def test_freq2transform(self, capsys):
times = np.linspace(0.1, 10, 101)
x = 900
model = {
'src': [0, 0, 0],
'rec': [x, 0, 0],
'res': 1,
'depth': [],
'verb': 1
}
# Initiate Fourier instance.
Fourier = time.Fourier(times, 0.001, 100)
# Calculate required frequencies.
data = empymod.dipole(freqtime=Fourier.freq_compute, **model)
# Transform the data.
tdata = Fourier.freq2time(data, x)
# Calculate data in empymod.
data_true = empymod.dipole(freqtime=times, signal=0, **model)
# Compare.
assert_allclose(data_true, tdata, rtol=1e-4)
def test_tem():
# Just ensure functionality stays the same, with one example.
for i in ['6', '7', '8']: # Signal = 0, 1, -1
res = DATAFEMTEM['out'+i][()]
tEM, _ = tem(**res['inp'])
assert_allclose(tEM, res['EM'])
# Test `xdirect=None` through analytical/dipole-comparison with a simple
# model
# Fullspace model
inp = {'src': [[0, -100], [0, -200], 200],
'rec': [np.arange(1, 11)*500, np.arange(1, 11)*100, 300],
'freqtime': [0.1, 1, 10], 'res': 1}
fEM_fs = analytical(**inp)
# Add two layers
inp['depth'] = [0, 500]
inp['res'] = [10, 1, 30]
fEM_tot1 = dipole(xdirect=False, **inp)
fEM_tot2 = dipole(xdirect=True, **inp)
fEM_secondary = dipole(xdirect=None, **inp)
# `xdirect=False` and `xdirect=True` have to agree
assert_allclose(fEM_tot2, fEM_tot1)
# Total field minus minus direct field equals secondary field
assert_allclose(fEM_tot1 - fEM_fs, fEM_secondary)
def test_dipole():
# As this is a subset of bipole, just run two tests to ensure
# it is equivalent to bipole.
# 1. Frequency
src = [5000, 1000, -200]
rec = [0, 0, 1200]
model = {'depth': [100, 1000], 'res': [2, 0.3, 100], 'aniso': [2, .5, 2]}
f = 0.01
# v dipole : ab = 26
# \> bipole : src-dip = 90, rec-azimuth=90, msrc=True
dip_res = dipole(src, rec, freqtime=f, ab=26, verb=0, **model)
bip_res = bipole([src[0], src[1], src[2], 0, 90],
[rec[0], rec[1], rec[2], 90, 0],
msrc=True,
freqtime=f,
verb=0,
**model)
assert_allclose(dip_res, bip_res)
# 2. Time
t = 1
dip_res = dipole(src, rec, freqtime=t, signal=1, ab=62, verb=0, **model)
bip_res = bipole([src[0], src[1], src[2], 0, 90],
[rec[0], rec[1], rec[2], 90, 0],
msrc=True,
freqtime=t,
signal=1,
verb=0,
**model)
assert_allclose(dip_res, bip_res)
def plot_coarse_model(self):
"""Update coarse model."""
# Calculate the f-responses for required and the calculation range.
f_req = empymod.dipole(freqtime=self.freq_req, **self.model)
f_calc = empymod.dipole(freqtime=self.freq_calc, **self.model)
# Interpolate from calculated to required frequencies and transform.
f_int = self.interpolate(f_calc)
t_int = self.freq2time(f_calc, self.model['rec'][0])
