=0.22) # 0.22 matches 0.2 of historical C bbfk.c
offset = 0
relpow_map = np.empty((grdpts_x, grdpts_y), dtype=np.float64)
abspow_map = np.empty((grdpts_x, grdpts_y), dtype=np.float64)
while eotr:
try:
for i, tr in enumerate(stream):
dat = tr.data[spoint[i] + offset:
spoint[i] + offset + nsamp]
dat = (dat - dat.mean()) * tap
ft[i, :] = np.fft.rfft(dat, nfft)[nlow:nlow + nf]
except IndexError:
break
ft = np.ascontiguousarray(ft, np.complex128)
relpow_map.fill(0.)
abspow_map.fill(0.)
# computing the covariances of the signal at different receivers
dpow = 0.
for i in range(nstat):
for j in range(i, nstat):
R[:, i, j] = ft[i, :] * ft[j, :].conj()
if method == 1:
R[:, i, j] /= np.abs(R[:, i, j].sum())
if i != j:
R[:, j, i] = R[:, i, j].conjugate()
else:
dpow += np.abs(R[:, i, j].sum())
dpow *= nstat
if method == 1:
# P(f) = 1/(e.H R(f)^-1 e)
for n in range(nf):
R[n, :, :] = np.linalg.pinv(R[n, :, :], rcond=1e-6)
errcode = clibsignal.generalizedBeamformer(
relpow_map, abspow_map, steer, R, nstat, prewhiten,
grdpts_x, grdpts_y, nf, dpow, method)
if errcode != 0:
msg = 'generalizedBeamforming exited with error %d'
raise Exception(msg % errcode)
ix, iy = np.unravel_index(relpow_map.argmax(), relpow_map.shape)
relpow, abspow = relpow_map[ix, iy], abspow_map[ix, iy]
if store is not None:
store(relpow_map, abspow_map, offset)
# here we compute baz, slow
slow_x = sll_x + ix * sl_s
slow_y = sll_y + iy * sl_s
slow = np.sqrt(slow_x ** 2 + slow_y ** 2)
if slow < 1e-8:
slow = 1e-8
azimut = 180 * math.atan2(slow_x, slow_y) / math.pi
baz = azimut % -360 + 180
if relpow > semb_thres and 1. / slow > vel_thres:
res.append(np.array([newstart.timestamp, relpow, abspow, baz,
slow]))
if verbose:
print(newstart, (newstart + (nsamp / fs)), res[-1][1:])
if (newstart + (nsamp + nstep) / fs) > etime:
eotr = False
offset += nstep
newstart += nstep / fs
res = np.array(res)
if timestamp == 'julsec':
pass
elif timestamp == 'mlabday':
# 719162 == hours between 1970 and 0001
res[:, 0] = res[:, 0] / (24. * 3600) + 719162
else:
msg = "Option timestamp must be one of 'julsec', or 'mlabday'"
raise ValueError(msg)
return np.array(res)