def dBzdtAnalCircTCole(a, t, sigma):
wt, tbase, omega_int = setFrequency(t)
hz = HzanalCirc(sigma, omega_int/2/np.pi, 1., a, 'secondary')
# Treatment for inaccuracy in analytic solutions
ind = omega_int < 0.2
hz[ind] = 0.
dhzdtTD = -transFiltImpulse(hz, wt, tbase, omega_int, t)
return dhzdtTD*mu_0
def projectFields(self, u):
"""
Transform frequency domain responses to time domain responses
"""
# Case1: Compute frequency domain reponses right at filter coefficient values
if self.switchInterp == False:
# Tx waveform: Step-off
if self.waveType == 'stepoff':
if self.rxType == 'Bz':
# Compute EM responses
if u.size == self.Nfreq:
resp, f0 = transFilt(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i], f0 = transFilt(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.time)
elif self.rxType == 'dBzdt':
# Compute EM responses
if u.size == self.Nfreq:
resp = -transFiltImpulse(u, self.wt,self.tbase, self.frequency*2*np.pi, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i] = -transFiltImpulse(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.time)
# Tx waveform: General (it can be any waveform)
# We evaluate this with time convolution
elif self.waveType == 'general':
# Compute EM responses
if u.size == self.Nfreq:
# TODO: write small code which compute f at t = 0
f, f0 = transFilt(Utils.mkvc(u), self.wt, self.tbase, self.frequency*2*np.pi, self.tconv)
fDeriv = -transFiltImpulse(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp = respint(self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
f, f0 = transFilt(u[:,i], self.wt, self.tbase, self.frequency*2*np.pi, self.tconv)
fDeriv = -transFiltImpulse(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp[:,i] = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp[:,i] = respint(self.time)
# Case2: Compute frequency domain reponses in logarithmic then intepolate
if self.switchInterp == True:
# Tx waveform: Step-off
if self.waveType == 'stepoff':
if self.rxType == 'Bz':
# Compute EM responses
if u.size == self.Nfreq:
resp, f0 = transFiltInterp(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i], f0 = transFiltInterp(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
elif self.rxType == 'dBzdt':
# Compute EM responses
if u.size == self.Nfreq:
resp = -transFiltImpulseInterp(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
resp[:,i] = -transFiltImpulseInterp(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.time)
# Tx waveform: General (it can be any waveform)
# We evaluate this with time convolution
elif self.waveType == 'general':
# Compute EM responses
if u.size == self.Nfreq:
# TODO: write small code which compute f at t = 0
f, f0 = transFiltInterp(Utils.mkvc(u), self.wt, self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
fDeriv = -transFiltImpulseInterp(Utils.mkvc(u), self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp = respint(self.time)
# Compute EM sensitivities
else:
resp = np.zeros((self.Nch, self.nlay))
for i in range (self.nlay):
f, f0 = transFiltInterp(u[:,i], self.wt, self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
fDeriv = -transFiltImpulseInterp(u[:,i], self.wt,self.tbase, self.frequency*2*np.pi, self.omega_int, self.tconv)
if self.rxType == 'Bz':
waveConvfDeriv = CausalConv(self.waveform, fDeriv, self.tconv)
resp1 = (self.waveform*self.hp*(1-f0[1]/self.hp)) - waveConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
# TODO: make it as an opition #2
# waveDerivConvf = CausalConv(self.waveformDeriv, f, self.tconv)
# resp2 = (self.waveform*self.hp) - waveDerivConvf
# respint = interp1d(self.tconv, resp2, 'linear')
resp[:,i] = respint(self.time)
if self.rxType == 'dBzdt':
waveDerivConvfDeriv = CausalConv(self.waveformDeriv, fDeriv, self.tconv)
resp1 = self.hp*self.waveformDeriv*(1-f0[1]/self.hp) - waveDerivConvfDeriv
respint = interp1d(self.tconv, resp1, 'linear')
resp[:,i] = respint(self.time)
return mu_0*resp