# Calculate the errors.
f_error = 100*abs((self.reim(f_int)-self.reim(f_req)) /
self.reim(f_req))
t_error = 100*abs((t_int-self.t_base)/self.t_base)
# Clear existing handles
self.clear_handle(['f_int', 't_int', 'f_inti', 'f_inte', 't_inte'])
# Plot frequency-domain result
self.h_f_inti, = self.axs[0].plot(
self.freq_req, self.reim(f_int), 'k.', ms=4)
self.h_f_int, = self.axs[0].plot(
self.freq_calc, self.reim(f_calc), 'C0.', ms=8)
self.h_f_inte, = self.axs[2].plot(self.freq_req, f_error, 'k')
# Plot time-domain result
self.h_t_int, = self.axs[1].plot(self.time, t_int, 'k--')
self.h_t_inte, = self.axs[3].plot(self.time, t_error, 'k')
# Update legend
self.print_legend()
def test_all_depths():
# Test RHS/LHS low-to-high/high-to-low
src = [0, 0, 10]
rec = [500, 100, 50]
freq = 1
depth = np.array([-50, 0, 100, 2000])
res = [6, 1, 2, 3, 4]
aniso = [6, 7, 8, 9, 10]
epermH = [1.0, 1.1, 1.2, 1.3, 1.4]
epermV = [1.5, 1.6, 1.7, 1.8, 1.9]
mpermH = [2.0, 2.1, 2.2, 2.3, 2.4]
mpermV = [2.5, 2.6, 2.7, 2.8, 2.9]
# 1. Ordering as internally used:
inp = {
'ab': 11,
'aniso': aniso,
'epermH': epermH,
'epermV': epermV,
'mpermH': mpermH,
'mpermV': mpermV
}
# LHS low-to-high (+1, ::+1)
lhs_l2h = dipole(src, rec, depth, res, freq, **inp)
# RHS high-to-low (-1, ::+1)
rhs_h2l = dipole([src[0], src[1], -src[2]], [rec[0], rec[1], -rec[2]],
-depth, res, freq, **inp)
# 2. Reversed ordering:
inp_r = {
'ab': 11,
'aniso': aniso[::-1],
'epermH': epermH[::-1],
'epermV': epermV[::-1],
'mpermH': mpermH[::-1],
'mpermV': mpermV[::-1]
}
# LHS high-to-low (+1, ::-1)
lhs_h2l = dipole(src, rec, depth[::-1], res[::-1], freq, **inp_r)
# RHS low-to-high (-1, ::-1)
rhs_l2h = dipole([src[0], src[1], -src[2]], [rec[0], rec[1], -rec[2]],
-depth[::-1], res[::-1], freq, **inp_r)
assert_allclose(lhs_l2h, lhs_h2l)
assert_allclose(lhs_l2h, rhs_l2h)
assert_allclose(lhs_l2h, rhs_h2l)
def test_dipole():
# As this is a subset of bipole, just run two tests to ensure
# it is equivalent to bipole.
# 1. Frequency
src = [5000, 1000, -200]
rec = [0, 0, 1200]
model = {'depth': [100, 1000], 'res': [2, 0.3, 100], 'aniso': [2, .5, 2]}
f = 0.01
# v dipole : ab = 26
# \> bipole : src-dip = 90, rec-azimuth=90, msrc=True
dip_res = dipole(src, rec, freqtime=f, ab=26, verb=0, **model)
bip_res = bipole([src[0], src[1], src[2], 0, 90],
[rec[0], rec[1], rec[2], 90, 0], msrc=True, freqtime=f,
verb=0, **model)
assert_allclose(dip_res, bip_res)
# 2. Time
t = 1
dip_res = dipole(src, rec, freqtime=t, signal=1, ab=62, verb=0, **model)
bip_res = bipole([src[0], src[1], src[2], 0, 90],
[rec[0], rec[1], rec[2], 90, 0], msrc=True, freqtime=t,
signal=1, verb=0, **model)
assert_allclose(dip_res, bip_res)
# 3. Check user-hook for eta/zeta
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
model = {'src': [0, 0, 500], 'rec': [500, 0, 600], 'depth': [0, 550],
'freqtime': [0.1, 1, 10]}
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
standard = dipole(res=res, **model)
outeta = dipole(res=eta, **model)
assert_allclose(standard, outeta)
outzeta = dipole(res=zeta, mpermH=fact, mpermV=fact, **model)
assert_allclose(standard, outzeta)
# Time domain
standard = dipole(res=res, signal=0, **model)
outeta = dipole(res=eta, signal=0, **model)
assert_allclose(standard, outeta)
outzeta = dipole(res=zeta, signal=0, mpermH=fact, mpermV=fact, **model)
assert_allclose(standard, outzeta)
def test_intracasing_segment(self):
print(
'VEB_Ez, Gij, and dipole agree for distant segments within one casing'
)
zi = 52.5
zj = 1352.5
segment_length = 5
zj1 = zj - segment_length / 2
zj2 = zj + segment_length / 2
gij = chs.Gij(zi,
zj,
segment_length,
frequency=freq,
background_conductivity=con,
outer_radius=outer_radius,
inner_radius=inner_radius)
gij = np.conj(gij)
epm_gij = dipole([0, 0, zj], [.01, 0, zi],
depth=[0],
res=[3e14, 1 / con],
freqtime=freq,
ab=33,
ht='quad',
verb=0) * casing_area * segment_length
veb_gij = chs.VEB_Ez(0,
0,
zi,
xp=0,
yp=0,
zp1=zj1,
zp2=zj2,
conductivity=con,
frequency=freq) * casing_area
self.assertTrue(np.isclose(gij, epm_gij, rtol=1e-4, atol=1e-20))
self.assertTrue(np.isclose(gij, veb_gij, rtol=1e-4, atol=1e-20))
def test_regres():
# Comparison to self (regression test)
# 1836 cases; f = [0.01, 1, 100] Hz.; 18 models, 34 ab's, f altern.
dat = REGRES['res'][()]
for _, val in dat.items():
res = dipole(**val[0])
assert_allclose(res, val[1], 3e-2, 1e-17, True)
def plot_base_model(self):
"""Update smooth, 'correct' model."""
