ensure there are no duplicate equation labels, move unused references…

… to unused_references.bib

_ext/__init__.py

@@ -1,7 +1,12 @@
 from autodoc import (
     make_formula_sheet, make_contributorslist, make_case_histories
 )
-from environmentSetup import supress_nonlocal_image_warn, checkDependencies, supress_citation_not_referenced
+from environmentSetup import (
+    # supress_nonlocal_image_warn,
+    checkDependencies,
+    # supress_citation_not_referenced,
+    # supress_nonlocal_image_and_citation_not_referenced
+)
 from copyImages import copyImages
 from edit_on_github import *
 from purpose import *

_ext/environmentSetup.py

@@ -5,28 +5,28 @@ def checkDependencies():
     try:
         import numpy, scipy, matplotlib, sphinxcontrib.bibtex, sphinx_bootstrap_theme
         pass
-    except (Exception, e):
+    except Exception:
         raise Exception("Requirements not installed, run: 'pip install -r requirements.txt' to install requirements")
     else:
         pass
 
-def supress_nonlocal_image_warn():
-    sphinx.environment.BuildEnvironment.warn_node = _supress_nonlocal_image_warn
+def supress_nonlocal_image_and_citation_not_referenced():
+    sphinx.environment.BuildEnvironment.warn_node = _supress_nonlocal_image_and_citation_not_referenced
 
-def _supress_nonlocal_image_warn(self, msg, node, **kwargs):
+def _supress_nonlocal_image_and_citation_not_referenced(self, msg, node, **kwargs):
 
     if not msg.startswith("nonlocal image URI found:"):
-        self._warnfunc(msg, "%s:%s" % get_source_line(node))
+        if not msg.startswith("Citation") and msg.endswith("is not referenced."):
+            self._warnfunc(msg, "%s:%s" % get_source_line(node))
 
-def supress_citation_not_referenced():
-    sphinx.environment.BuildEnvironment.warn_node = _supress_citation_not_referenced
+# def supress_citation_not_referenced():
+#     sphinx.environment.BuildEnvironment.warn_node = _supress_citation_not_referenced
 
-def _supress_citation_not_referenced(self, msg, node, **kwargs):
-    print(msg)
-    if not (
-        msg.lower().startswith("citation") and msg.lower().endswith("is not referenced.")
-    ):
-        self._warnfunc(msg, "%s:%s" % get_source_line(node))
+# def _supress_citation_not_referenced(self, msg, node, **kwargs):
+#     if not (
+#         msg.lower().startswith("citation") and msg.lower().endswith("is not referenced.")
+#     ):
+#         self._warnfunc(msg, "%s:%s" % get_source_line(node))
 
 
 

conf.py

@@ -541,14 +541,18 @@
 
 from _ext import (
     make_contributorslist, make_formula_sheet, make_case_histories,
-    checkDependencies, supress_nonlocal_image_warn, copyImages,
-    supress_citation_not_referenced
+    checkDependencies,
+    # supress_nonlocal_image_warn,
+    copyImages,
+    # supress_citation_not_referenced,
+    # supress_nonlocal_image_and_citation_not_referenced
 )
 
 make_contributorslist()
 # make_formula_sheet()
 make_case_histories()
 # checkDependencies()
-supress_nonlocal_image_warn()
-supress_citation_not_referenced()
+# supress_nonlocal_image_warn()
+# supress_citation_not_referenced()
+# supress_nonlocal_image_and_citation_not_referenced()
 copyImages()

content/maxwell1_fundamentals/appendix/wave_eq_derivation.rst

@@ -8,31 +8,30 @@ Here, we derive the wave equations in time for the electric and magnetic fields.
 .. math::
     \boldsymbol{\nabla} \times \mathbf{e}
     = -\frac{\partial \mathbf{b}}{\partial t}
-    :label: faraday_time
+    :label: faraday_time_derivation
 
 .. math::
     \boldsymbol{\nabla} \times \mathbf{h}
     = \mathbf{j} + \frac{\partial \mathbf{d}}{\partial t}
-    :label: ampere_maxwell_time
+    :label: ampere_maxwell_time_derive
 
 as well as the three constitutive relations:
 
 .. math::
-    \boldsymbol{\nabla} \times \mathbf{h}
-    = \mathbf{j} + \frac{\partial \mathbf{d}}{\partial t}
-    :label: ampere_maxwell_time
+    \mathbf{j} = \sigma \mathbf{e}
+    :label: jsigmae
 
