def coherence(datai, datas): """ Calculate time domain coherence. Coherence is 1 - sin of the angle made by two vectors: di and ds. Di is data vector, and ds is the unit vector of array stack. res(di) = di - (di . ds) ds coh(di) = 1 - res(di) / ||di|| """ return 1 - l2norm(datai - dot(datai, datas)*datas)/l2norm(datai)
def coherence(datai, datas): """ Calculate time domain coherence. Coherence is 1 - sin of the angle made by two vectors: di and ds. Di is data vector, and ds is the unit vector of array stack. res(di) = di - (di . ds) ds coh(di) = 1 - res(di) / ||di|| """ return 1 - l2norm(datai - dot(datai, datas)*datas)/l2norm(datai)
def snratio(data, delta, timewindow):
"""
Calculate signal/noise ratio within the given time window.
Time window is relative, such as [-10, 20], to the onset of the arrival.
"""
tw0, tw1 = timewindow
nn = round(-tw0/delta)
yn = data[:nn]
ys = data[nn:]
ns = len(ys)
rr = l2norm(ys)/l2norm(yn)*sqrt(nn)/sqrt(ns)
if l2norm(yn) == 0:
print ('snr', l2norm(yn))
### the same as:
#rr = sqrt(sum(square(ys))/sum(square(yn))*nn/ns)
# shoud signal be the whole time seris?
#yw = data[:]
#nw = len(yw)
#rw = sqrt(sum(square(yw))/sum(square(yn))*nn/nw)
return rr
def snratio(data, delta, timewindow):
"""
Calculate signal/noise ratio within the given time window.
Time window is relative, such as [-10, 20], to the onset of the arrival.
"""
tw0, tw1 = timewindow
nn = int(round(-tw0/delta))
yn = data[:nn]
ys = data[nn:]
ns = len(ys)
rr = l2norm(ys)/l2norm(yn)*sqrt(nn)/sqrt(ns)
if l2norm(yn) == 0:
print ('snr', l2norm(yn))
### the same as:
#rr = sqrt(sum(square(ys))/sum(square(yn))*nn/ns)
# shoud signal be the whole time seris?
#yw = data[:]
#nw = len(yw)
#rw = sqrt(sum(square(yw))/sum(square(yn))*nn/nw)
return rr
def checkCoverage(gsac, opts, textra=0.0):
""" Check if each seismogram has enough samples around the time window relative to ipick.
"""
ipick = opts.ipick
tw0, tw1 = opts.twcorr
saclist = gsac.saclist
nsac = len(saclist)
indsel, inddel = [], []
for i in range(nsac):
sacdh = saclist[i]
t0 = sacdh.gethdr(ipick)
b = sacdh.b
e = b + (sacdh.npts-1)*sacdh.delta
if b-textra > t0+tw0 or e+textra < t0+tw1:
inddel.append(i)
print ('Seismogram {0:s} does not have enough sample. Deleted.'.format(sacdh.filename))
elif l2norm(sacdh.data) == 0.0:
inddel.append(i)
print ('Seismogram {0:s} has zero l2norm. Deleted.'.format(sacdh.filename))
else:
indsel.append(i)
if inddel != []:
gsac.saclist = [ saclist[i] for i in indsel ]
def checkCoverage(gsac, opts, textra=0.0):
""" Check if each seismogram has enough samples around the time window relative to ipick.
"""
ipick = opts.ipick
tw0, tw1 = opts.twcorr
saclist = gsac.saclist
nsac = len(saclist)
indsel, inddel = [], []
for i in range(nsac):
sacdh = saclist[i]
t0 = sacdh.gethdr(ipick)
b = sacdh.b
e = b + (sacdh.npts-1)*sacdh.delta
if b-textra > t0+tw0 or e+textra < t0+tw1:
inddel.append(i)
print ('Seismogram {0:s} does not have enough sample. Deleted.'.format(sacdh.filename))
elif l2norm(sacdh.data) == 0.0:
inddel.append(i)
print ('Seismogram {0:s} has zero l2norm. Deleted.'.format(sacdh.filename))
else:
indsel.append(i)
if inddel != []:
gsac.saclist = [ saclist[i] for i in indsel ]
def reConverg(stack0, stack1): """ Calcuate criterion of convergence by change of stack. stack0 and stack1 are current stack and stack from last iteration. """ return l1norm(stack0-stack1)/l2norm(stack0)/len(stack0)
def ccWeightStack(saclist, opts):
"""
Align seismograms by the iterative cross-correlation and stack algorithm.
