def Envelope(syn, obs, nt, dt, eps=0.05):
# envelope difference
# (Yuan et al 2015, eq 9)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
ersd = esyn - eobs
return _np.sqrt(_np.sum(ersd * ersd * dt))
def Envelope(syn, obs, nt, dt, eps=0.05):
# envelope difference
# (Yuan et al 2015, eq 9)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
ersd = esyn-eobs
return np.sqrt(np.sum(ersd*ersd*dt))
def Envelope(syn, obs, nt, dt, eps=0.05):
# envelope difference
# (Yuan et al 2015, eq 16)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
etmp = (esyn - eobs)/(esyn + eps*esyn.max())
wadj = etmp*syn - _np.imag(_analytic(etmp*_np.imag(_analytic(syn))))
return wadj
def Envelope(syn, obs, nt, dt, eps=0.05):
# envelope difference
# (Yuan et al 2015, eq 16)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
etmp = (esyn - eobs) / (esyn + eps * esyn.max())
wadj = etmp * syn - _np.imag(_analytic(etmp * _np.imag(_analytic(syn))))
return wadj
def InstantaneousPhase2(syn, obs, nt, dt, eps=0.):
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
esyn1 = esyn + eps * max(esyn)
eobs1 = eobs + eps * max(eobs)
diff = syn / esyn1 - obs / eobs1
return _np.sqrt(_np.sum(diff * diff * dt))
def AnalyticSignal(syn, obs, nt, dt, eps=0.):
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
esyn1 = esyn + eps * max(esyn)
eobs1 = eobs + eps * max(eobs)
diff = syn / esyn1 - obs / eobs1
return _np.sqrt(_np.sum(diff * diff * dt))
def InstantaneousPhase2(syn, obs, nt, dt, eps=0.):
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
esyn1 = esyn + eps*max(esyn)
eobs1 = eobs + eps*max(eobs)
diff = syn/esyn1 - obs/eobs1
return np.sqrt(np.sum(diff*diff*dt))
def AnalyticSignal(syn, obs, nt, dt, eps=0.):
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
esyn1 = esyn + eps*max(esyn)
eobs1 = eobs + eps*max(eobs)
diff = syn/esyn1 - obs/eobs1
return _np.sqrt(_np.sum(diff*diff*dt))
def Envelope3(syn, obs, nt, dt, eps=0.):
# envelope lag
# (Yuan et al 2015, eqs B-2, B-5)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
erat = _np.zeros(nt)
erat[1:-1] = (esyn[2:] - esyn[0:-2])/(2.*dt)
erat[1:-1] /= esyn[1:-1]
erat *= misfit.Envelope3(syn, obs, nt, dt)
wadj = -erat*syn + _hilbert(erat*_hilbert(esyn))
return wadj
def Envelope3(syn, obs, nt, dt, eps=0.):
# envelope lag
# (Yuan et al 2015, eqs B-2, B-5)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
erat = _np.zeros(nt)
erat[1:-1] = (esyn[2:] - esyn[0:-2]) / (2. * dt)
erat[1:-1] /= esyn[1:-1]
erat *= misfit.Envelope3(syn, obs, nt, dt)
wadj = -erat * syn + _hilbert(erat * _hilbert(esyn))
return wadj
def InstantaneousPhase(syn, obs, nt, dt, eps=0.05):
""" Instantaneous phase from Bozdag et al. 2011
"""
r = np.real(_analytic(syn))
i = np.imag(_analytic(syn))
phi_syn = np.arctan2(i, r)
r = np.real(_analytic(obs))
i = np.imag(_analytic(obs))
phi_obs = np.arctan2(i, r)
phi_rsd = phi_syn - phi_obs
return np.sqrt(np.sum(phi_rsd * phi_rsd * dt))
def InstantaneousPhase(syn, obs, nt, dt, eps=0.05):
# instantaneous phase
# from Bozdag et al. 2011
r = _np.real(_analytic(syn))
i = _np.imag(_analytic(syn))
phi_syn = _np.arctan2(i, r)
r = _np.real(_analytic(obs))
i = _np.imag(_analytic(obs))
phi_obs = _np.arctan2(i, r)
phi_rsd = phi_syn - phi_obs
return _np.sqrt(_np.sum(phi_rsd * phi_rsd * dt))
def InstantaneousPhase(syn, obs, nt, dt, eps=0.05):
# instantaneous phase
# from Bozdag et al. 2011
r = np.real(_analytic(syn))
