diff --git a/docs/LaTeX/tmtemod.tex b/docs/LaTeX/tmtemod.tex index c100cd59..be0af76b 100644 --- a/docs/LaTeX/tmtemod.tex +++ b/docs/LaTeX/tmtemod.tex @@ -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)} diff --git a/examples/educational/coordinate_system.py b/examples/educational/coordinate_system.py index 9aa1b2e8..b5177548 100644 --- a/examples/educational/coordinate_system.py +++ b/examples/educational/coordinate_system.py @@ -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: diff --git a/examples/educational/dipoles_and_loops.py b/examples/educational/dipoles_and_loops.py index 512d145d..66e80196 100644 --- a/examples/educational/dipoles_and_loops.py +++ b/examples/educational/dipoles_and_loops.py @@ -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') @@ -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') @@ -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') diff --git a/examples/frequency_domain/magnetotelluric.py b/examples/frequency_domain/magnetotelluric.py index 850df5dc..b229be7e 100644 --- a/examples/frequency_domain/magnetotelluric.py +++ b/examples/frequency_domain/magnetotelluric.py @@ -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 diff --git a/examples/reproducing/ward1988.py b/examples/reproducing/ward1988.py index ec12fe4d..136b6fea 100644 --- a/examples/reproducing/ward1988.py +++ b/examples/reproducing/ward1988.py @@ -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) # diff --git a/examples/time_domain/step_and_impulse.py b/examples/time_domain/step_and_impulse.py index 56bb4cb0..56e6f598 100644 --- a/examples/time_domain/step_and_impulse.py +++ b/examples/time_domain/step_and_impulse.py @@ -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)}`