Parameters
----------
opts.delta : sample time interval
opts.ccpara : a class instance for ICCS parameters
* qqhdrs : SAC headers to save quality factors: ccc, snr, coh
* maxiter : maximum number of iteration
* converg : convergence critrion
* cchdrs : inputand output picks of cross-correlation
* twcorr : time window for cross-correlation
"""
ccpara = opts.ccpara
delta = opts.delta
maxiter = ccpara.maxiter
convtype = ccpara.convtype
convepsi = ccpara.convepsi
taperwidth = ccpara.taperwidth
tapertype = ccpara.tapertype
xcorr = ccpara.xcorr
shift = ccpara.shift
twhdrs = ccpara.twhdrs
qqhdrs = ccpara.qheaders
cchdrs = ccpara.cchdrs
twcorr = ccpara.twcorr
hdrccc, hdrsnr, hdrcoh, = qqhdrs[:3]
cchdr0, cchdr1 = cchdrs
if convtype == 'coef':
convergence = coConverg
elif convtype == 'resi':
convergence = reConverg
else:
print('Unknown convergence criterion: {:s}. Exit.'.format(convtype))
sys.exit()
out = '\n--> Run ICCS at window [{0:5.1f}, {1:5.1f}] wrt {2:s}. Write to header: {3:s}'
print(out.format(twcorr[0], twcorr[1], cchdr0, cchdr1))
print(' Convergence criterion: {:s}'.format(convtype))
if ccpara.stackwgt == 'coef':
wgtcoef = True
else:
wgtcoef = False
taperwindow = taperWindow(twcorr, taperwidth)
# get initial time picks
tinis = array([ sacdh.gethdr(cchdr0) for sacdh in saclist])
tfins = tinis.copy()
nseis = len(saclist)
ccc = zeros(nseis)
snr = zeros(nseis)
coh = zeros(nseis)
wgts = ones(nseis)
stkdata = []
for it in range(maxiter):
# recut data and update array stack
nstart, ntotal = windowIndex(saclist, tfins, twcorr, taperwindow)
windata = windowData(saclist, nstart, ntotal, taperwidth, tapertype)
sdata = normWeightStack(windata, wgts, taperwidth, tapertype)
stkdata.append(sdata)
if it == 0:
print ('=== Iteration {0:d} : epsilon'.format(it))
else:
conv = convergence(stkdata[it], stkdata[it-1])
print ('=== Iteration {0:d} : {1:8.6f}'.format(it, conv))
if conv <= convepsi:
print ('Array stack converged... Done. Mean corrcoef={0:.3f}'.format(mean(ccc)))