i = np.imag(_analytic(syn))
phi_syn = np.arctan2(i,r)
r = np.real(_analytic(obs))
i = np.imag(_analytic(obs))
phi_obs = np.arctan2(i,r)
phi_rsd = phi_syn - phi_obs
return np.sqrt(np.sum(phi_rsd*phi_rsd*dt))
def InstantaneousPhase2(syn, obs, nt, dt, eps=0.):
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
esyn1 = esyn + eps*max(esyn)
eobs1 = eobs + eps*max(eobs)
esyn3 = esyn**3 + eps*max(esyn**3)
diff1 = syn/(esyn1) - obs/(eobs1)
diff2 = _hilbert(syn)/esyn1 - _hilbert(obs)/eobs1
part1 = diff1*_hilbert(syn)**2/esyn3 - diff2*syn*_hilbert(syn)/esyn3
part2 = diff1*syn*_hilbert(syn)/esyn3 - diff2*syn**2/esyn3
wadj = part1 + _hilbert(part2)
return wadj
def InstantaneousPhase2(syn, obs, nt, dt, eps=0.):
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
esyn1 = esyn + eps*max(esyn)
eobs1 = eobs + eps*max(eobs)
esyn3 = esyn**3 + eps*max(esyn**3)
diff1 = syn/(esyn1) - obs/(eobs1)
diff2 = _hilbert(syn)/esyn1 - _hilbert(obs)/eobs1
part1 = diff1*_hilbert(syn)**2/esyn3 - diff2*syn*_hilbert(syn)/esyn3
part2 = diff1*syn*_hilbert(syn)/esyn3 - diff2*syn**2/esyn3
wadj = part1 + _hilbert(part2)
return wadj
def Envelope(syn, obs, nt, dt, eps=0.05):
# envelope difference
# (Yuan et al 2015, eq 16)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
#######original########
#etmp = (esyn - eobs)/(esyn + eps*esyn.max())
#######original########
#######jiang change start########
# avoid divide zero when mute near-offset data
if esyn.max() == 0.0:
etmp = (esyn - eobs) / (esyn + eps * esyn.max() + eps)
else:
etmp = (esyn - eobs) / (esyn + eps * esyn.max())
#######jiang change end########
wadj = etmp * syn - _np.imag(_analytic(etmp * _np.imag(_analytic(syn))))
return wadj
def InstantaneousPhase(syn, obs, nt, dt, eps=0.05):
# instantaneous phase
# (Bozdag et al 2011, eq 27)
r = _np.real(_analytic(syn))
i = _np.imag(_analytic(syn))
phi_syn = _np.arctan2(i, r)
r = _np.real(_analytic(obs))
i = _np.imag(_analytic(obs))
phi_obs = _np.arctan2(i, r)
phi_rsd = phi_syn - phi_obs
esyn = abs(_analytic(syn))
emax = max(esyn**2.)
wadj = phi_rsd*_np.imag(_analytic(syn))/(esyn**2. + eps*emax) + \
_np.imag(_analytic(phi_rsd * syn/(esyn**2. + eps*emax)))
return wadj
def InstantaneousPhase(syn, obs, nt, dt, eps=0.05):
# instantaneous phase
# (Bozdag et al 2011, eq 27)
r = _np.real(_analytic(syn))
i = _np.imag(_analytic(syn))
phi_syn = _np.arctan2(i,r)
r = _np.real(_analytic(obs))
i = _np.imag(_analytic(obs))
phi_obs = _np.arctan2(i,r)
phi_rsd = phi_syn - phi_obs
esyn = abs(_analytic(syn))
emax = max(esyn**2.)
wadj = phi_rsd*_np.imag(_analytic(syn))/(esyn**2. + eps*emax) + \
_np.imag(_analytic(phi_rsd * syn/(esyn**2. + eps*emax)))
return wadj
def Envelope3(syn, obs, nt, dt, eps=0.):
# envelope cross-correlation lag
# (Yuan et al 2015, eqs B-4)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
return Traveltime(esyn, eobs, nt, dt)
def Envelope3(syn, obs, nt, dt, eps=0.):
# envelope cross-correlation lag
# (Yuan et al 2015, eqs B-4)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
return Traveltime(esyn, eobs, nt, dt)
def Envelope2(syn, obs, nt, dt, eps=0.):
# envelope amplitude ratio
# (Yuan et al 2015, eq B-1)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
raise NotImplementedError
def Envelope2(syn, obs, nt, dt, eps=0.):
# envelope amplitude ratio
# (Yuan et al 2015, eq B-1)
esyn = abs(_analytic(syn))
eobs = abs(_analytic(obs))
raise NotImplementedError
