def test_array_transff_freqslowness(self):
coords = np.array(
[[10.0, 60.0, 0.0], [200.0, 50.0, 0.0], [-120.0, 170.0, 0.0], [-100.0, -150.0, 0.0], [30.0, -220.0, 0.0]]
)
coords /= 1000.0
coordsll = np.zeros(coords.shape)
for i in np.arange(len(coords)):
coordsll[i, 0], coordsll[i, 1] = utlLonLat(0.0, 0.0, coords[i, 0], coords[i, 1])
slim = 40.0
fmin = 1.0
fmax = 10.0
fstep = 1.0
sstep = slim / 2.0
transff = array_transff_freqslowness(coords, slim, sstep, fmin, fmax, fstep, coordsys="xy")
transffll = array_transff_freqslowness(coordsll, slim, sstep, fmin, fmax, fstep, coordsys="lonlat")
transffth = np.array(
[
[0.41915119, 0.33333333, 0.32339525, 0.24751548, 0.67660475],
[0.25248452, 0.41418215, 0.34327141, 0.65672859, 0.33333333],
[0.24751548, 0.25248452, 1.00000000, 0.25248452, 0.24751548],
[0.33333333, 0.65672859, 0.34327141, 0.41418215, 0.25248452],
[0.67660475, 0.24751548, 0.32339525, 0.33333333, 0.41915119],
]
)
np.testing.assert_array_almost_equal(transff, transffth, decimal=6)
np.testing.assert_array_almost_equal(transffll, transffth, decimal=6)
def plotARF_slowaz(coords, slim, sstep, freqlow, freqhigh, fstep, coordsys='xy'):
"""
Add ability to plot range of frequency ranges
"""
transff = array_transff_freqslowness(coords, slim, sstep, freqlow, freqhigh, fstep, coordsys=coordsys)
xgrid = np.arange(-slim, slim+sstep, sstep)
slow = np.empty((len(xgrid), len(xgrid)))
baz = slow.copy()
for i in np.arange(len(xgrid)):
for j in np.arange(len(xgrid)):
# compute baz, slow
slow_x = xgrid[i]
slow_y = xgrid[j]
slow[i, j] = np.sqrt(slow_x ** 2 + slow_y ** 2)
if slow[i, j] < 1e-8:
slow[i, j] = 1e-8
azimut = 180 * math.atan2(slow_x, slow_y) / math.pi
baz[i, j] = azimut % -360 + 180
baz[baz < 0.0] += 360
# transform to radian,
baz = np.radians(baz)
cmap = cm.RdYlBu
fig = plt.figure(figsize=(8, 8))
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.pcolormesh(baz, slow, transff, vmin=0., vmax=1., cmap=cmap)
ax.set_theta_direction(-1)
ax.set_theta_zero_location("N")
ax.set_ylim(0, slim)
ax.grid()
fig.suptitle('Array response function')
ColorbarBase(cax, cmap=cmap, norm=Normalize(vmin=0., vmax=1.))
plt.show()
def test_array_transff_freqslowness(self):
coords = np.array([[10., 60., 0.], [200., 50., 0.], [-120., 170., 0.],
[-100., -150., 0.], [30., -220., 0.]])
coords /= 1000.
coordsll = np.zeros(coords.shape)
for i in np.arange(len(coords)):
coordsll[i, 0], coordsll[i, 1] = utlLonLat(0., 0., coords[i, 0],
coords[i, 1])
slim = 40.
fmin = 1.
fmax = 10.
fstep = 1.
sstep = slim / 2.
