def test_get_geometry(self):
"""
test get_geometry() in array_analysis.py
"""
ll = np.array([[24.5797167, 121.4842444, 385.106],
[24.5797611, 121.4842333, 384.893],
[24.5796694, 121.4842556, 385.106]])
la = get_geometry(ll)
np.testing.assert_almost_equal(la[:, 0].sum(), 0., decimal=8)
np.testing.assert_almost_equal(la[:, 1].sum(), 0., decimal=8)
np.testing.assert_almost_equal(la[:, 2].sum(), 0., decimal=8)
ll = np.array([[10., 10., 10.], [0., 5., 5.], [0., 0., 0.]])
la = get_geometry(ll, coordsys='xy')
np.testing.assert_almost_equal(la[:, 0].sum(), 0., decimal=8)
np.testing.assert_almost_equal(la[:, 1].sum(), 0., decimal=8)
np.testing.assert_almost_equal(la[:, 2].sum(), 0., decimal=8)
def test_get_geometry(self):
"""
test get_geometry() in array_analysis.py
"""
ll = np.array(
[[24.5797167, 121.4842444, 385.106], [24.5797611, 121.4842333, 384.893], [24.5796694, 121.4842556, 385.106]]
)
la = get_geometry(ll)
np.testing.assert_almost_equal(la[:, 0].sum(), 0.0, decimal=8)
np.testing.assert_almost_equal(la[:, 1].sum(), 0.0, decimal=8)
np.testing.assert_almost_equal(la[:, 2].sum(), 0.0, decimal=8)
ll = np.array([[10.0, 10.0, 10.0], [0.0, 5.0, 5.0], [0.0, 0.0, 0.0]])
la = get_geometry(ll, coordsys="xy")
np.testing.assert_almost_equal(la[:, 0].sum(), 0.0, decimal=8)
np.testing.assert_almost_equal(la[:, 1].sum(), 0.0, decimal=8)
np.testing.assert_almost_equal(la[:, 2].sum(), 0.0, decimal=8)
def beamform_spherical(st, slim, sstep, freqlow, freqhigh, win_len, minbeampow, percdiv, stepdiv, Dmin, Dmax, Dstep, stime=None, etime=None, win_frac=0.05, outfolder=None, coordsys='xy', verbose=False):
"""
Uses plane wave beamforming to approximate answer, then searches in finer grid around answer from that for spherical wave best solution
Almendros et al 1999 methods
"""
if outfolder is None:
outfolder = os.getcwd()
def dump(pow_map, apow_map, i):
"""Example function to use with `store` kwarg in
:func:`~obspy.signal.array_analysis.array_processing`.
"""
np.savez(outfolder+'/pow_map_%d.npz' % i, pow_map)
if stime is None:
stime = st[0].stats.starttime
if etime is None:
etime = st[0].stats.endtime
kwargs = dict(
# slowness grid: X min, X max, Y min, Y max, Slow Step
sll_x=-slim, slm_x=slim, sll_y=-slim, slm_y=slim, sl_s=sstep,
# sliding window properties
win_len=win_len, win_frac=win_frac,
# frequency properties
frqlow=freqlow, frqhigh=freqhigh, prewhiten=0,
# restrict output
semb_thres=-1e9, vel_thres=-1e9,
stime=stime,
etime=etime, coordsys=coordsys, store=None)
t, rel_power, abs_power, baz, slow = array_processing(st, **kwargs)
# Will need this for next step
geometry = get_geometry(st, coordsys=coordsys)
# Initiate zero result matrix for entire possible area (sparse?) - Will be
# Generate time shift table for entire area for all stations (This would be 4D)
# Filter seismograms to freqlims
# Pull out just the data from the stream into an array
for i, t1 in enumerate(t):
pass
def beamform_spherical(st,
slim,
sstep,
freqlow,
freqhigh,
win_len,
minbeampow,
percdiv,
stepdiv,
Dmin,
Dmax,
Dstep,
stime=None,
etime=None,
win_frac=0.05,
outfolder=None,
coordsys='xy',
verbose=False):
"""
Uses plane wave beamforming to approximate answer, then searches in finer grid around answer from that for spherical wave best solution
Almendros et al 1999 methods
"""
if outfolder is None:
outfolder = os.getcwd()
def dump(pow_map, apow_map, i):
"""Example function to use with `store` kwarg in
:func:`~obspy.signal.array_analysis.array_processing`.