 .. math:: \mathbf{d} = \epsilon \mathbf{e}
-    :label: depse
+    :label: depse_derivation
 
 .. math:: \mathbf{b} = \mu \mathbf{h}
-    :label: bmuh
+    :label: bmuh_derivation
 
 Derivation for the Electric Field
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
 To derive the wave equation for :math:`\mathbf{e}`, we first take
-the curl of Faraday's Law, shown in equation :eq:`faraday_time`:
+the curl of Faraday's Law, shown in equation :eq:`faraday_time_derivation`:
 
 .. math:: \boldsymbol{\nabla} \times (\boldsymbol{\nabla} \times \mathbf{e}) = - \boldsymbol{\nabla} \times \frac{\partial \mathbf{b}}{\partial t}
     :label: hme1
@@ -60,10 +59,10 @@ time derivatives. Equation :eq:`hme3` can then also be written as:
 
 This expression is now solely in terms of :math:`\boldsymbol{\nabla} \times
 \mathbf{e}` and :math:`\boldsymbol{\nabla} \times \mathbf{h}`. Thus, we can
-use Equation :eq:`ampere_maxwell_time` to generate an equation with only
-:math:`\mathbf{e}`. We substitute in Equation :eq:`ampere_maxwell_time` into
+use Equation :eq:`ampere_maxwell_time_derive` to generate an equation with only
+:math:`\mathbf{e}`. We substitute in Equation :eq:`ampere_maxwell_time_derive` into
 Equation :eq:`hme4` and simplify using the constitutive relations in Equations
-:eq:`ohms_law_time` and :eq:`depse`:
+:eq:`ohms_law_time` and :eq:`depse_derivation`:
 
 .. math::  \boldsymbol{\nabla} \times \boldsymbol{\nabla} \times \mathbf{e} = - \mu \frac{\partial}{\partial t} \left ( \mathbf{j} + \frac{\partial \mathbf{d}}{\partial t} \right )
 
@@ -92,7 +91,7 @@ Derivation for the Magnetic Field
 
 To derive the wave equation for :math:`\mathbf{h}`, we repeat the above
 derivation but start by taking the curl of Ampere's Law, shown in
-equation :eq:`ampere_maxwell_time`:
+equation :eq:`ampere_maxwell_time_derive`:
 
 .. math:: \boldsymbol{\nabla} \times (\boldsymbol{\nabla} \times \mathbf{h}) = \boldsymbol{\nabla} \times \mathbf{j} + \boldsymbol{\nabla} \times \frac{\partial \mathbf{d}}{\partial t}
     :label: hmh1
@@ -119,7 +118,7 @@ written as:
 
 These expressions are now in terms of :math:`\boldsymbol{\nabla} \times
 \mathbf{e}` and :math:`\boldsymbol{\nabla} \times \mathbf{h}`. Thus, we can
-use Equation :eq:`faraday_time` to generate an equation with only
+use Equation :eq:`faraday_time_derivation` to generate an equation with only
 :math:`\mathbf{h}`. We then again use the vector identity
 :math:`\boldsymbol{\nabla} \times \boldsymbol{\nabla} \times \mathbf{x} =
 \boldsymbol{\nabla} \boldsymbol{\nabla} \cdot \mathbf{x} -

content/maxwell1_fundamentals/dipole_sources_in_homogeneous_media/magnetic_dipole_frequency/analytic_solution.rst

@@ -8,15 +8,15 @@ Analytic Solution
     Here, Maxwell's equations are solved for a harmonic magnetic dipole source.
     This is accomplished by using the method of Schelkunoff potentials, as shown in Ward and Hohmann (:cite:`ward1988`).
     Analytic expressions for the electric field, the magnetic field and the corresponding vector potential are provided.
-    
+
 
 
 
 For a magnetic source (:math:`\mathbf{J_m^s}`), Maxwell's equations in the frequency domain are given by:
 