transff = array_transff_freqslowness(coords,
slim,
sstep,
fmin,
fmax,
fstep,
coordsys='xy')
transffll = array_transff_freqslowness(coordsll,
slim,
sstep,
fmin,
fmax,
fstep,
coordsys='lonlat')
transffth = np.array(
[[0.41915119, 0.33333333, 0.32339525, 0.24751548, 0.67660475],
[0.25248452, 0.41418215, 0.34327141, 0.65672859, 0.33333333],
[0.24751548, 0.25248452, 1.00000000, 0.25248452, 0.24751548],
[0.33333333, 0.65672859, 0.34327141, 0.41418215, 0.25248452],
[0.67660475, 0.24751548, 0.32339525, 0.33333333, 0.41915119]])
np.testing.assert_array_almost_equal(transff, transffth, decimal=6)
np.testing.assert_array_almost_equal(transffll, transffth, decimal=6)
def arf(self, coords, fmin, flim, slim, sgrid):
sstep = sgrid
fstep = flim / 40
fmax = flim
transff = array_transff_freqslowness(coords,
slim,
sstep,
fmin,
fmax,
fstep,
coordsys='lonlat')
return transff
def plotARF_slowaz(coords,
slim,
sstep,
freqlow,
freqhigh,
fstep,
coordsys='xy'):
"""
Add ability to plot range of frequency ranges
"""
transff = array_transff_freqslowness(coords,
slim,
sstep,
freqlow,
freqhigh,
fstep,
coordsys=coordsys)
xgrid = np.arange(-slim, slim + sstep, sstep)
slow = np.empty((len(xgrid), len(xgrid)))
baz = slow.copy()
for i in np.arange(len(xgrid)):
for j in np.arange(len(xgrid)):
# compute baz, slow
slow_x = xgrid[i]
slow_y = xgrid[j]
slow[i, j] = np.sqrt(slow_x**2 + slow_y**2)
if slow[i, j] < 1e-8:
slow[i, j] = 1e-8
azimut = 180 * math.atan2(slow_x, slow_y) / math.pi
baz[i, j] = azimut % -360 + 180
baz[baz < 0.0] += 360
# transform to radian,
baz = np.radians(baz)
cmap = cm.RdYlBu
fig = plt.figure(figsize=(8, 8))
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.pcolormesh(baz, slow, transff, vmin=0., vmax=1., cmap=cmap)
ax.set_theta_direction(-1)
ax.set_theta_zero_location("N")
ax.set_ylim(0, slim)
ax.grid()
fig.suptitle('Array response function')
ColorbarBase(cax, cmap=cmap, norm=Normalize(vmin=0., vmax=1.))
plt.show()
def array_analysis_helper(stream, inventory, method, frqlow, frqhigh,
filter=True, baz_plot=True, static3D=False,
vel_corr=4.8, wlen=-1, slx=(-10, 10),
sly=(-10, 10), sls=0.5, array_response=True):
"""
Array analysis wrapper routine for MESS 2014.
:param stream: Waveforms for the array processing.
:type stream: :class:`obspy.core.stream.Stream`
:param inventory: Station metadata for waveforms
:type inventory: :class:`obspy.station.inventory.Inventory`
:param method: Method used for the array analysis
(one of "FK": Frequnecy Wavenumber, "DLS": Delay and Sum,
"PWS": Phase Weighted Stack, "SWP": Slowness Whitened Power).
:type method: str
:param filter: Whether to bandpass data to selected frequency range
:type filter: bool
:param frqlow: Low corner of frequency range for array analysis
:type frqlow: float
:param frqhigh: High corner of frequency range for array analysis
:type frqhigh: float
:param baz_plot: Whether to show backazimuth-slowness map (True) or
slowness x-y map (False).
:type baz_plot: str
:param static3D: static correction of topography using `vel_corr` as
velocity (slow!)
:type static3D: bool
:param vel_corr: Correction velocity for static topography correction in
km/s.
:type vel_corr: float
:param wlen: sliding window for analysis in seconds, use -1 to use the
whole trace without windowing.
:type wlen: float
:param slx: Min/Max slowness for analysis in x direction.
:type slx: (float, float)
:param sly: Min/Max slowness for analysis in y direction.
:type sly: (float, float)
:param sls: step width of slowness grid
:type sls: float
:param array_response: superimpose array reponse function in plot (slow!)