# Calculate responses
self.f_dense = empymod.dipole(freqtime=self.freq_dense, **self.model)
self.t_base = empymod.dipole(
freqtime=self.time, signal=self.signal, **self.model)
# Clear existing handles
self.clear_handle(['f_base', 't_base'])
# Plot new result
self.h_f_base, = self.axs[0].plot(
self.freq_dense, self.reim(self.f_dense), 'C3')
self.h_t_base, = self.axs[1].plot(self.time, self.t_base, 'C3')
self.adjust_lim()
def test_analytical():
# 1. fullspace
model = {'src': [500, -100, -200],
'rec': [0, 1000, 200],
'res': 6.71,
'aniso': 1.2,
'freqtime': 40,
'ab': 42,
'verb': 0}
dip_res = dipole(depth=[], **model)
ana_res = analytical(**model)
assert_allclose(dip_res, ana_res)
# \= Check 36/63
model['ab'] = 63
ana_res2 = analytical(**model)
assert_allclose(ana_res.shape, ana_res.shape)
assert np.count_nonzero(ana_res2) == 0
# 2. halfspace
for signal in [0, 1]: # Frequency, Time
model = {'src': [500, -100, 5],
'rec': [0, 1000, 20],
'res': 6.71,
'aniso': 1.2,
'freqtime': 1,
'signal': signal,
'ab': 12,
'verb': 0}
# Check dhs, dsplit, and dtetm
ana_res = analytical(solution='dhs', **model)
res1, res2, res3 = analytical(solution='dsplit', **model)
dTE, dTM, rTE, rTM, air = analytical(solution='dtetm', **model)
model['res'] = [2e14, model['res']]
model['aniso'] = [1, model['aniso']]
dip_res = dipole(depth=0, **model)
# Check dhs, dsplit
assert_allclose(dip_res, ana_res, rtol=1e-3)
assert_allclose(ana_res, res1+res2+res3)
# Check dsplit and dtetm
assert_allclose(res1, dTE+dTM)
assert_allclose(res2, rTE+rTM)
assert_allclose(res3, air)
def test_HED_Ez(self):
print('HED_Ez and dipole agree')
epm_hed = dipole([0, 0, 1e-2], [1, 0, 100],
depth=[0],
res=[3e14, 1 / con],
freqtime=freq,
ab=31,
epermH=[0, 1],
epermV=[0, 1],
verb=0)
chs_hed = chs.HED_Ez(1, 0, 100, 0, 0, conductivity=con, frequency=freq)
self.assertTrue(np.isclose(epm_hed, chs_hed, atol=1e-20))
def test_analytical():
# 1. fullspace
model = {
'src': [500, -100, -200],
'rec': [0, 1000, 200],
'res': 6.71,
'aniso': 1.2,
'freqtime': 40,
'ab': 42,
'verb': 0
}
dip_res = dipole(depth=[], **model)
ana_res = analytical(**model)
assert_allclose(dip_res, ana_res)
# 2. halfspace
model = {
'src': [500, -100, 5],
'rec': [0, 1000, 20],
'res': 6.71,
'aniso': 1.2,
'freqtime': 10,
'signal': 1,
'ab': 12,
'verb': 0
}
# Check dhs, dsplit, and dtetm
ana_res = analytical(solution='dhs', **model)
res1, res2, res3 = analytical(solution='dsplit', **model)
dTE, dTM, rTE, rTM, air = analytical(solution='dtetm', **model)
model['res'] = [2e14, model['res']]
model['aniso'] = [1, model['aniso']]
dip_res = dipole(depth=0, **model)
# Check dhs, dsplit
assert_allclose(dip_res, ana_res, rtol=1e-4)
assert_allclose(ana_res, res1 + res2 + res3)
# Check dsplit and dtetm
assert_allclose(res1, dTE + dTM)
assert_allclose(res2, rTE + rTM)
assert_allclose(res3, air)
def test_interpolation(self, capsys):
times = np.logspace(-2, 1, 201)
model = {
'src': [0, 0, 0],
'rec': [900, 0, 0],
'res': 1,
'depth': [],
'verb': 1
}
Fourier = time.Fourier(times, 0.005, 10)
# Calculate data.
data_true = empymod.dipole(freqtime=Fourier.freq_required, **model)
data = empymod.dipole(freqtime=Fourier.freq_compute, **model)
# Interpolate.
data_int = Fourier.interpolate(data)
# Compare, extrapolate < 0.05; interpolate equal.
assert_allclose(data_int[Fourier.ifreq_extrapolate].imag,
data_true[Fourier.ifreq_extrapolate].imag,
rtol=0.05)
assert_allclose(data_int[Fourier.ifreq_compute].imag,
data_true[Fourier.ifreq_compute].imag)