 
 .. math::
-	\nabla \times \mathbf{E_m} + i\omega \mu \mathbf{H_m} = - \mathbf{J_m^s} 
+	\nabla \times \mathbf{E_m} + i\omega \mu \mathbf{H_m} = - \mathbf{J_m^s}
 	:label: Faraday_m
 .. math::
 	\nabla \times \mathbf{H_m} - (\sigma + i\omega \varepsilon) \mathbf{E_m} = 0
@@ -40,24 +40,24 @@ and
 Eq. :eq:`E_F_potential` can be obtained simply by taking the divergence of Eq. :eq:`Ampere_m`.
 Eq. :eq:`H_F_potential` is obtained by manipulating Eqs. :eq:`Faraday_m`, :eq:`Ampere_m` and :eq:`E_F_potential`, and choosing an appropriate Gauge.
 We can see from Eqs. :eq:`H_F_potential` and :eq:`E_F_potential` that :math:`\mathbf{F}` contains all the information corresponding to the electric and magnetic fields.
-Therefore, Maxwell's equations will be manipulated to solve for :math:`\mathbf{F}`; which can then be used to obtain :math:`\mathbf{E_m}` and :math:`\mathbf{H_m}`. 
+Therefore, Maxwell's equations will be manipulated to solve for :math:`\mathbf{F}`; which can then be used to obtain :math:`\mathbf{E_m}` and :math:`\mathbf{H_m}`.
 
 By manipulating Eqs. :eq:`Faraday_m`, :eq:`Ampere_m` and :eq:`E_F_potential` and choosing an appropriate Gauge, we find that :math:`\mathbf{F}` can be expressed using the Helmholtz equation:
 
 
 .. math::
 	\nabla^2 \mathbf{F} + k^2 \mathbf{F} = - \mathbf{J}_m^s, \  \  \  \  \text{where} \  \  k^2 = \omega^2\mu\varepsilon -i\omega\mu\sigma
-	:label: Helmholtz_F 
+	:label: Helmholtz_F
 
-The Helmholtz equation with boundary conditions can be solved to generate :math:`\mathbf{F}`. 
+The Helmholtz equation with boundary conditions can be solved to generate :math:`\mathbf{F}`.
 For infinite media, the boundary condition is such that :math:`\mathbf{F} \rightarrow 0` as :math:`r \rightarrow \infty`.
 From the Helmholtz equation, we can see that :math:`\mathbf{F}` will only have a component along the direction of :math:`\mathbf{J_m^s}`.
 The scalar Green's function for the Helmholtz equation is:
 
 
 .. math::
 	G(r) = \frac{e^{-ikr}}{4\pi r}.
-	:label: GreensFncFullSpace
+	:label: GreensFncFullSpaceMag
 
 and hence the vector potential for an arbitrary magnetic source is:
 

content/maxwell1_fundamentals/dipole_sources_in_homogeneous_media/magnetic_dipole_frequency/asymptotics.rst

@@ -6,7 +6,7 @@ Asymptotic Approximations
 .. purpose::
 
     Here, simplified expressions for the electric and magnetic fields are presented for several cases.
-    By examining simplified expressions, we can more easily see how the fields depend on certain parameters. 
+    By examining simplified expressions, we can more easily see how the fields depend on certain parameters.
 
 
 .. _frequency_domain_magnetic_dipole_asymptotics_DC:
@@ -42,14 +42,14 @@ In this case, the exponential term in :math:`\mathbf{E}_m` and :math:`\mathbf{H}
 
 .. math::
 	e^{-ikr} \approx 1 - ikr + O \left ( k^2 r^2 \right )
-	:label: eq_exp_TaylorO2
+	:label: eq_exp_TaylorO2_mag
 
-The near-field approximation for :math:`\mathbf{H}_m` can be obtained by replacing the exponential term in the full analytic solution with the Taylor series approximation from Eq. :eq:`eq_exp_TaylorO2`.
+The near-field approximation for :math:`\mathbf{H}_m` can be obtained by replacing the exponential term in the full analytic solution with the Taylor series approximation from Eq. :eq:`eq_exp_TaylorO2_mag`.
 Thus:
 
 .. math::
 	\begin{split}
-	\mathbf{H_m} \approx \frac{m}{4 \pi r^3} \Big ( 1 - ikr + O ( k^2 r^2 ) \Big ) \Bigg [ \Bigg ( & \frac{x^2}{r^2} \mathbf{\hat x} + \frac{xy}{r^2} \mathbf{\hat y} + \frac{xz}{r^2} \mathbf{\hat z} \Bigg ) ... \\ 
+	\mathbf{H_m} \approx \frac{m}{4 \pi r^3} \Big ( 1 - ikr + O ( k^2 r^2 ) \Big ) \Bigg [ \Bigg ( & \frac{x^2}{r^2} \mathbf{\hat x} + \frac{xy}{r^2} \mathbf{\hat y} + \frac{xz}{r^2} \mathbf{\hat z} \Bigg ) ... \\
 	& \Big ( -k^2 r^2 + 3ikr +3 \Big ) + \Big ( k^2 r^2 - ikr -1 \Big ) \mathbf{\hat x} \Bigg ]
 	\end{split}
 	:label: eq_Mdip_Hnear1
@@ -63,7 +63,7 @@ Eq. :eq:`eq_Mdip_Hnear1` can be simplified by neglecting polynomial terms which
 According to Eq. :eq:`eq_Mdip_Hnear2`, the near magnetic field depends only on the observation location and the magnetic dipole moment.
 Additionally, the source and the magnetic field are completely in-phase.
 
