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 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