"""
np.savez(outfolder + '/pow_map_%d.npz' % i, pow_map)
if stime is None:
stime = st[0].stats.starttime
if etime is None:
etime = st[0].stats.endtime
kwargs = dict(
# slowness grid: X min, X max, Y min, Y max, Slow Step
sll_x=-slim,
slm_x=slim,
sll_y=-slim,
slm_y=slim,
sl_s=sstep,
# sliding window properties
win_len=win_len,
win_frac=win_frac,
# frequency properties
frqlow=freqlow,
frqhigh=freqhigh,
prewhiten=0,
# restrict output
semb_thres=-1e9,
vel_thres=-1e9,
stime=stime,
etime=etime,
coordsys=coordsys,
store=None)
t, rel_power, abs_power, baz, slow = array_processing(st, **kwargs)
# Will need this for next step
geometry = get_geometry(st, coordsys=coordsys)
# Initiate zero result matrix for entire possible area (sparse?) - Will be
# Generate time shift table for entire area for all stations (This would be 4D)
# Filter seismograms to freqlims
# Pull out just the data from the stream into an array
for i, t1 in enumerate(t):
pass
def call(self):
try:
from obspy.core import UTCDateTime, stream
from obspy.signal import array_analysis
from obspy.imaging.cm import obspy_sequential as cmap
except ImportError as _import_error:
self.fail('ImportError:\n%s' % _import_error)
from matplotlib.colorbar import ColorbarBase
from matplotlib.colors import Normalize
import matplotlib.dates as mdates
self.cleanup()
viewer = self.get_viewer()
if viewer.lowpass is None or viewer.highpass is None:
self.fail('highpass and lowpass in viewer must be set!')
traces = []
for trs in self.chopper_selected_traces(fallback=True):
for tr in trs:
tr.lowpass(2, viewer.lowpass)
tr.highpass(2, viewer.highpass)
traces.extend(trs)
if not traces:
self.fail('no traces selected')
if self.downresample == 'resample':
dt_want = min([t.deltat for t in traces])
for t in traces:
t.resample(dt_want)
elif self.downresample == 'downsample':
dt_want = max([t.deltat for t in traces])
for t in traces:
t.downsample_to(dt_want)
elif self.downresample == 'downsample to "target dt"':
for t in traces:
t.downsample_to(float(self.target_dt))
tmin = max([t.tmin for t in traces])
tmax = min([t.tmax for t in traces])
try:
obspy_traces = [
p2o_trace(tr, viewer.get_station(viewer.station_key(tr)))
for tr in traces
]
except KeyError:
self.fail('station information missing')
st = stream.Stream(traces=obspy_traces)
center = array_analysis.get_geometry(st, return_center=True)
center_lon, center_lat, center_ele = center[len(center) - 1]
# Execute sonic
kwargs = dict(sll_x=-self.smax,
slm_x=self.smax,
sll_y=-self.smax,
slm_y=self.smax,
sl_s=self.smax / self.divisor,
win_len=self.window_lenth,
win_frac=self.win_frac,
frqlow=viewer.highpass,
frqhigh=viewer.lowpass,
prewhiten=0,
semb_thres=-1.0e9,
vel_thres=-1.0e9,
verbose=True,
timestamp='mlabday',
stime=UTCDateTime(tmin),
etime=UTCDateTime(tmax))
try:
out = array_analysis.array_processing(st, **kwargs)
except AttributeError:
from obspy.signal.array_analysis import sonic
out = sonic(st, **kwargs)
pi = num.pi
# make output human readable, adjust backazimuth to values between 0
# and 360
t, rel_power, abs_power, baz, slow = out.T
baz[baz < 0.0] += 360.