break
# Find time lag at peak correlation between each trace and the array stack.
# Calculate cross correlation coefficient, signal/noise ratio and temporal coherence
sdatanorm = sdata/l2norm(sdata)
for i in range(nseis):
datai = windata[i]
delay, ccmax, ccpol = corrmax(sdata, datai, delta, xcorr, shift)
tfins[i] += delay
sacdh = saclist[i]
sacdh.sethdr(cchdr1, tfins[i])
if wgtcoef: # update weight only when stackwgt == coef
wgts[i] = ccpol * ccmax
ccc[i] = ccmax
sacdh.sethdr(hdrccc, ccc[i])
snr[i] = snratio(datai, delta, twcorr)
sacdh.sethdr(hdrsnr, snr[i])
coh[i] = coherence(datai*ccpol, sdatanorm)
sacdh.sethdr(hdrcoh, coh[i])
# get maximum time window for plot (excluding taperwindow)
bb, ee = [], []
for i in range(nseis):
sacdh = saclist[i]
b = sacdh.b - tfins[i]
e = b + (sacdh.npts-1)* delta
bb.append(b+delta)
ee.append(e-delta)
b = max(bb)
e = min(ee)
d = (e-b)*taperwidth/2
twplot = [b+d, e-d]
# calculate final stack at twplot, save to a sacdh object: stkdh
# set time picks of stkdh as mean of tinis and tfins
taperwindow = taperWindow(twplot, taperwidth)
nstart, ntotal = windowIndex(saclist, tfins, twplot, taperwindow)
windata = windowData(saclist, nstart, ntotal, taperwidth, tapertype)
sdata = normWeightStack(windata, wgts, taperwidth, tapertype)
tinimean = mean(tinis)
tfinmean = mean(tfins)
stkdh = copy.copy(saclist[0])
stkdh.thdrs = [-12345.,] * 10
stkdh.users = [-12345.,] * 10
stkdh.kusers = ['-12345 ',] * 3
stkdh.b = twplot[0] - taperwindow*0.5 + tfinmean
stkdh.npts = len(sdata)
stkdh.data = sdata
stkdh.sethdr(cchdr0, tinimean)
stkdh.sethdr(cchdr1, tfinmean)
stkdh.knetwk = 'Array '
stkdh.kstnm = 'Stack '
stkdh.netsta = 'Array.Stack'
stkdh.gcarc = -1
stkdh.dist = -1
stkdh.baz = -1
stkdh.az = -1
# set time window
stkdh.sethdr(twhdrs[0], twcorr[0]+tfinmean)
stkdh.sethdr(twhdrs[1], twcorr[1]+tfinmean)
if opts.fstack is None:
stkdh.filename = ccpara.fstack
else:
stkdh.filename = opts.fstack
for sacdh, tfin in zip(saclist, tfins):
sacdh.sethdr(twhdrs[0], tfin+twcorr[0])
sacdh.sethdr(twhdrs[1], tfin+twcorr[1])
quas = array([ ccc, snr, coh ])
return stkdh, stkdata, quas
def reConverg(stack0, stack1): """ Calcuate criterion of convergence by change of stack. stack0 and stack1 are current stack and stack from last iteration. """ return l1norm(stack0-stack1)/l2norm(stack0)/len(stack0)
def ccWeightStack(saclist, opts):
"""
Align seismograms by the iterative cross-correlation and stack algorithm.
Parameters
----------
opts.delta : sample time interval
opts.ccpara : a class instance for ICCS parameters
* qqhdrs : SAC headers to save quality factors: ccc, snr, coh
* maxiter : maximum number of iteration
* converg : convergence critrion
* cchdrs : inputand output picks of cross-correlation
* twcorr : time window for cross-correlation
"""
ccpara = opts.ccpara
delta = opts.delta
maxiter = ccpara.maxiter
convtype = ccpara.convtype
convepsi = ccpara.convepsi
taperwidth = ccpara.taperwidth
tapertype = ccpara.tapertype
xcorr = ccpara.xcorr
shift = ccpara.shift
twhdrs = ccpara.twhdrs
qqhdrs = ccpara.qheaders
cchdrs = ccpara.cchdrs
twcorr = ccpara.twcorr
hdrccc, hdrsnr, hdrcoh, = qqhdrs[:3]
cchdr0, cchdr1 = cchdrs
if convtype == 'coef':
convergence = coConverg
elif convtype == 'resi':
convergence = reConverg
else:
print('Unknown convergence criterion: {:s}. Exit.'.format(convtype))
sys.exit()
out = '\n--> Run ICCS at window [{0:5.1f}, {1:5.1f}] wrt {2:s}. Write to header: {3:s}'
print(out.format(twcorr[0], twcorr[1], cchdr0, cchdr1))
print(' Convergence criterion: {:s}'.format(convtype))
if ccpara.stackwgt == 'coef':
wgtcoef = True
else:
wgtcoef = False
taperwindow = taperWindow(twcorr, taperwidth)
# get initial time picks
tinis = array([ sacdh.gethdr(cchdr0) for sacdh in saclist])
tfins = tinis.copy()
nseis = len(saclist)
ccc = zeros(nseis)
snr = zeros(nseis)
coh = zeros(nseis)
wgts = ones(nseis)
stkdata = []
for it in range(maxiter):
# recut data and update array stack
nstart, ntotal = windowIndex(saclist, tfins, twcorr, taperwindow)
windata = windowData(saclist, nstart, ntotal, taperwidth, tapertype)
sdata = normWeightStack(windata, wgts, taperwidth, tapertype)
stkdata.append(sdata)
if it == 0:
print ('=== Iteration {0:d} : epsilon'.format(it))
else:
conv = convergence(stkdata[it], stkdata[it-1])
print ('=== Iteration {0:d} : {1:8.6f}'.format(it, conv))
if conv <= convepsi:
print ('Array stack converged... Done. Mean corrcoef={0:.3f}'.format(mean(ccc)))