:type array_response: bool
"""
if method not in ("FK", "DLS", "PWS", "SWP"):
raise ValueError("Invalid method: ''" % method)
sllx, slmx = slx
slly, slmy = sly
starttime = max([tr.stats.starttime for tr in stream])
endtime = min([tr.stats.endtime for tr in stream])
stream.trim(starttime, endtime)
#stream.attach_response(inventory)
stream.merge()
for tr in stream:
for station in inventory[0].stations:
if tr.stats.station == station.code:
tr.stats.coordinates = \
AttribDict(dict(latitude=station.latitude,
longitude=station.longitude,
elevation=station.elevation))
break
if filter:
stream.filter('bandpass', freqmin=frqlow, freqmax=frqhigh,
zerophase=True)
print stream
spl = stream.copy()
tmpdir = tempfile.mkdtemp(prefix="obspy-")
filename_patterns = (os.path.join(tmpdir, 'pow_map_%03d.npy'),
os.path.join(tmpdir, 'apow_map_%03d.npy'))
def dump(pow_map, apow_map, i):
np.save(filename_patterns[0] % i, pow_map)
np.save(filename_patterns[1] % i, apow_map)
try:
# next step would be needed if the correction velocity needs to be
# estimated
#
sllx /= KM_PER_DEG
slmx /= KM_PER_DEG
slly /= KM_PER_DEG
slmy /= KM_PER_DEG
sls /= KM_PER_DEG
vc = vel_corr
if method == 'FK':
kwargs = dict(
#slowness grid: X min, X max, Y min, Y max, Slow Step
sll_x=sllx, slm_x=slmx, sll_y=slly, slm_y=slmy, sl_s=sls,
# sliding window properties
win_len=wlen, win_frac=0.8,
# frequency properties
frqlow=frqlow, frqhigh=frqhigh, prewhiten=0,
# restrict output
store=dump,
semb_thres=-1e9, vel_thres=-1e9, verbose=False,
timestamp='julsec', stime=starttime, etime=endtime,
method=0, correct_3dplane=False, vel_cor=vc,
static_3D=static3D)
# here we do the array processing
start = UTCDateTime()
out = AA.array_processing(stream, **kwargs)
print "Total time in routine: %f\n" % (UTCDateTime() - start)
# make output human readable, adjust backazimuth to values
# between 0 and 360
t, rel_power, abs_power, baz, slow = out.T
else:
kwargs = dict(
# slowness grid: X min, X max, Y min, Y max, Slow Step
sll_x=sllx, slm_x=slmx, sll_y=slly, slm_y=slmy, sl_s=sls,
# sliding window properties
# frequency properties
frqlow=frqlow, frqhigh=frqhigh,
# restrict output
store=dump,
win_len=wlen, win_frac=0.5,
nthroot=4, method=method,
verbose=False, timestamp='julsec',
stime=starttime, etime=endtime, vel_cor=vc,
static_3D=False)
# here we do the array processing
start = UTCDateTime()
out = AA.beamforming(stream, **kwargs)
print "Total time in routine: %f\n" % (UTCDateTime() - start)
# make output human readable, adjust backazimuth to values
# between 0 and 360
trace = []
t, rel_power, baz, slow_x, slow_y, slow = out.T
# calculating array response
if array_response:
stepsfreq = (frqhigh - frqlow) / 10.