# choose number of fractions in plot (desirably 360 degree/N is an
# integer!)
N = int(self.numberOfFraction)
abins = num.arange(N + 1) * 360. / N
sbins = num.linspace(0., self.smax, N + 1)
# sum rel power in bins given by abins and sbins
hist, baz_edges, sl_edges = num.histogram2d(baz,
slow,
bins=[abins, sbins],
weights=rel_power)
# transform to gradient
baz_edges = baz_edges / 180. * pi
fig = self.pylab(get='figure')
cax = fig.add_axes([0.85, 0.2, 0.05, 0.5])
ax = fig.add_axes([0.10, 0.1, 0.70, 0.7], polar=True)
ax.grid(False)
dh = abs(sl_edges[1] - sl_edges[0])
dw = abs(baz_edges[1] - baz_edges[0])
# circle through backazimuth
for i, row in enumerate(hist):
ax.bar(left=(pi / 2 - (i + 1) * dw) * num.ones(N),
height=dh * num.ones(N),
width=dw,
bottom=dh * num.arange(N),
color=cmap(row / hist.max()))
ax.set_xticks([pi / 2, 0, 3. / 2 * pi, pi])
ax.set_xticklabels(['N', 'E', 'S', 'W'])
ax.set_ylim(0., self.smax)
ColorbarBase(cax,
cmap=cmap,
norm=Normalize(vmin=hist.min(), vmax=hist.max()))
fig2 = self.pylab(get='figure')
labels = ['rel.power', 'abs.power', 'baz', 'slow']
xlocator = mdates.AutoDateLocator()
ax = None
for i, lab in enumerate(labels):
ax = fig2.add_subplot(4, 1, i + 1, sharex=ax)
ax.scatter(out[:, 0],
out[:, i + 1],
c=out[:, 1],
alpha=0.6,
edgecolors='none',
cmap=cmap)
ax.set_ylabel(lab)
ax.set_xlim(out[0, 0], out[-1, 0])
ax.set_ylim(out[:, i + 1].min(), out[:, i + 1].max())
ax.xaxis.set_tick_params(which='both', direction='in')
ax.xaxis.set_major_locator(xlocator)
ax.xaxis.set_major_formatter(mdates.AutoDateFormatter(xlocator))
if i != 3:
ax.set_xticklabels([])
fig2.subplots_adjust(hspace=0.)
fig2.canvas.draw()
fig.canvas.draw()
print('Center of Array at latitude %s and longitude %s' %
(center_lat, center_lon))
def call(self):
try:
from obspy.core import UTCDateTime, stream
from obspy.signal import array_analysis
from obspy.imaging.cm import obspy_sequential as cmap
except ImportError as _import_error:
self.fail('ImportError:\n%s' % _import_error)
from matplotlib.colorbar import ColorbarBase
from matplotlib.colors import Normalize
import matplotlib.dates as mdates
self.cleanup()
viewer = self.get_viewer()
if viewer.lowpass is None or viewer.highpass is None:
self.fail('highpass and lowpass in viewer must be set!')
traces = []
for trs in self.chopper_selected_traces(fallback=True):
for tr in trs:
tr.lowpass(2, viewer.lowpass)
tr.highpass(2, viewer.highpass)
traces.extend(trs)
if not traces:
self.fail('no traces selected')
if self.downresample == 'resample':
dt_want = min([t.deltat for t in traces])
for t in traces:
t.resample(dt_want)
elif self.downresample == 'downsample':
dt_want = max([t.deltat for t in traces])
for t in traces:
t.downsample_to(dt_want)
elif self.downresample == 'downsample to "target dt"':
for t in traces:
t.downsample_to(float(self.target_dt))
tmin = max([t.tmin for t in traces])
tmax = min([t.tmax for t in traces])
try:
obspy_traces = [p2o_trace(
tr, viewer.get_station(viewer.station_key(tr)))
for tr in traces]
except KeyError:
self.fail('station information missing')
st = stream.Stream(traces=obspy_traces)
center = array_analysis.get_geometry(st, return_center=True)
center_lon, center_lat, center_ele = center[len(center)-1]
# Execute sonic
kwargs = dict(
sll_x=-self.smax, slm_x=self.smax, sll_y=-self.smax,
slm_y=self.smax, sl_s=self.smax/self.divisor,
win_len=self.window_lenth, win_frac=self.win_frac,
frqlow=viewer.highpass, frqhigh=viewer.lowpass, prewhiten=0,
semb_thres=-1.0e9, vel_thres=-1.0e9, verbose=True,
timestamp='mlabday', stime=UTCDateTime(tmin),
etime=UTCDateTime(tmax)
)
try:
out = array_analysis.array_processing(st, **kwargs)
except AttributeError:
from obspy.signal.array_analysis import sonic
out = sonic(st, **kwargs)
pi = num.pi
# make output human readable, adjust backazimuth to values between 0
# and 360
t, rel_power, abs_power, baz, slow = out.T
baz[baz < 0.0] += 360.