# Now set every_x_freq and again.
Fourier.every_x_freq = 2
data = empymod.dipole(freqtime=Fourier.freq_compute, **model)
# Interpolate.
data_int = Fourier.interpolate(data)
# Compare, extrapolate < 0.05; interpolate < 0.01.
assert_allclose(data_int[Fourier.ifreq_extrapolate].imag,
data_true[Fourier.ifreq_extrapolate].imag,
rtol=0.05)
assert_allclose(data_int[Fourier.ifreq_interpolate].imag,
data_true[Fourier.ifreq_interpolate].imag,
rtol=0.01)
def test_dipole():
for lay in [0, 1, 5]: # Src/rec in first, second, and last layer
for f in freq: # One freq at a time
src = [0, 0, depth[lay + 1] - 50]
# Offset depending on frequency
if f < 1:
rec = [10000, 0, depth[lay + 1] - 10]
elif f > 10:
rec = [2, 0, depth[lay + 1] - 10]
else:
rec = [1000, 0, depth[lay + 1] - 10]
inp = {
'src': src,
'rec': rec,
'depth': depth[1:-1],
'res': res,
'freqtime': f,
'aniso': aniso,
'verb': 0
}
# empymod-version
out = dipole(epermH=eperm,
epermV=eperm,
mpermH=mperm,
mpermV=mperm,
xdirect=False,
**inp)
# empymod.scripts-version
TM, TE = tmtemod.dipole(eperm=eperm, mperm=mperm, **inp)
TM = TM[0] + TM[1] + TM[2] + TM[3] + TM[4]
TE = TE[0] + TE[1] + TE[2] + TE[3] + TE[4]
# Check
assert_allclose(out, TM + TE, rtol=1e-5, atol=1e-50)
# Check the 3 errors
with pytest.raises(ValueError): # scr/rec not in same layer
tmtemod.dipole([0, 0, 90], [4000, 0, 180], depth[1:-1], res, 1)
with pytest.raises(ValueError): # more than one frequency
tmtemod.dipole([0, 0, 90], [4000, 0, 110], depth[1:-1], res, [1, 10])
with pytest.raises(ValueError): # only one layer
tmtemod.dipole([0, 0, 90], [4000, 0, 110], [], 10, 1)
def plotresult(depth, res, zsrc, zrec):
x = np.arange(1, 101) * 200
inp = {
'src': [0, 0, depth[1] - zsrc],
'rec': [x, x * 0, depth[1] - zrec],
'depth': depth,
'res': res,
'ab': 11,
'freqtime': 1,
'verb': 1,
}
kong241 = empymod.dipole(htarg={'dlf': 'kong_241_2007'}, **inp)
key201 = empymod.dipole(htarg={'dlf': 'key_201_2012'}, **inp)
and801 = empymod.dipole(htarg={'dlf': 'anderson_801_1982'}, **inp)
test = empymod.dipole(htarg={'dlf': filt}, **inp)
wer201 = empymod.dipole(htarg={'dlf': 'wer_201_2018'}, **inp)
qwe = empymod.dipole(ht='qwe', **inp)
plt.figure(figsize=(8, 3.5))
plt.subplot(121)
plt.semilogy(x, qwe.amp(), c='0.5', label='QWE')
plt.semilogy(x, kong241.amp(), 'k--', label='Kong241')
plt.semilogy(x, key201.amp(), 'k:', label='Key201')
plt.semilogy(x, and801.amp(), 'k-.', label='And801')
plt.semilogy(x, test.amp(), 'r', label='This filter')
plt.semilogy(x, wer201.amp(), 'b', label='Wer201')
plt.legend()
plt.xticks([0, 5e3, 10e3, 15e3, 20e3])
plt.xlim([0, 20e3])
plt.subplot(122)
plt.semilogy(x, np.abs((kong241 - qwe) / qwe), 'k--', label='Kong241')
plt.semilogy(x, np.abs((key201 - qwe) / qwe), 'k:', label='Key201')
plt.semilogy(x, np.abs((and801 - qwe) / qwe), 'k-.', label='And801')
plt.semilogy(x, np.abs((test - qwe) / qwe), 'r', label='This filter')
plt.semilogy(x, np.abs((wer201 - qwe) / qwe), 'b', label='Wer201')
plt.legend()
plt.xticks([0, 5e3, 10e3, 15e3, 20e3])
plt.xlim([0, 20e3])
plt.ylim([1e-14, 1])
plt.show()
'depth': [], # Homogenous space
'res': 3, # 3 Ohm.m
'ab': 11, # Ex-source, Ex-receiver}
}
# Single offset and offsets
offs = np.linspace(1000, 15000, 201)
off = 5000
