.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "content/examples/06-tdem/plot_0_tdem_analytic.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_content_examples_06-tdem_plot_0_tdem_analytic.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_content_examples_06-tdem_plot_0_tdem_analytic.py:


Simulation with Analytic TDEM Solutions
=======================================

Here, the module *SimPEG.electromagnetics.analytics.TDEM* is used to simulate
transient electric and magnetic field for both electric and magnetic dipole
sources in a wholespace.

.. GENERATED FROM PYTHON SOURCE LINES 13-16

Import modules
--------------


.. GENERATED FROM PYTHON SOURCE LINES 16-28

.. code-block:: Python


    import numpy as np
    from SimPEG import utils
    from SimPEG.electromagnetics.analytics.TDEM import (
        TransientElectricDipoleWholeSpace,
        TransientMagneticDipoleWholeSpace,
    )

    import matplotlib.pyplot as plt
    from matplotlib.colors import LogNorm









.. GENERATED FROM PYTHON SOURCE LINES 29-37

Magnetic Fields for a Transient Magnetic Dipole Source
------------------------------------------------------

Here, we compute the magnetic field and its time-derivative for a transient
magnetic dipole source in the z direction. Based on the geometry of the problem, we
expect magnetic fields in the x and z directions, but none in the y
direction.


.. GENERATED FROM PYTHON SOURCE LINES 37-118

.. code-block:: Python


    # Defining electric dipole location and frequency
    source_location = np.r_[0, 0, 0]
    t = [1e-4, 1e-3, 1e-2]

    # Defining observation locations (avoid placing observation at source)
    x = np.arange(-201, 201, step=2.0)
    y = np.r_[0]
    z = x
    observation_locations = utils.ndgrid(x, y, z)

    # Define wholespace conductivity
    sig = 1e0

    # Plot the magnetic field
    fig = plt.figure(figsize=(14, 3))
    ax = 3 * [None]
    cb = 3 * [None]
    pc = 3 * [None]

    for ii in range(0, 3):
        # Compute the fields
        Hx, Hy, Hz = TransientMagneticDipoleWholeSpace(
            observation_locations,
            source_location,
            sig,
            t[ii],
            moment="Z",
            fieldType="h",
            mu_r=1,
        )

        hxplt = Hx.reshape(x.size, z.size)
        hzplt = Hz.reshape(x.size, z.size)

        ax[ii] = fig.add_axes([0.1 + 0.28 * ii, 0.1, 0.2, 0.8])
        absH = np.sqrt(Hx**2 + Hy**2 + Hz**2)
        pc[ii] = ax[ii].pcolor(x, z, absH.reshape(x.size, z.size), norm=LogNorm())
        ax[ii].streamplot(x, z, hxplt.real, hzplt.real, color="k", density=1)
        ax[ii].set_xlim([x.min(), x.max()])
        ax[ii].set_ylim([z.min(), z.max()])
        ax[ii].set_title("H at t = {} s".format(t[ii]))
        ax[ii].set_xlabel("x")
        ax[ii].set_ylabel("z")
        cb[ii] = plt.colorbar(pc[ii], ax=ax[ii])
        cb[ii].set_label("H (A/m)")

    # Plot the time-derivative
    fig = plt.figure(figsize=(14, 3))
    ax = 3 * [None]
    cb = 3 * [None]
    pc = 3 * [None]

    for ii in range(0, 3):
        # Compute the fields
        dHdtx, dHdty, dHdtz = TransientMagneticDipoleWholeSpace(
            observation_locations,
            source_location,
            sig,
            t[ii],
            moment="Z",
            fieldType="dhdt",
            mu_r=1,
        )

        dhdtxplt = dHdtx.reshape(x.size, z.size)
        dhdtzplt = dHdtz.reshape(x.size, z.size)

        ax[ii] = fig.add_axes([0.1 + 0.28 * ii, 0.1, 0.2, 0.8])
        absdHdt = np.sqrt(dHdtx**2 + dHdty**2 + dHdtz**2)
        pc[ii] = ax[ii].pcolor(x, z, absdHdt.reshape(x.size, z.size), norm=LogNorm())
        ax[ii].streamplot(x, z, dhdtxplt.real, dhdtzplt.real, color="k", density=1)
        ax[ii].set_xlim([x.min(), x.max()])
        ax[ii].set_ylim([z.min(), z.max()])
        ax[ii].set_title("dH/dt at t = {} s".format(t[ii]))
        ax[ii].set_xlabel("x")
        ax[ii].set_ylabel("z")
        cb[ii] = plt.colorbar(pc[ii], ax=ax[ii])
        cb[ii].set_label("dH/dt (A/m*s)")