# choose number of fractions in plot (desirably 360 degree/N is an
# integer!)
N = int(self.numberOfFraction)
abins = num.arange(N + 1) * 360. / N
sbins = num.linspace(0., self.smax, N + 1)
# sum rel power in bins given by abins and sbins
hist, baz_edges, sl_edges = num.histogram2d(
baz, slow, bins=[abins, sbins], weights=rel_power)
# transform to gradient
baz_edges = baz_edges / 180. * pi
fig = self.pylab(get='figure')
cax = fig.add_axes([0.85, 0.2, 0.05, 0.5])
ax = fig.add_axes([0.10, 0.1, 0.70, 0.7], polar=True)
ax.grid(False)
dh = abs(sl_edges[1] - sl_edges[0])
dw = abs(baz_edges[1] - baz_edges[0])
# circle through backazimuth
for i, row in enumerate(hist):
ax.bar(left=(pi / 2 - (i + 1) * dw) * num.ones(N),
height=dh * num.ones(N), width=dw,
bottom=dh * num.arange(N), color=cmap(row / hist.max()))
ax.set_xticks([pi / 2, 0, 3. / 2 * pi, pi])
ax.set_xticklabels(['N', 'E', 'S', 'W'])
ax.set_ylim(0., self.smax)
ColorbarBase(cax, cmap=cmap,
norm=Normalize(vmin=hist.min(), vmax=hist.max()))
fig2 = self.pylab(get='figure')
labels = ['rel.power', 'abs.power', 'baz', 'slow']
xlocator = mdates.AutoDateLocator()
ax = None
for i, lab in enumerate(labels):
ax = fig2.add_subplot(4, 1, i + 1, sharex=ax)
ax.scatter(out[:, 0], out[:, i + 1], c=out[:, 1], alpha=0.6,
edgecolors='none', cmap=cmap)
ax.set_ylabel(lab)
ax.set_xlim(out[0, 0], out[-1, 0])
ax.set_ylim(out[:, i + 1].min(), out[:, i + 1].max())
ax.xaxis.set_tick_params(which='both', direction='in')
ax.xaxis.set_major_locator(xlocator)
ax.xaxis.set_major_formatter(mdates.AutoDateFormatter(xlocator))
if i != 3:
ax.set_xticklabels([])
fig2.subplots_adjust(hspace=0.)
fig2.canvas.draw()
fig.canvas.draw()
print('Center of Array at latitude %s and longitude %s' %
(center_lat, center_lon))
def __vespa_az(self, st):
def find_nearest(array, value):
idx, val = min(enumerate(array), key=lambda x: abs(x[1] - value))
return idx, val
sides = 'onesided'
pi = math.pi
st.sort()
n = len(st)
for i in range(n):
coords = self.inv.get_coordinates(st[i].id)
st[i].stats.coordinates = AttribDict({
'latitude':
coords['latitude'],
'elevation':
coords['elevation'],
'longitude':
coords['longitude']
})
coord = get_geometry(st, coordsys='lonlat', return_center=True)
tr = st[0]
win = len(tr.data)
if (win % 2) == 0:
nfft = win / 2 + 1
else:
nfft = (win + 1) / 2
nr = st.count() # number of stations
delta = st[0].stats.delta
fs = 1 / delta
fn = fs / 2
freq = np.arange(0, fn, fn / nfft)
value1, freq1 = find_nearest(freq, self.linf)
value2, freq2 = find_nearest(freq, self.lsup)
df = value2 - value1
m = np.zeros((win, nr))
WW = np.hamming(int(win))
WW = np.transpose(WW)
for i in range(nr):
tr = st[i]
if self.method == "FK":
m[:, i] = (tr.data - np.mean(tr.data)) * WW
else:
m[:, i] = (tr.data - np.mean(tr.data))
pdata = np.transpose(m)
#####Coherence######
NW = 2 # the time-bandwidth product##Buena seleccion de 2-3
K = 2 * NW - 1
tapers, eigs = alg.dpss_windows(win, NW, K)
tdata = tapers[None, :, :] * pdata[:, None, :]
tspectra = fftpack.fft(tdata)