# Single frequency and frequencies
freqs = np.logspace(-3, 2, 201)
freq = 1
# Responses
oresp = empymod.dipole(
rec=(offs, offs * 0, 0), # Inline receivers
freqtime=freq,
**model)
fresp = empymod.dipole(
rec=(5000, 0, 0), # Inline receiver
freqtime=freqs,
**model,
)
# Relative error, noise floor, mean of noise
rel_error = 0.05
noise_floor = 1e-15
n_stack = 1000
# Phase settings: wrapped, radians, lag-defined (+iw)
phase = {'unwrap': False, 'deg': False, 'lag': True}
inp3 = {
'src': [0, 0, 900],
'rec': [x, np.zeros(x.shape), 1000],
'depth': [0, 1000, 2000, 2100],
'res': [2e14, 0.3, 1, 100, 1],
'freqtime': 1,
'verb': 1
}
# HS model
inp4 = dc(inp3)
inp4['depth'] = inp3['depth'][:2]
inp4['res'] = inp3['res'][:3]
# Compute radial responses
rhs = empymod.dipole(**inp4) # Step, HS
rhs = empymod.utils.EMArray(np.nan_to_num(rhs))
rtg = empymod.dipole(**inp3) # " " Target
rtg = empymod.utils.EMArray(np.nan_to_num(rtg))
# Compute azimuthal response
ahs = empymod.dipole(**inp4, ab=22) # Step, HS
ahs = empymod.utils.EMArray(np.nan_to_num(ahs))
atg = empymod.dipole(**inp3, ab=22) # " " Target
atg = empymod.utils.EMArray(np.nan_to_num(atg))
###############################################################################
# Plot
# ----
plt.figure(figsize=(9, 13))
def plot_t(EM, HS, title, i):
plt.figure(title, figsize=(10, 8))
plt.subplot(i)
plt.semilogx(t, EM)
plt.semilogx(t, HS, '--')
###############################################################################
# Impulse HS
plt.figure('Impulse HS')
i = 330
for ab in all_abs:
i += 1
EM = empymod.dipole(**inpEM, **modHS, ab=ab, signal=0, depth=0)
HS = empymod.analytical(**inpEM, **modFS, solution='dhs', ab=ab, signal=0)
plot_t(EM, HS, 'Impulse HS', i)
plt.suptitle('Impulse HS')
plt.show()
###############################################################################
# Switch-on HS
plt.figure('Switch-on HS')
i = 330
for ab in all_abs:
i += 1
EM = empymod.dipole(**inpEM, **modHS, ab=ab, signal=1, depth=0)
HS = empymod.analytical(**inpEM, **modFS, solution='dhs', ab=ab, signal=1)
plot_t(EM, HS, 'Switch-on HS', i)
def test_analytical():
# 1. fullspace
model = {'src': [500, -100, -200],
'rec': [0, 1000, 200],
'res': 6.71,
'aniso': 1.2,
'freqtime': 40,
'ab': 42,
'verb': 0}
dip_res = dipole(depth=[], **model)
ana_res = analytical(**model)
assert_allclose(dip_res, ana_res)
# \= Check 36/63
model['ab'] = 63
ana_res2 = analytical(**model)
assert_allclose(ana_res.shape, ana_res.shape)
assert np.count_nonzero(ana_res2) == 0
# 2. halfspace
for signal in [None, 0, 1]: # Frequency, Time
model = {'src': [500, -100, 5],
'rec': [0, 1000, 20],
'res': 6.71,
'aniso': 1.2,
'freqtime': 1,
'signal': signal,
'ab': 12,
'verb': 0}
# Check dhs, dsplit, and dtetm
ana_res = analytical(solution='dhs', **model)
res1, res2, res3 = analytical(solution='dsplit', **model)
dTE, dTM, rTE, rTM, air = analytical(solution='dtetm', **model)
model['res'] = [2e14, model['res']]
model['aniso'] = [1, model['aniso']]
dip_res = dipole(depth=0, **model)
# Check dhs, dsplit
assert_allclose(dip_res, ana_res, rtol=1e-3)
assert_allclose(ana_res, res1+res2+res3)
# Check dsplit and dtetm
assert_allclose(res1, dTE+dTM)
assert_allclose(res2, rTE+rTM)
assert_allclose(res3, air)
