def test_bipole(self, capsys):
# 1. Compare to bipole in the frequency domain, to ensure it is the
# same.
# Survey parameters.
depth = [0, 200]
res = [2e14, 100, 200]
freq = np.logspace(-4, 4, 101)
# 1.a: msrc-mrec; nrec==nrecz, nsrc!=nsrcz.
rec = [100, 0, 0, 23, -50]
src = [[0, 0, 0], [0, 0, 0], 0, 45, 33]
loo = loop(src, rec, depth, res, freq)
bip = bipole(src, rec, depth, res, freq, msrc=True, mrec=True)
bip *= 2j*np.pi*freq[:, None]*4e-7*np.pi
assert_allclose(bip, loo, rtol=1e-4, atol=1e-18)
# 1.b: msrc-erec; nrec!=nrecz, nsrc!=nsrcz.
rec = [[100, 200, 300], [-10, 0, 10], 0, 23, -50]
src = [[0, 0, 0], [0, 0, 0], 0, 45, 33]
loo = loop(src, rec, depth, res, freq, mrec=False, strength=np.pi)
bip = bipole(src, rec, depth, res, freq, msrc=True, mrec=False,
strength=np.pi)*2j*np.pi*freq[:, None, None]*4e-7*np.pi
assert_allclose(bip, loo, rtol=1e-4, atol=1e-18)
# 1.c: msrc-looprec; nrec==nrecz, nsrc!=nsrcz.
rec = [[100, 100, 100], [0, 0, 0], [-10, 0, 10], 23, -50]
src = [[0, 0, 0], [0, 0, 0], 0, 45, 33]
loo = loop(src, rec, depth, res, freq, mrec='loop')
bip = bipole(src, rec, depth, res, freq, msrc=True, mrec=True)
bip *= (2j*np.pi*freq[:, None, None]*4e-7*np.pi)**2
assert_allclose(bip, loo, rtol=1e-4, atol=1e-18)
# 1.d: msrc-loopre; nrec!=nrecz, nsrc==nsrcz.
_, _ = capsys.readouterr() # Empty it
rec = [[100, 100, 100], [0, 0, 0], 0, 23, -50]
src = [[0, 0, 0], [0, 0, 0], [-10, 0, 10], 45, 33]
mpermH = [1, 1, 1]
mpermV = [1.5, 2, 1]
loo = loop(src, rec, depth, res, freq, mrec='loop', mpermH=mpermH,
mpermV=mpermV)
out, _ = capsys.readouterr()
bip = bipole(src, rec, depth, res, freq, msrc=True, mrec=True,
mpermH=mpermH, mpermV=mpermV)
bip *= (2j*np.pi*freq[:, None, None]*4e-7*np.pi)**2
assert_allclose(bip, loo, rtol=1e-4, atol=1e-18)
assert '* WARNING :: `mpermH != mpermV` at source level, ' in out
assert '* WARNING :: `mpermH != mpermV` at receiver level, ' in out
def test_iso_hs(self):
# 3. Test with isotropic half-space solution, Ward and Hohmann, 1988.
# => mm with ab=66; Eq. 4.70, Ward and Hohmann, 1988.
# Survey parameters.
# time: cut out zero crossing.
mu_0 = 4e-7*np.pi
time = np.r_[np.logspace(-7.3, -5.7, 101), np.logspace(-4.3, 0, 101)]
src = [0, 0, 0, 0, 90]
rec = [100, 0, 0, 0, 90]
res = 100.
# Calculation.
fhz_num1 = loop(src, rec, 0, [2e14, res], time, xdirect=True, verb=1,
epermH=[0, 1], epermV=[0, 1], signal=0)
# Analytical solution.
theta = np.sqrt(mu_0/(4*res*time))
theta_r = theta*rec[0]
ana_sol1 = (9 + 6 * theta_r**2 + 4 * theta_r**4) * np.exp(-theta_r**2)
ana_sol1 *= -2 * theta_r / np.sqrt(np.pi)
ana_sol1 += 9 * erf(theta_r)
ana_sol1 *= -res/(2*np.pi*mu_0*rec[0]**5)
# Check.
assert_allclose(fhz_num1, ana_sol1, rtol=1e-4)
def test_iso_fs(self):
# 2. Test with isotropic full-space solution, Ward and Hohmann, 1988.
# => em with ab=24; Eq. 2.58, Ward and Hohmann, 1988.
# Survey parameters.
src = [0, 0, 0, 0, 0]
rec = [100, 0, 100, -90, 0]
res = 100
time = np.logspace(-4, 0, 301)
# Calculation.
fhz_num2 = loop(src,
rec, [],
res,
time,
mrec=False,
xdirect=True,
verb=1,
signal=1)
# Analytical solution.
mu_0 = 4e-7 * np.pi
r = np.sqrt(rec[0]**2 + rec[1]**2 + rec[2]**2)
theta = np.sqrt(mu_0 / (4 * res * time))
theta_r = theta * r
ana_sol2 = -mu_0 * theta**3 * rec[2] * np.exp(-theta_r**2)
