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4 changes: 2 additions & 2 deletions docs/LaTeX/tmtemod.tex
Original file line number Diff line number Diff line change
Expand Up @@ -199,13 +199,13 @@ \section*{Adjust Hunziker et al. (2015) for TM/TE-split}
\hat{E}^{+-}_{xx;H} &= \frac{y^2}{4\pi r^2}
\int^\infty_{\kappa=0} \frac{\zeta_1}{\Gamma_1}
\frac{R^-_{H;1}}{M_{H;1}}
\exp(-\Gamma_1 h^{+-})J_0(\kappa r)\kappa\rm{d}\kappa \nonumber \\
\exp(-\Gamma_1 h^{+-})J_0(\kappa r)\kappa\mr{d}\kappa \nonumber \\
%
&\quad + \frac{x^2-y^2}{4\pi r^3}
\int^\infty_{\kappa=0} \frac{\zeta_1}{\Gamma_1}
\left(\frac{R^-_{H;1}}{M_{H;1}} -
\frac{R^-_{H;1}(\kappa=0)}{M_{H;1}(\kappa=0)}\right)
\exp(-\Gamma_1 h^{+-})J_1(\kappa r)\rm{d}\kappa \nonumber \\
\exp(-\Gamma_1 h^{+-})J_1(\kappa r)\mr{d}\kappa \nonumber \\
%
&\quad - \frac{\zeta_1 (x^2-y^2)}{4\pi\gamma_1 r^4}
\frac{R^-_{H;1}(\kappa=0)}{M_{H;1}(\kappa=0)}
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13 changes: 7 additions & 6 deletions examples/educational/coordinate_system.py
Original file line number Diff line number Diff line change
Expand Up @@ -57,12 +57,13 @@
- ``depth = [0, -100, -1000, -1050]``: **RHS** (+z up)

- A source or a receiver *exactly on* a boundary is taken as being in the lower
layer. Hence, if :math:`z_\rm{rec} = z_0`, where :math:`z_0` is the surface,
then the receiver is taken as in the air in the LHS, but as in the subsurface
in the RHS. Similarly, if :math:`z_\rm{rec} = z_\rm{seafloor}`, then the
receiver is taken as in the sea in the LHS, but as in the subsurface in the
RHS. This can be avoided by never placing it exactly on a boundary, but
slightly (e.g., 1 mm) in the layer where you want to have it.
layer. Hence, if :math:`z_\mathrm{rec} = z_0`, where :math:`z_0` is the
surface, then the receiver is taken as in the air in the LHS, but as in the
subsurface in the RHS. Similarly, if :math:`z_\mathrm{rec} =
z_\mathrm{seafloor}`, then the receiver is taken as in the sea in the LHS,
but as in the subsurface in the RHS. This can be avoided by never placing it
exactly on a boundary, but slightly (e.g., 1 mm) in the layer where you want
to have it.

- Sign switches:

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6 changes: 3 additions & 3 deletions examples/educational/dipoles_and_loops.py
Original file line number Diff line number Diff line change
Expand Up @@ -126,7 +126,7 @@

# Frequency Domain
plt.subplot(231)
plt.title(r'$G^{ee}_{\rm{dip-dip}}$', fontsize=fs)
plt.title(r'$G^{ee}_\mathrm{dip-dip}$', fontsize=fs)
plt.plot(freq, fee_dip_dip.real, 'C0-', label='Real')
plt.plot(freq, -fee_dip_dip.real, 'C0--')
plt.plot(freq, fee_dip_dip.imag, 'C1-', label='Imag')
Expand All @@ -136,7 +136,7 @@
plt.ylim([5e-8, 2e-5])

ax1 = plt.subplot(232)
plt.title(r'$G^{mm}_{\rm{dip-dip}}$', fontsize=fs)
plt.title(r'$G^{mm}_\mathrm{dip-dip}$', fontsize=fs)
plt.plot(freq, fmm_dip_dip.real, 'C0-', label='Real')
plt.plot(freq, -fmm_dip_dip.real, 'C0--')
plt.plot(freq, fmm_dip_dip.imag, 'C1-', label='Imag')
Expand All @@ -147,7 +147,7 @@
plt.legend()

plt.subplot(233)
plt.title(r'$G^{mm}_{\rm{loop-dip}}$', fontsize=fs)
plt.title(r'$G^{mm}_\mathrm{loop-dip}$', fontsize=fs)
plt.plot(freq, f_loo_dip.real, 'C0-', label='Real')
plt.plot(freq, -f_loo_dip.real, 'C0--')
plt.plot(freq, f_loo_dip.imag, 'C1-', label='Imag')
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2 changes: 1 addition & 1 deletion examples/frequency_domain/magnetotelluric.py
Original file line number Diff line number Diff line change
Expand Up @@ -45,7 +45,7 @@
:label: ph-13

z_{oj} \equiv \text{intrinsic impedance}
\equiv \sqrt{\rm{i}\omega \mu \rho_j} \, ,
\equiv \sqrt{\mathrm{i}\omega \mu \rho_j} \, ,

.. math::
:label: ph-14
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7 changes: 4 additions & 3 deletions examples/reproducing/ward1988.py
Original file line number Diff line number Diff line change
Expand Up @@ -33,16 +33,17 @@
# .. math::
#
# h_z = \frac{m}{4\pi r^3} \left[
# \frac{9}{2\theta^2 r^2} \rm{erf}(\theta r) - \rm{erf}(\theta r) -
# \frac{9}{2\theta^2 r^2} \mathrm{erf}(\theta r) -
# \mathrm{erf}(\theta r) -
# \frac{1}{\pi^{1/2}} \left(\frac{9}{\theta r} + 4\theta r\right)
# \exp(-\theta^2 r^2) \right] \, , \qquad (4.69\rm{a})
# \exp(-\theta^2 r^2) \right] \, , \qquad (4.69\mathrm{a})
#
# and
#
# .. math::
#
# \frac{\partial h_z}{\partial t} = -\frac{m\rho}{2\pi\mu_0 r^5} \left[
# 9\rm{erf}(\theta r) -
# 9\mathrm{erf}(\theta r) -
# \frac{2\theta r}{\pi^{1/2}} \left(9 + 6\theta^2 r^2 +
# 4\theta^4 r^4\right) \exp(-\theta^2 r^2) \right] \, , \qquad (4.70)
#
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5 changes: 3 additions & 2 deletions examples/time_domain/step_and_impulse.py
Original file line number Diff line number Diff line change
Expand Up @@ -39,8 +39,9 @@
# .. math::
#
# E_x(\rho_h,\lambda,r,t) = \frac{\rho_h}{2 \pi r^3} \left[ 2\lambda +
# \rm{erf}\left(\frac{\tau_h}{2}\right) - 2\lambda
# \rm{erf}\left(\frac{\tau_h}{2\lambda}\right) + \frac{\tau_h}{\sqrt{\pi}}
# \mathrm{erf}\left(\frac{\tau_h}{2}\right) - 2\lambda
# \mathrm{erf}\left(\frac{\tau_h}{2\lambda}\right) +
# \frac{\tau_h}{\sqrt{\pi}}
# \exp\left(- \frac{\tau_h^2}{4\lambda^2}\right) \right]
#
# Time Domain: Impulse Response :math:`\mathbf{\delta(t)}`
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