Ziolkowski et al., 2007

Reproducing Figure 3 of Ziolkowski et al., 2007, Geophysics. This is a land MTEM example.

Reference

• Ziolkowski, A., B. Hobbs, and D. Wright, 2007, Multitransient electromagnetic demonstration survey in France: Geophysics, 72, F197-F209; DOI: 10.1190/1.2735802.

import empymod
import numpy as np
import matplotlib.pyplot as plt

Computation

# Time
t = np.linspace(0.001, 0.06, 101)

# Target model
inp_tg = {
    '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
inp_hs = inp_tg.copy()
inp_hs['depth'] = inp_tg['depth'][0]
inp_hs['res'] = inp_tg['res'][:2]

# Compute responses
sths = empymod.dipole(**inp_hs, signal=1)               # Step, Halfspace
sttg = empymod.dipole(**inp_tg, signal=1)               # Step, Target
imhs = empymod.dipole(**inp_hs, signal=0, ft='fftlog')  # Impulse, Halfspace
imtg = empymod.dipole(**inp_tg, signal=0, ft='fftlog')  # Impulse, Target

Plot

fig, (ax1, ax2) = plt.subplots(
        1, 2, figsize=(8, 4), sharex=True, constrained_layout=True)

# Step response
ax1.set_title('(a)')
ax1.plot(np.r_[0, 0, t], np.r_[0, sths[0], sths], 'k',
         label='Uniform half-space')
ax1.plot(np.r_[0, 0, t], np.r_[0, sttg[0], sttg], 'r',
         label='Hydrocarbon reservoir')
ax1.axis([-.02, 0.06, 0, 8e-9])
ax1.set_xlabel('Time (s)')
ax1.set_ylabel('Electric field amplitude (V/m/A-m)')
ax1.legend()

# Impulse response
ax2.set_title('(b)')
ax2.plot(np.r_[0, 0, t], np.r_[2, 0, imhs/imtg.max()],
         'k', label='Uniform half-space')
ax2.plot(np.r_[0, t], np.r_[0, imtg/imtg.max()],
         'r', label='Hydrocarbon reservoir')
ax2.axis([-.02, 0.06, 0, 1.02])
ax2.set_xlabel('Time (s)')
ax2.set_ylabel('Normalized derivative (Ω/m²/s)')
ax2.legend()

Original Figure

Figure 3 of Ziolkowski et al., 2007, Geophysics:

empymod.Report()

Sat Jan 17 19:16:46 2026 UTC
OS	Linux (Ubuntu 22.04)	CPU(s)	2	Machine	x86_64
Architecture	64bit	RAM	7.6 GiB	Environment	Python
File system	ext4
Python 3.11.12 (main, May 6 2025, 10:45:53) [GCC 11.4.0]
numpy	2.3.5	scipy	1.17.0	numba	0.63.1
empymod	2.5.4.dev4+g4866dc83a	libdlf	0.3.0	IPython	9.9.0
matplotlib	3.10.8

Estimated memory usage: 193 MB