ana_sol2 /= 2 * np.pi**1.5 * time
# Check.
assert_allclose(fhz_num2, ana_sol2, rtol=1e-4, atol=1e-18)
def calc_vmd_time(time, filter_name='key201'):
# emulatte
emsrc = fwd.transmitter(emsrc_name, time, moment=1)
model.locate(emsrc, src[:3], rec[:3])
tEMF, time_thz = model.emulate(hankel_filter=filter_name, td_transform='DLAG', time_diff=False, ignore_displacement_current=True)
thz_emu = tEMF['h_z'].real
tEMF_dt, time_thzdt = model.emulate(hankel_filter=filter_name, td_transform='DLAG', time_diff=True, ignore_displacement_current=True)
thzdt_emu = tEMF_dt['h_z'].real
# empymod
epermH = [0, 1]
thz_emp = empymod.loop(signal=-1, freqtime=time_thz, xdirect=True, epermH=epermH, **inp) # スイッチオン応答(微分なし)
thzdt_emp = empymod.loop(signal=0, freqtime=time_thzdt, xdirect=True, epermH=epermH, **inp) # インパルス応答 (微分あり)
# 解析解
thz_ana = vmd.td_hz(time_thz)
thzdt_ana = vmd.td_dhzdt(time_thzdt)
return [thz_emu, thz_emp, thz_ana], time_thz, [thzdt_emu, thzdt_emp, thzdt_ana], time_thzdt
def test_cole_cole(self):
# Just compare to bipole.
def func_eta(inp, pdict):
# Dummy function to check if it works.
etaH = pdict['etaH'].real * inp['fact'] + 1j * pdict['etaH'].imag
etaV = pdict['etaV'].real * inp['fact'] + 1j * pdict['etaV'].imag
return etaH, etaV
def func_zeta(inp, pdict):
# Dummy function to check if it works.
etaH = pdict['zetaH'] / inp['fact']
etaV = pdict['zetaV'] / inp['fact']
return etaH, etaV
freq = 1.
model = {
'src': [0, 0, 500, 0, 0],
'rec': [500, 0, 600, 0, 0],
'depth': [0, 550],
'freqtime': freq
}
res = np.array([2, 10, 5])
fact = np.array([2, 2, 2])
eta = {'res': fact * res, 'fact': fact, 'func_eta': func_eta}
zeta = {'res': res, 'fact': fact, 'func_zeta': func_zeta}
# Frequency domain
etabip = bipole(res=eta, msrc=True, mrec=True, **model)
etabip *= 2j * np.pi * freq * 4e-7 * np.pi
etaloo = loop(res=eta, **model)
assert_allclose(etabip, etaloo)
zetabip = bipole(res=zeta,
mpermH=fact,
mpermV=fact,
msrc=True,
mrec=True,
**model)
zetabip *= 2j * np.pi * freq * 4e-7 * np.pi
zetaloo = loop(res=zeta, mpermH=fact, mpermV=fact, **model)
assert_allclose(zetabip, zetaloo)
def calc_vmd_freq(freq, filter_name='key201'):
# emulatte
emsrc = fwd.transmitter(emsrc_name, freq, moment=1)
model.locate(emsrc, src[:3], rec[:3])
fEMF = model.emulate(hankel_filter=filter_name)
fhz_emu = fEMF['h_z']
# empymod
fhz_emp = empymod.loop(freqtime=freq, **inp)
# 解析解
fhz_ana = vmd.fd_hz(freq)
return [fhz_emu, fhz_emp, fhz_ana], freq
# Numerical result
# ~~~~~~~~~~~~~~~~
eperm = [0, 0] # Reduce early time numerical noise (diffusive approx for air)
inp = {
'src': src,
'rec': rec,
'depth': depth,
'res': res,
'freqtime': time,
'verb': 1,
'xdirect': True,
'epermH': eperm
}
hz_num = empymod.loop(signal=-1, **inp)
dhz_num = empymod.loop(signal=0, **inp)
###############################################################################
# Plot the result
# ~~~~~~~~~~~~~~~
plt.figure(figsize=(5, 6))
plt.plot(time * 1e3, abs(dhz_ana), 'k-', lw=2, label='Ward & Hohmann')
plt.plot(time * 1e3, dhz_num, 'C1-', label='empymod; dHz/dt')
plt.plot(time * 1e3, -dhz_num, 'C1--')
plt.plot(time * 1e3, abs(hz_ana), 'k-', lw=2)
plt.plot(time * 1e3, hz_num, 'C0-', label='empymod; Hz')
plt.plot(time * 1e3, -hz_num, 'C0--')
src = [0, 0, 0, 0, 0] # x-dir. source at the origin [x, y, z, azimuth, dip]
rec = [100, 0, 0, 0, 0] # x-dir. receiver 100m away from source, inline
cond = 0.01 # Conductivity (S/m)
###############################################################################
# Calculation using ``empymod``
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Collect common parameters
inp = {'src': src, 'rec': rec, 'depth': [], 'res': 1/cond, 'verb': 1}
# Frequency domain
inp['freqtime'] = freq
fee_dip_dip = empymod.bipole(**inp)
fmm_dip_dip = empymod.bipole(msrc=True, mrec=True, **inp)
f_loo_dip = empymod.loop(**inp)
# Time domain
inp['freqtime'] = time
# ee
ee_dip_dip_of = empymod.bipole(signal=-1, **inp)
ee_dip_dip_im = empymod.bipole(signal=0, **inp)
ee_dip_dip_on = empymod.bipole(signal=1, **inp)
# mm dip-dip
dip_dip_of = empymod.bipole(signal=-1, msrc=True, mrec=True, **inp)
dip_dip_im = empymod.bipole(signal=0, msrc=True, mrec=True, **inp)
dip_dip_on = empymod.bipole(signal=1, msrc=True, mrec=True, **inp)
# mm loop-dip