-The near-field approximation for :math:`\mathbf{E}_m` can be obtained by replacing the exponential term in the full analytic solution with the Taylor series approximation from Eq. :eq:`eq_exp_TaylorO2`.
+The near-field approximation for :math:`\mathbf{E}_m` can be obtained by replacing the exponential term in the full analytic solution with the Taylor series approximation from Eq. :eq:`eq_exp_TaylorO2_mag`.
 Thus:
 
 .. math::

content/maxwell1_fundamentals/dipole_sources_in_homogeneous_media/magnetic_dipole_time/analytic_solution.rst

@@ -9,7 +9,7 @@ Analytic Solution
     This is accomplished by applying the inverse Laplace transform to frequency domain solutions for the harmonic magnetic dipole.
     Analytic expressions for the electric field, the magnetic field and the corresponding vector potential are provided.
     Due to the difficulties which arise in deriving the final expressions, we will not include the effects of dielectric permittivity (:math:`\varepsilon`); this is known as the quasi-static approximation.
-    
+
 
 
 **Obtaining the Transient Response from a Harmonic Solution**
@@ -19,7 +19,7 @@ For a causal system, the unit step-response (:math:`g_+`) at :math:`t \geq 0` is
 
 .. math::
 	g_+(t) = \int_{-\infty}^\infty f(\tau) u(t - \tau) d\tau = \int_0^t f(\tau) d\tau \; \; \; \textrm{for} \; \; \; t\geq 0
-	:label: causal_step
+	:label: causal_step_mag
 
 where :math:`f(t)` is the system's impulse response.
 For most geophysical problems however, we are interested in the step-off or transient response (:math:`g_-`).
@@ -30,7 +30,7 @@ The step-off response for a causal system may be given by:
 	g_-(t) = \int_{-\infty}^\infty f(\tau) \big [ 1 - &u(t - \tau) \big ] d\tau = \; ... \\
 	& \int_0^\infty f(\tau) d\tau - \int_0^t f(\tau) d\tau = g_+ (\infty) - g_+(t) \; \; \; \textrm{for} \; \; \; t\geq 0
 	\end{split}
-	:label: causal_step_off
+	:label: causal_step_mag_off
 
 where :math:`g_+ (\infty )` represents the step-response at :math:`t = \infty`.
 Therefore, if the step-response is known for :math:`t \geq 0`, it can be used to obtain the step-off response at :math:`t \geq 0`.
@@ -39,15 +39,15 @@ From Ward and Hohmann :cite:`ward1988`, the step-response can be obtained via th
 
 .. math::
 	g_+(t) = L^{-1} \Bigg [ \frac{F(s)}{s} \Bigg ]
-	:label: step_Laplace_transform
+	:label: step_Laplace_transform_mag
 
 where :math:`F(s)` is obtained by replacing :math:`s=i\omega` in the system's harmonic response function.
 For the electric field, magnetic field and vector potential arising from a harmonic magnetic dipole in the :math:`\mathbf{\hat x}` direction, these have :ref:`already been derived<frequency_domain_magnetic_dipole_analytic_solution>`.
 
 
 **Harmonic Solutions for a Magnetic Dipole**
 
-As we just mentionned, harmonic solutions for the electric field, magnetic field and vector potential have :ref:`already been derived<frequency_domain_magnetic_dipole_analytic_solution>` for a source term :math:`\mathbf{J_m^s} = -i\omega IS \delta (x) \delta (y) \delta (z) \mathbf{\hat x}`. 
+As we just mentionned, harmonic solutions for the electric field, magnetic field and vector potential have :ref:`already been derived<frequency_domain_magnetic_dipole_analytic_solution>` for a source term :math:`\mathbf{J_m^s} = -i\omega IS \delta (x) \delta (y) \delta (z) \mathbf{\hat x}`.
 