w = np.empty((nr, int(K), int(nfft)))
for i in range(nr):
w[i], _ = utils.adaptive_weights(tspectra[i], eigs, sides=sides)
Cx = np.ones((nr, nr, df), dtype=np.complex128)
if self.method == "MTP.COHERENCE":
for i in range(nr):
for j in range(nr):
sxy = alg.mtm_cross_spectrum(tspectra[i], (tspectra[j]),
(w[i], w[j]),
sides='onesided')
sxx = alg.mtm_cross_spectrum(tspectra[i],
tspectra[i],
w[i],
sides='onesided')
syy = alg.mtm_cross_spectrum(tspectra[j],
tspectra[j],
w[j],
sides='onesided')
s = sxy / np.sqrt((sxx * syy))
cxcohe = s[value1:value2]
Cx[i, j, :] = cxcohe
####Calculates Conventional FK-power ##without normalization
if self.method == "FK":
for i in range(nr):
for j in range(nr):
A = np.fft.rfft(m[:, i])
B = np.fft.rfft(m[:, j])
#Power
#out = A * np.conjugate(B)
#Relative Power
den = np.absolute(A) * np.absolute(np.conjugate(B))
out = (A * np.conjugate(B)) / den
cxcohe = out[value1:value2]
Cx[i, j, :] = cxcohe
r = np.zeros((nr, 2))
S = np.zeros((1, 2))
Pow = np.zeros((360, df))
for n in range(nr):
r[n, :] = coord[n][0:2]
freq = freq[value1:value2]
rad = np.pi / 180
slow_range = np.linspace(0, self.slow, 360)
for j in range(360):
ang = self.azimuth2mathangle(self.baz)
S[0, 0] = slow_range[j] * np.cos(rad * ang)
S[0, 1] = slow_range[j] * np.sin(rad * ang)
k = (S * r)
K = np.sum(k, axis=1)
n = 0
for f in freq:
A = np.exp(-1j * 2 * pi * f * K)
B = np.conjugate(np.transpose(A))
D = np.matmul(B, Cx[:, :, n]) / nr
P = np.matmul(D, A) / nr
Pow[j, n] = np.abs(P)
n = n + 1
Pow = np.mean(Pow, axis=1)
return Pow
def FKCoherence(self, st, inv, DT, linf, lsup, slim, win_len, sinc,
method):
def find_nearest(array, value):
idx, val = min(enumerate(array), key=lambda x: abs(x[1] - value))
return idx, val
sides = 'onesided'
pi = math.pi
smax = slim
smin = -1 * smax
Sx = np.arange(smin, smax, sinc)[np.newaxis]
Sy = np.arange(smin, smax, sinc)[np.newaxis]
nx = ny = len(Sx[0])
Sy = np.fliplr(Sy)
#####Convert start from Greogorian to actual date###############
Time = DT
Time = Time - int(Time)
d = date.fromordinal(int(DT))
date1 = d.isoformat()
H = (Time * 24)
H1 = int(H) # Horas
minutes = (H - int(H)) * 60
minutes1 = int(minutes)
seconds = (minutes - int(minutes)) * 60
H1 = str(H1).zfill(2)
minutes1 = str(minutes1).zfill(2)
seconds = "%.2f" % seconds
seconds = str(seconds).zfill(2)
DATE = date1 + "T" + str(H1) + minutes1 + seconds
t1 = UTCDateTime(DATE)
########End conversion###############################
st.trim(starttime=t1, endtime=t1 + win_len)
st.sort()
n = len(st)
for i in range(n):
coords = inv.get_coordinates(st[i].id)
st[i].stats.coordinates = AttribDict({
'latitude':
coords['latitude'],
'elevation':
coords['elevation'],
'longitude':
coords['longitude']
})
coord = get_geometry(st, coordsys='lonlat', return_center=True)
tr = st[0]
win = len(tr.data)
if (win % 2) == 0:
nfft = win / 2 + 1
else:
nfft = (win + 1) / 2
nr = st.count() # number of stations
delta = st[0].stats.delta
fs = 1 / delta
fn = fs / 2
freq = np.arange(0, fn, fn / nfft)