tf_slx = sllx
tf_smx = slmx
tf_sly = slly
tf_smy = slmy
transff = AA.array_transff_freqslowness(
stream, (tf_slx, tf_smx, tf_sly, tf_smy), sls, frqlow,
frqhigh, stepsfreq, coordsys='lonlat',
correct_3dplane=False, static_3D=False, vel_cor=vc)
# now let's do the plotting
cmap = cm.rainbow
#
# we will plot everything in s/deg
slow *= KM_PER_DEG
sllx *= KM_PER_DEG
slmx *= KM_PER_DEG
slly *= KM_PER_DEG
slmy *= KM_PER_DEG
sls *= KM_PER_DEG
numslice = len(t)
powmap = []
slx = np.arange(sllx-sls, slmx, sls)
sly = np.arange(slly-sls, slmy, sls)
if baz_plot:
maxslowg = np.sqrt(slmx*slmx + slmy*slmy)
bzs = np.arctan2(sls, np.sqrt(slmx*slmx + slmy*slmy))*180/np.pi
xi = np.arange(0., maxslowg, sls)
yi = np.arange(-180., 180., bzs)
grid_x, grid_y = np.meshgrid(xi, yi)
# reading in the rel-power maps
for i in xrange(numslice):
powmap.append(np.load(filename_patterns[0] % i))
if method != 'FK':
trace.append(np.load(filename_patterns[1] % i))
npts = stream[0].stats.npts
df = stream[0].stats.sampling_rate
T = np.arange(0, npts / df, 1 / df)
# if we choose windowlen > 0. we now move through our slices
for i in xrange(numslice):
slow_x = np.sin((baz[i]+180.)*np.pi/180.)*slow[i]
slow_y = np.cos((baz[i]+180.)*np.pi/180.)*slow[i]
st = UTCDateTime(t[i]) - starttime
if wlen <= 0:
en = endtime
else:
en = st + wlen
print UTCDateTime(t[i])
# add polar and colorbar axes
fig = plt.figure(figsize=(12, 12))
ax1 = fig.add_axes([0.1, 0.87, 0.7, 0.10])
# here we plot the first trace on top of the slowness map
# and indicate the possibiton of the lsiding window as green box
if method == 'FK':
ax1.plot(T, spl[0].data, 'k')
if wlen > 0.:
try:
ax1.axvspan(st, en, facecolor='g', alpha=0.3)
except IndexError:
pass
else:
T = np.arange(0, len(trace[i])/df, 1 / df)
ax1.plot(T, trace[i], 'k')
ax1.yaxis.set_major_locator(MaxNLocator(3))
ax = fig.add_axes([0.10, 0.1, 0.70, 0.7])
# if we have chosen the baz_plot option a re-griding
# of the sx,sy slowness map is needed
if baz_plot:
slowgrid = []
transgrid = []
pow = np.asarray(powmap[i])
for ix, sx in enumerate(slx):
for iy, sy in enumerate(sly):
bbaz = np.arctan2(sx, sy)*180/np.pi+180.
if bbaz > 180.:
bbaz = -180. + (bbaz-180.)
slowgrid.append((np.sqrt(sx*sx+sy*sy), bbaz,
pow[ix, iy]))
if array_response:
tslow = (np.sqrt((sx+slow_x) *
(sx+slow_x)+(sy+slow_y) *
(sy+slow_y)))
tbaz = (np.arctan2(sx+slow_x, sy+slow_y) *
180 / np.pi + 180.)
if tbaz > 180.:
tbaz = -180. + (tbaz-180.)