# As above, but Laplace domain.
model = {'src': [500, -100, 5],
'rec': [0, 1000, 20],
'res': 6.71,
'aniso': 1.2,
'freqtime': -1,
'signal': None,
'ab': 12,
'verb': 0}
# Check dhs, dsplit, and dtetm
ana_res = analytical(solution='dhs', **model)
res1, res2, res3 = analytical(solution='dsplit', **model)
dTE, dTM, rTE, rTM, air = analytical(solution='dtetm', **model)
model['res'] = [2e14, model['res']]
model['aniso'] = [1, model['aniso']]
dip_res = dipole(depth=0, **model)
# Check dhs, dsplit
assert_allclose(dip_res, ana_res, rtol=1e-3)
assert_allclose(ana_res, res1+res2+res3)
# Check dsplit and dtetm
assert_allclose(res1, dTE+dTM)
assert_allclose(res2, rTE+rTM)
assert_allclose(res3, air)
# 3. Check user-hook for eta/zeta
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
model = {'src': [0, 0, 500], 'rec': [500, 0, 600],
'freqtime': [0.1, 1, 10]}
res = 10
fact = 2
eta = {'res': fact*res, 'fact': fact, 'func_eta': func_eta}
zeta = {'res': res, 'fact': fact, 'func_zeta': func_zeta}
# Frequency domain fs
standard = analytical(res=res, **model)
outeta = analytical(res=eta, **model)
assert_allclose(standard, outeta)
outzeta = analytical(res=zeta, mpermH=fact, mpermV=fact, **model)
assert_allclose(standard, outzeta)
# Time domain dhs
standard = analytical(res=res, solution='dhs', signal=0, **model)
outeta = analytical(res=eta, solution='dhs', signal=0, **model)
assert_allclose(standard, outeta)
outzeta = analytical(res=zeta, solution='dhs',
signal=0, mpermH=fact, mpermV=fact, **model)
assert_allclose(standard, outzeta)
'res': [2e14, 10, 100, 10], # Res: [air, overb., target, half-space]
'epermH': [1, 1, 1, 1], # El. permittivity: default values
'freqtime': t, # Times
'signal': 0, # 0: Impulse response
'ftarg': {
'dlf': 'key_81_CosSin_2009'
}, # Shorter filter then the default
'verb': 1, # Verbosity; set to 3 to see all parameters
}
###############################################################################
# Compute
# -------
# Compute with default eperm_air = 1
res_1 = empymod.dipole(**model)
# Set horizontal and vertical electric permittivity of air to 0
model['epermH'][0] = 0
# Note that for empymod < v2.0.0 you have to set `epermH` AND `epermV`. From
# v2.0.0 onwards `eperm` is assumed isotropic if `epermV` is not provided, and
# `epermV` is therefore internally a copy of `epermH`.
# Compute with eperm_air = 0
res_0 = empymod.dipole(**model)
###############################################################################
# Plot result
# -----------
#
# As it can be seen, setting :math:`\varepsilon_{air} =` 0 improves the land
np.repeat(y * scl, 7), (depth[rr] + dfrec[dfsw]) * scl
]
# Get model-name
modname = str(ab) + '_' + str(freq) + '_' + str(sr) + str(rr)
# Run model
inp = {
'src': isrc,
'rec': irec,
'depth': depth[:-1] * scl,
'res': ires,
'aniso': ianiso,
'freqtime': ifreq,
'ab': ab,
'opt': 'parallel',
'epermH': iepermH,
'epermV': iepermV,
'mpermH': impermH,
'mpermV': impermV,
'verb': 0,
'xdirect': True
}
em = dipole(**inp)
# Store input and result
out[modname] = (inp, em)
# Store data
np.savez_compressed('../data/regression.npz', res=out)
# ----------------------------------
#
# Calculate
# ~~~~~~~~~
inpdat = {
'src': [0, 0, zsrc],
'rec': [fx, fy, zrec],
'depth': depth,
'freqtime': 1,
'aniso': aniso,
'ab': ab,
'verb': verb
}
fEM = empymod.dipole(**inpdat, res=res)
fEMBG = empymod.dipole(**inpdat, res=resBG)
###############################################################################
# Plot
# ~~~~
fig = plt.figure(figsize=(8, 6), facecolor='w')
fig.subplots_adjust(wspace=.25, hspace=.4)
fig.suptitle(name + ': src-x, rec-x; f = 1 Hz', fontsize=16, y=1)
# Plot Amplitude
ax1 = plt.subplot(2, 2, 1)
plt.semilogy(fx / 1000, fEMBG.amp, label='BG')
plt.semilogy(fx / 1000, fEM.amp, label='Anomaly')
plt.legend(loc='best')
rhs = [2e14, 1 / 3, 1, 1, 1] # Half-space
# Common model parameters (deep sea parameters)
model = {
'src': [0, 0, 975], # Source location
'rec': [x, x * 0, 1000], # Receiver location
'depth': [0, 1000, 2000, 2040], # 1 km water, target 40 m thick 1 km below
'freqtime': 0.5, # Frequencies
'verb': 1, # Verbosity
}
###############################################################################
# Calculation
# -----------
target = empymod.dipole(res=rtg, **model)
tgTM, tgTE = empymod.tmtemod.dipole(res=rtg, **model)
# Without reservoir
notarg = empymod.dipole(res=rhs, **model)
ntTM, ntTE = empymod.tmtemod.dipole(res=rhs, **model)