value1, freq1 = find_nearest(freq, linf)
value2, freq2 = find_nearest(freq, lsup)
df = value2 - value1
m = np.zeros((win, nr))
WW = np.hamming(int(win))
WW = np.transpose(WW)
for i in range(nr):
tr = st[i]
if method == "FK":
m[:, i] = (tr.data - np.mean(tr.data)) * WW
else:
m[:, i] = (tr.data - np.mean(tr.data))
pdata = np.transpose(m)
#####Coherence######
NW = 2 # the time-bandwidth product##Buena seleccion de 2-3
K = 2 * NW - 1
tapers, eigs = alg.dpss_windows(win, NW, K)
tdata = tapers[None, :, :] * pdata[:, None, :]
tspectra = fftpack.fft(tdata)
w = np.empty((nr, int(K), int(nfft)))
for i in range(nr):
w[i], _ = utils.adaptive_weights(tspectra[i], eigs, sides=sides)
nseq = nr
L = int(nfft)
#csd_mat = np.zeros((nseq, nseq, L), 'D')
#psd_mat = np.zeros((2, nseq, nseq, L), 'd')
coh_mat = np.zeros((nseq, nseq, L), 'd')
#coh_var = np.zeros_like(coh_mat)
Cx = np.ones((nr, nr, df), dtype=np.complex128)
if method == "MTP.COHERENCE":
for i in range(nr):
for j in range(nr):
sxy = alg.mtm_cross_spectrum(tspectra[i], (tspectra[j]),
(w[i], w[j]),
sides='onesided')
sxx = alg.mtm_cross_spectrum(tspectra[i],
tspectra[i],
w[i],
sides='onesided')
syy = alg.mtm_cross_spectrum(tspectra[j],
tspectra[j],
w[j],
sides='onesided')
s = sxy / np.sqrt((sxx * syy))
cxcohe = s[value1:value2]
Cx[i, j, :] = cxcohe
# Calculates Conventional FK-power
if method == "FK":
for i in range(nr):
for j in range(nr):
A = np.fft.rfft(m[:, i])
B = np.fft.rfft(m[:, j])
#Relative Power
den = np.absolute(A) * np.absolute(np.conjugate(B))
out = (A * np.conjugate(B)) / den
cxcohe = out[value1:value2]
Cx[i, j, :] = cxcohe
r = np.zeros((nr, 2), dtype=np.complex128)
S = np.zeros((1, 2), dtype=np.complex128)
Pow = np.zeros((len(Sx[0]), len(Sy[0]), df))
for n in range(nr):
r[n, :] = coord[n][0:2]
freq = freq[value1:value2]
for i in range(ny):
for j in range(nx):
S[0, 0] = Sx[0][j]
S[0, 1] = Sy[0][i]
k = (S * r)
K = np.sum(k, axis=1)
n = 0
for f in freq:
A = np.exp(-1j * 2 * pi * f * K)
B = np.conjugate(np.transpose(A))
D = np.matmul(B, Cx[:, :, n]) / nr
P = np.matmul(D, A) / nr
Pow[i, j, n] = np.abs(P)
n = n + 1
Pow = np.mean(Pow, axis=2)
#Pow = Pow / len(freq)
Pow = np.fliplr(Pow)
x = y = np.linspace(smin, smax, nx)
nn = len(x)
maximum_power = np.where(Pow == np.amax(Pow))
Sxpow = (maximum_power[1] - nn / 2) * sinc
Sypow = (maximum_power[0] - nn / 2) * sinc
return Pow, Sxpow, Sypow, coord
def plotFK(st,
startTime,
endTime,
frqlow,
frqhigh,
sll_x=-3.6,
slm_x=3.6,
sll_y=-3.6,
slm_y=3.6,
sl_s=0.18,
beam='bartlett',
prewhiten=0,
coordsys='lonlat',
verbose=False,
plot=True,
normalize=True,
cmap='inferno_r',
sl_circle=True,
interpolation=None,
vmin=None,
vmax=None,
plot_normalize=False,
sl_corr=[0., 0.]):
'''
Modified from Stephen Arrowsmith's ROSES 2020 class
Computes and displays an FK plot for an ObsPy Stream object, st, given
a start time and end time (as UTCDateTime objects) and a frequency band
defined by frqlow and frqhigh. The slowness grid is defined as optional
parameters (in s/km).