transgrid.append((tslow, tbaz,
transff[ix, iy]))
slowgrid = np.asarray(slowgrid)
sl = slowgrid[:, 0]
bz = slowgrid[:, 1]
slowg = slowgrid[:, 2]
grid = spi.griddata((sl, bz), slowg, (grid_x, grid_y),
method='nearest')
ax.pcolormesh(xi, yi, grid, cmap=cmap)
if array_response:
level = np.arange(0.1, 0.5, 0.1)
transgrid = np.asarray(transgrid)
tsl = transgrid[:, 0]
tbz = transgrid[:, 1]
transg = transgrid[:, 2]
trans = spi.griddata((tsl, tbz), transg,
(grid_x, grid_y),
method='nearest')
ax.contour(xi, yi, trans, level, colors='k',
linewidth=0.2)
ax.set_xlabel('slowness [s/deg]')
ax.set_ylabel('backazimuth [deg]')
ax.set_xlim(xi[0], xi[-1])
ax.set_ylim(yi[0], yi[-1])
else:
ax.set_xlabel('slowness [s/deg]')
ax.set_ylabel('slowness [s/deg]')
slow_x = np.cos((baz[i]+180.)*np.pi/180.)*slow[i]
slow_y = np.sin((baz[i]+180.)*np.pi/180.)*slow[i]
ax.pcolormesh(slx, sly, powmap[i].T)
ax.arrow(0, 0, slow_y, slow_x, head_width=0.005,
head_length=0.01, fc='k', ec='k')
if array_response:
tslx = np.arange(sllx+slow_x, slmx+slow_x+sls, sls)
tsly = np.arange(slly+slow_y, slmy+slow_y+sls, sls)
try:
ax.contour(tsly, tslx, transff.T, 5, colors='k',
linewidth=0.5)
except:
pass
ax.set_ylim(slx[0], slx[-1])
ax.set_xlim(sly[0], sly[-1])
new_time = t[i]
result = "BAZ: %.2f, Slow: %.2f s/deg, Time %s" % (
baz[i], slow[i], UTCDateTime(new_time))
ax.set_title(result)
plt.show()
finally:
shutil.rmtree(tmpdir)
def array_transfer_helper(stream, inventory, sx=(-10, 10), sy=(-10, 10),
sls=0.5, freqmin=0.1, freqmax=4.0, numfreqs=10,
coordsys='lonlat', correct3dplane=False,
static3D=False, velcor=4.8):
"""
Array Response wrapper routine for MESS 2014.
:param stream: Waveforms for the array processing.
:type stream: :class:`obspy.core.stream.Stream`
:param inventory: Station metadata for waveforms
:type inventory: :class:`obspy.station.inventory.Inventory`
:param slx: Min/Max slowness for analysis in x direction.
:type slx: (float, float)
:param sly: Min/Max slowness for analysis in y direction.
:type sly: (float, float)
:param sls: step width of slowness grid
:type sls: float
:param frqmin: Low corner of frequency range for array analysis
:type frqmin: float
:param frqmax: High corner of frequency range for array analysis
:type frqmax: float
:param numfreqs: number of frequency values used for computing array
transfer function
:type numfreqs: int
:param coordsys: defined coordingate system of stations (lonlat or km)
:type coordsys: string
:param correct_3dplane: correct for an inclined surface (not used)
:type correct_3dplane: bool
:param static_3D: correct topography
:type static_3D: bool
:param velcor: velocity used for static_3D correction
:type velcor: float
"""
for tr in stream:
for station in inventory[0].stations:
if tr.stats.station == station.code:
tr.stats.coordinates = \
AttribDict(dict(latitude=station.latitude,
longitude=station.longitude,
elevation=station.elevation))
break
sllx, slmx = sx
slly, slmy = sx
sllx /= KM_PER_DEG
slmx /= KM_PER_DEG
slly /= KM_PER_DEG
slmy /= KM_PER_DEG
sls = sls/KM_PER_DEG
stepsfreq = (freqmax - freqmin) / float(numfreqs)
transff = AA.array_transff_freqslowness(
stream, (sllx, slmx, slly, slmy), sls, freqmin, freqmax, stepsfreq,
coordsys=coordsys, correct_3dplane=False, static_3D=static3D,
vel_cor=velcor)
sllx *= KM_PER_DEG
slmx *= KM_PER_DEG
slly *= KM_PER_DEG
slmy *= KM_PER_DEG
sls *= KM_PER_DEG
slx = np.arange(sllx, slmx+sls, sls)
sly = np.arange(slly, slmy+sls, sls)
fig = plt.figure(figsize=(12, 12))
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8])
#ax.pcolormesh(slx, sly, transff.T)
ax.contour(sly, slx, transff.T, 10)
ax.set_xlabel('slowness [s/deg]')
ax.set_ylabel('slowness [s/deg]')
ax.set_ylim(slx[0], slx[-1])
ax.set_xlim(sly[0], sly[-1])
plt.show()