###############################################################################
# Figure 1
# ~~~~~~~~
#
# Plot all reflected contributions (without direct field), for the models with
# and without a reservoir.
plt.figure(figsize=(10, 4))
'aniso': aniso,
'epermH': eperm,
'epermV': eperm,
'ht': 'fht',
'verb': 2
}
###############################################################################
# Impulse response
# ~~~~~~~~~~~~~~~~
ex = ee_xx_impulse(res[1], aniso[1], rec[0], t)
inparg['signal'] = 0 # signal 0 = impulse
print('QWE')
qwe = empymod.dipole(**inparg, ft='qwe')
print('FHT (Sine)')
sin = empymod.dipole(**inparg, ft='sin', ftarg='key_81_CosSin_2009')
print('FFTLog')
ftl = empymod.dipole(**inparg, ft='fftlog')
print('FFT')
fft = empymod.dipole(**inparg, ft='fft', ftarg=[.0005, 2**20, '', 10])
###############################################################################
# => `FFTLog` is the fastest by quite a margin, followed by the `Sine`-filter.
# What cannot see from the output (set `verb` to something bigger than 2 to see
# it) is how many frequencies each method used:
#
# - QWE: 159 (0.000794328 - 63095.7 Hz)
# - Sine: 116 (5.33905E-06 - 52028 Hz)
# - FFTLog: 60 (0.000178575 - 141.847 Hz)
epm_loop = empymod.loop(src=[0, 0, 0, 0, 90], rec=[rxx, ryy, 10, 0, 0],
**model).reshape(np.shape(rx))
###############################################################################
# 2.1 Point dipoles at (x, y) using ``empymod.dipole``
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# - (0.5, 0), ab=42
# - (0, 0.5), ab=41
# - (-0.5, 0), ab=-42
# - (0, -0.5), ab=-41
#
rec_dip = [rxx, ryy, 10]
square_pts = +empymod.dipole(src=[+0.5, +0.0, 0], rec=rec_dip, ab=42,
**model).reshape(np.shape(rx))
square_pts += empymod.dipole(src=[+0.0, +0.5, 0], rec=rec_dip, ab=41,
**model).reshape(np.shape(rx))
square_pts -= empymod.dipole(src=[-0.5, +0.0, 0], rec=rec_dip, ab=42,
**model).reshape(np.shape(rx))
square_pts -= empymod.dipole(src=[+0.0, -0.5, 0], rec=rec_dip, ab=41,
**model).reshape(np.shape(rx))
plot_result(epm_loop, square_pts, x, 'Loop made of four points',
vmin=-13, vmax=-5, rx=x)
###############################################################################
# 2.2 Finite length dipoles using ``empymod.bipole``
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# Each simulated with a 5pt Gaussian quadrature. The dipoles are:
off = np.linspace(500, 10000, 301)
###############################################################################
# LHS
# ```
#
# In the left-handed system positive :math:`z` is downwards. So we have to
# define our model by beginning with the air layer, followed by water,
# background, target, and background again. This means that all our
# depth-values are positive, as the air-interface :math:`z_0` is at 0 m.
lhs = empymod.dipole(
src=[0, 0, 100],
rec=[off, np.zeros(off.size), 200],
depth=[0, 300, 1000, 1050],
res=[1e20, 0.3, 1, 50, 1],
# depth=[1050, 1000, 300, 0], # Alternative way, LHS high to low.
# res=[1, 50, 1, 0.3, 1e20], # " " "
freqtime=1,
verb=0)
###############################################################################
# RHS
# ```
#
# In the right-handed system positive :math:`z` is upwards. So we have to
# define our model by beginning with the background, followed by the target,
# background again, water, and air. This means that all our depth-values are
# negative.
rhs = empymod.dipole(
x,
], np.size(y), axis=0)
ry = np.repeat([
y,
], np.size(x), axis=0)
ry = ry.transpose()
# Compute the electric field
efield = empymod.dipole(
src=[0, 0, 150],
rec=[rx.ravel(), ry.ravel(), 200],
depth=[0, 200, 1000, 1200],
res=[2e14, 1 / 3, 1, 50, 1],
aniso=[1, 1, np.sqrt(10), 1, 1],
freqtime=0.5,
epermH=[1, 80, 17, 2.1, 17],
epermV=[1, 80, 17, 2.1, 17],
mpermH=[1, 1, 1, 1, 1],
mpermV=[1, 1, 1, 1, 1],
ab=11,
htarg={
'pts_per_dec': -1
},
).reshape(np.shape(rx))