break
# Find time lag at peak correlation between each trace and the array stack.
# Calculate cross correlation coefficient, signal/noise ratio and temporal coherence
sdatanorm = sdata/l2norm(sdata)
for i in range(nseis):
datai = windata[i]
delay, ccmax, ccpol = corrmax(sdata, datai, delta, xcorr, shift)
tfins[i] += delay
sacdh = saclist[i]
sacdh.sethdr(cchdr1, tfins[i])
if wgtcoef: # update weight only when stackwgt == coef
wgts[i] = ccpol * ccmax
ccc[i] = ccmax
sacdh.sethdr(hdrccc, ccc[i])
snr[i] = snratio(datai, delta, twcorr)
sacdh.sethdr(hdrsnr, snr[i])
coh[i] = coherence(datai*ccpol, sdatanorm)
sacdh.sethdr(hdrcoh, coh[i])
# get maximum time window for plot (excluding taperwindow)
bb, ee = [], []
for i in range(nseis):
sacdh = saclist[i]
b = sacdh.b - tfins[i]
e = b + (sacdh.npts-1)* delta
bb.append(b+delta)
ee.append(e-delta)
b = max(bb)
e = min(ee)
d = (e-b)*taperwidth/2
twplot = [b+d, e-d]
# calculate final stack at twplot, save to a sacdh object: stkdh
# set time picks of stkdh as mean of tinis and tfins
taperwindow = taperWindow(twplot, taperwidth)
nstart, ntotal = windowIndex(saclist, tfins, twplot, taperwindow)
windata = windowData(saclist, nstart, ntotal, taperwidth, tapertype)
sdata = normWeightStack(windata, wgts, taperwidth, tapertype)
tinimean = mean(tinis)
tfinmean = mean(tfins)
stkdh = copy.copy(saclist[0])
stkdh.thdrs = [-12345.,] * 10
stkdh.users = [-12345.,] * 10
stkdh.kusers = ['-12345 ',] * 3
stkdh.b = twplot[0] - taperwindow*0.5 + tfinmean
stkdh.npts = len(sdata)
stkdh.data = sdata
stkdh.sethdr(cchdr0, tinimean)
stkdh.sethdr(cchdr1, tfinmean)
stkdh.knetwk = 'Array '
stkdh.kstnm = 'Stack '
stkdh.netsta = 'Array.Stack'
stkdh.gcarc = -1
stkdh.dist = -1
stkdh.baz = -1
stkdh.az = -1
# set time window
stkdh.sethdr(twhdrs[0], twcorr[0]+tfinmean)
stkdh.sethdr(twhdrs[1], twcorr[1]+tfinmean)
if opts.fstack is None:
stkdh.filename = ccpara.fstack
else:
stkdh.filename = opts.fstack
for sacdh, tfin in zip(saclist, tfins):
sacdh.sethdr(twhdrs[0], tfin+twcorr[0])
sacdh.sethdr(twhdrs[1], tfin+twcorr[1])
quas = array([ ccc, snr, coh ])
return stkdh, stkdata, quas