 
 For the vector potential:
@@ -73,7 +73,7 @@ where the wavenumber :math:`k` is given by:
 
 .. math::
 	k = \big ( \omega^2\mu\varepsilon - i \omega \mu \sigma \big )^{1/2}
-	:label: wave_number
+	:label: wave_number_mag
 
 
 
@@ -84,7 +84,7 @@ Due to the difficulties which arise in deriving the final expressions, we will n
 
 .. math::
 	k = \big (- i \omega \mu \sigma \big )^{1/2}
-	:label: wave_number_quasi_static
+	:label: wave_number_mag_quasi_static
 
 If we substitute :math:`s = i\omega` in Eqs. :eq:`F_harmonic_response`, :eq:`E_harmonic_response` and :eq:`H_harmonic_response` and divide by :math:`s` then:
 
@@ -133,13 +133,13 @@ Thus:
 
 .. math::
 	L^{-1} \Bigg [ \frac{{\bf F}(s)}{s} \Bigg ] = \frac{m\theta^3}{\pi^{3/2} \sigma} e^{-\theta^2 r^2} \mathbf{\hat x} \; ,
-	:label: a_step_response
+	:label: a_step_response_mag
 
 
 
 .. math::
 	L^{-1}\Bigg [ \frac{{\bf E_m}(s)}{s} \Bigg ] = \frac{2 m \theta^5 }{\pi^{3/2} \sigma} e^{-\theta^2 r^2} \big ( z \, \mathbf{\hat y} - y \, \mathbf{\hat z} \big )
-	:label: e_step_response
+	:label: e_step_response_mag
 
 
 and
@@ -149,7 +149,7 @@ and
 	L^{-1}\Bigg [ \frac{{\bf H_m}(s)}{s} \Bigg ] = \frac{m}{4\pi r^3} \Bigg [ & \Bigg ( \frac{x^2}{r^2}\mathbf{\hat x} + \frac{xy}{r^2}\mathbf{\hat y} + \frac{xz}{r^2}\mathbf{\hat z} \Bigg ) \Bigg ( \bigg ( \frac{4}{\sqrt{\pi}} \theta^3 r^3 + \frac{6}{\sqrt{\pi}} \theta r \bigg ) e^{-\theta^2 r^2}  \, ...  \\
 	& + 3\, \textrm{erfc} (\theta r) \Bigg ) - \Bigg ( \bigg ( \frac{4}{\sqrt{\pi}} \theta^3 r^3 + \frac{2}{\sqrt{\pi}} \theta r \bigg ) e^{-\theta^2 r^2} +  \textrm{erfc} (\theta r) \Bigg ) \mathbf{\hat x} \Bigg ]
 	\end{split}
-	:label: h_step_response
+	:label: h_step_response_mag
 
 where
 
@@ -158,7 +158,7 @@ where
 	:label: theta_quasi_static
 
 
-Using the previous three expressions, we can determine the transient vector potential, electric field magnetic fields according to Eq. :eq:`causal_step_off`.
+Using the previous three expressions, we can determine the transient vector potential, electric field magnetic fields according to Eq. :eq:`causal_step_mag_off`.
 For the vector potential, the transient response is given by:
 
 
@@ -179,7 +179,7 @@ And for the magnetic field, the transient response is given by:
 
 .. math::
 	\begin{split}
-	{\bf h_m}(t) = \frac{m}{4\pi r^3} \Bigg [ & \Bigg ( \frac{x^2}{r^2} \mathbf{\hat x} + \frac{xy}{r^2}\mathbf{\hat y} + \frac{xz}{r^2} \mathbf{\hat z} \Bigg ) \Bigg ( 3 \, \textrm{erf}(\theta r) - \bigg ( \frac{4}{\sqrt{\pi}}\theta^3 r^3  \; ... \\ 
+	{\bf h_m}(t) = \frac{m}{4\pi r^3} \Bigg [ & \Bigg ( \frac{x^2}{r^2} \mathbf{\hat x} + \frac{xy}{r^2}\mathbf{\hat y} + \frac{xz}{r^2} \mathbf{\hat z} \Bigg ) \Bigg ( 3 \, \textrm{erf}(\theta r) - \bigg ( \frac{4}{\sqrt{\pi}}\theta^3 r^3  \; ... \\
 	&+ \frac{6}{\sqrt{\pi}}\theta r \bigg ) e^{-\theta^2 r^2} \Bigg ) - \Bigg (\textrm{erf}(\theta r) - \bigg ( \frac{4}{\sqrt{\pi}}\theta^3 r^3 + \frac{2}{\sqrt{\pi}}\theta r \bigg ) e^{-\theta^2 r^2} \Bigg ) \mathbf{\hat x}  \Bigg ]
 	\end{split}
 	:label: h_step_off_response