###############################################################################
# Plot
# ----
# Create a similar colormap as Hunziker et al., 2015.
cmap = plt.cm.get_cmap("jet", 61)
def test_coordinate_systems():
srcLHS = (0, 0, -10)
srcRHS = (0, 0, +10)
x = np.arange(1, 11) * 1000
recLHS = (x, x, +3)
recRHS = (x, x, -3)
air, hs, tg = 2e14, 100, 1000
z0, z1, z2 = 0, 10, 20
inp = {'freqtime': 1, 'verb': 1}
inpLHS = {'src': srcLHS, 'rec': recLHS}
inpRHS = {'src': srcRHS, 'rec': recRHS}
for ab in [11, 31, 23, 33, 25, 35, 16, 66, 51, 61, 43, 63, 44, 65, 56, 66]:
# Sign switches occur for each z-component; each m-component
sign = 1
if ab % 10 > 3: # If True: magnetic src
sign *= -1
if ab // 10 > 3: # If True: magnetic rec
sign *= -1
if str(ab)[0] in ['3', '6']: # Vertical source component
sign *= -1
if str(ab)[1] in ['3', '6']: # Vertical receiver component
sign *= -1
inp['ab'] = ab
# # 2-layer case
# Default/original: LHS low to high
orig = dipole(depth=z0, res=[air, hs], **inpLHS, **inp)
# Alternatives LHS: low to high and high to low
LHSl2h = dipole(depth=[z0, np.infty], res=[air, hs], **inpLHS, **inp)
LHSh2l = dipole(depth=[np.infty, z0], res=[hs, air], **inpLHS, **inp)
assert_allclose(orig, LHSl2h)
assert_allclose(orig, LHSh2l)
# Alternatives LHS: low to high and high to low
RHSlth = sign * dipole(
depth=[-np.infty, -z0], res=[hs, air], **inpRHS, **inp)
RHSh2l = sign * dipole(
depth=[-z0, -np.infty], res=[air, hs], **inpRHS, **inp)
assert_allclose(orig, RHSlth)
assert_allclose(orig, RHSh2l)
# # 4-layer case
# Default/original: LHS low to high
orig = dipole(depth=[z0, z1, z2],
res=[air, hs, tg, hs],
**inpLHS,
**inp)
# Alternatives LHS: low to high and high to low
LHSh2l = dipole(depth=[z2, z1, z0],
res=[hs, tg, hs, air],
**inpLHS,
**inp)
assert_allclose(orig, LHSh2l)
# Alternatives LHS: low to high and high to low
RHSlth = sign * dipole(
depth=[-z2, -z1, -z0], res=[hs, tg, hs, air], **inpRHS, **inp)
RHSh2l = sign * dipole(
depth=[-z0, -z1, -z2], res=[air, hs, tg, hs], **inpRHS, **inp)
assert_allclose(orig, RHSlth)
assert_allclose(orig, RHSh2l)
# Calculate analytical solution
resp = empymod.analytical(params['src'],
params['rec'],
params['res'][1],
params['freqtime'],
solution='dhs',
aniso=params['aniso'][1],
ab=params['ab'],
verb=params['verb'])
###############################################################################
# Calculate numerically the model using different Hankel options
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
standard = empymod.dipole(**params, htarg=[hfilt, 0])
laggedco = empymod.dipole(**params, htarg=[hfilt, -1])
spline10 = empymod.dipole(**params, htarg=[hfilt, 10])
spline30 = empymod.dipole(**params, htarg=[hfilt, 30])
splin100 = empymod.dipole(**params, htarg=[hfilt, 100])
###############################################################################
# Results
# ~~~~~~~
plt.figure(figsize=(10, 4))
plt.suptitle('Hankel transform example; frequency = ' +
str(params['freqtime']) + ' Hz',
y=1.05,
fontsize=15)
inp2 = {
'src': [0, 0, 0.001],
'rec': [1000, 0, 0.001],
'depth': [0, 500, 525],
'res': [2e14, 20, 500, 20],
'freqtime': t,
'verb': 1
}
# HS model
inp1 = dc(inp2)
inp1['depth'] = inp2['depth'][0]
inp1['res'] = inp2['res'][:2]
# Calculate responses
sths = empymod.dipole(**inp1, signal=1) # Step, HS
sttg = empymod.dipole(**inp2, signal=1) # " " Target
imhs = empymod.dipole(**inp1, signal=0, ft='fftlog') # Impulse, HS
imtg = empymod.dipole(**inp2, signal=0, ft='fftlog') # " " Target
###############################################################################
# Plot
# ~~~~
plt.figure(figsize=(9, 4))
plt.subplots_adjust(wspace=.3)
# Step response
plt.subplot(121)
plt.title('(a)')
plt.plot(np.r_[0, 0, t],