This function implements code directly from ObsPy, which has been optimized,
for simply plotting the FK spectrum
It includes the option to normalize the data in the time window before running FK
It also includes the option to apply a slowness correction, defined by sl_corr
'''
stream = st.copy()
stream = stream.trim(startTime, endTime)
nstat = len(stream)
fk_methods = dict(bartlett=0, capon=1)
if nstat > 0:
if normalize:
for ms in stream:
ms.data = ms.data / np.max(np.abs(ms.data))
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)
time_shift_table = get_timeshift(geometry, sll_x, sll_y, sl_s,
grdpts_x, grdpts_y)
fs = stream[0].stats.sampling_rate
nsamp = stream[0].stats.npts
# 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)
# 0.22 matches 0.2 of historical C bbfk.c
tap = cosine_taper(nsamp, p=0.22)
relpow_map = np.empty((grdpts_x, grdpts_y), dtype=np.float64)
abspow_map = np.empty((grdpts_x, grdpts_y), dtype=np.float64)
for i, tr in enumerate(stream):
dat = tr.data
dat = (dat - dat.mean()) * tap
ft[i, :] = np.fft.rfft(dat, nfft)[nlow:nlow + nf]
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 i != j:
_r[:, j, i] = _r[:, i, j].conjugate()
else:
dpow += np.abs(_r[:, i, j].sum())
dpow *= nstat
clibsignal.generalizedBeamformer(relpow_map, abspow_map, steer, _r,
nstat, prewhiten, grdpts_x, grdpts_y,
nf, dpow, fk_methods[beam])
fisher_map = (nstat - 1) * relpow_map / (1 - relpow_map)
(ix, iy) = np.unravel_index(relpow_map.argmax(), relpow_map.shape)
# here we compute baz, slow
slow_x = sll_x + ix * sl_s
slow_y = sll_y + iy * sl_s
# ---------
slow_x = slow_x - sl_corr[0]
slow_y = slow_y - sl_corr[1]
#print(slow_x, slow_y)
# ---------
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 plot:
n_frames = 3
(fig, ax) = plt.subplots(1,
n_frames,
sharey=True,
figsize=(8, 3.5),
constrained_layout=True)
extent = extent = [sll_x, slm_x + sl_s, sll_y, slm_y + sl_s]
# FK power
i = 0
H = np.flipud(np.fliplr(abspow_map.T))
if plot_normalize:
H = H / H.max()
im = ax[i].imshow(H,
extent=extent,
origin='lower',
aspect='auto',
cmap=cmap,
interpolation=interpolation)
plt.colorbar(im,
ax=ax[i],
orientation="horizontal",
label='FK Power')
# Semblance
i += 1
H = np.flipud(np.fliplr(relpow_map.T))
if plot_normalize:
H = H / H.max()
im = ax[i].imshow(H,
extent=extent,
origin='lower',
aspect='auto',
cmap=cmap,
interpolation=interpolation)
plt.colorbar(im,
ax=ax[i],
orientation="horizontal",
label='Semblance')
# Fisher ratio
i += 1
H = np.flipud(np.fliplr(fisher_map.T))
if plot_normalize:
H = H / H.max()
im = ax[i].imshow(H,
extent=extent,
origin='lower',
aspect='auto',
cmap=cmap,
interpolation=interpolation)
plt.colorbar(im,
ax=ax[i],
orientation="horizontal",
label='Fisher ratio')
for i in range(0, n_frames):
if sl_circle:
angles = np.deg2rad(np.arange(0., 360, 1.))
slowness = dict(seismic_P=6.0,
Rayleigh=3.0,
infrasound=0.34)
for (key, radius) in slowness.items():
x_circle = np.sin(angles) / radius
y_circle = np.cos(angles) / radius
ax[i].plot(x_circle,
y_circle,
linestyle='solid',
label=key,
alpha=0.6)
ax[i].plot(0, 0, 'k+')
ax[i].plot(-slow_x, -slow_y, 'w+')
ax[i].set_xlabel('x-slowness [s/km]')
ax[0].set_ylabel('y-slowness [s/km]')
baz_max = round(baz % 360., 2)
appvel_max = round(1 / slow, 2)
title_str = (f'Peak semblance at {baz_max:.2f} deg. '
f'and {appvel_max:.2f} km/s '
f'between [ {frqlow:.2f} - {frqhigh:.2f} ] Hz')
fig.suptitle(title_str)
return fig, ax
# # only flipping left-right, when using imshow to plot the matrix is takes
# # points top to bottom points are now starting at top-left in row major
# return np.fliplr(relpow_map.T), baz % 360, 1. / slow
else:
print(f'No data present for timerange {startTime} - {endTime}')
return