.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_001.png
         :alt: H at t = 0.0001 s, H at t = 0.001 s, H at t = 0.01 s
         :srcset: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_002.png
         :alt: dH/dt at t = 0.0001 s, dH/dt at t = 0.001 s, dH/dt at t = 0.01 s
         :srcset: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_002.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 119-127

Electric Field from a Transient Electric Current Dipole Source
--------------------------------------------------------------

Here, we compute the electric fields for a transient electric current dipole
source in the z direction. Based on the geometry of the problem, we
expect electric fields in the x and z directions, but none in the y
direction.


.. GENERATED FROM PYTHON SOURCE LINES 127-174

.. code-block:: Python


    # Defining electric dipole location and frequency
    source_location = np.r_[0, 0, 0]
    t = [1e-4, 1e-3, 1e-2]

    # Defining observation locations (avoid placing observation at source)
    x = np.arange(-201, 201, step=2.0)
    y = np.r_[0]
    z = x
    observation_locations = utils.ndgrid(x, y, z)

    # Define wholespace conductivity
    sig = 1e0

    fig = plt.figure(figsize=(14, 3))
    ax = 3 * [None]
    cb = 3 * [None]
    pc = 3 * [None]

    for ii in range(0, 3):
        # Compute the fields
        Ex, Ey, Ez = TransientElectricDipoleWholeSpace(
            observation_locations,
            source_location,
            sig,
            t[ii],
            moment="Z",
            fieldType="e",
            mu_r=1,
        )

        explt = Ex.reshape(x.size, z.size)
        ezplt = Ez.reshape(x.size, z.size)

        ax[ii] = fig.add_axes([0.1 + 0.28 * ii, 0.1, 0.2, 0.8])
        absE = np.sqrt(Ex**2 + Ey**2 + Ez**2)
        pc[ii] = ax[ii].pcolor(x, z, absE.reshape(x.size, z.size), norm=LogNorm())
        ax[ii].streamplot(x, z, explt.real, ezplt.real, color="k", density=1)
        ax[ii].set_xlim([x.min(), x.max()])
        ax[ii].set_ylim([z.min(), z.max()])
        ax[ii].set_title("E at t = {} s".format(t[ii]))
        ax[ii].set_xlabel("x")
        ax[ii].set_ylabel("z")
        cb[ii] = plt.colorbar(pc[ii], ax=ax[ii])
        cb[ii].set_label("E (V/m)")





.. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_003.png
   :alt: E at t = 0.0001 s, E at t = 0.001 s, E at t = 0.01 s
   :srcset: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 175-183

Magnetic Field from a Transient Electric Dipole Source
------------------------------------------------------

Here, we compute the magnetic fields for a transient electric current dipole
source in the y direction. Based on the geometry of the problem, we
expect rotational magnetic fields in the x and z directions, but no fields
in the y direction.


.. GENERATED FROM PYTHON SOURCE LINES 183-228

.. code-block:: Python


    # Defining electric dipole location and frequency
    source_location = np.r_[0, 0, 0]
    t = [1e-4, 1e-3, 1e-2]

    # Defining observation locations (avoid placing observation at source)
    x = np.arange(-201, 201, step=2.0)
    y = np.r_[0]
    z = x
    observation_locations = utils.ndgrid(x, y, z)

    # Define wholespace conductivity
    sig = 1e0

    fig = plt.figure(figsize=(14, 3))
    ax = 3 * [None]
    cb = 3 * [None]
    pc = 3 * [None]

    for ii in range(0, 3):
        # Compute the fields
        Hx, Hy, Hz = TransientElectricDipoleWholeSpace(
            observation_locations,
            source_location,
            sig,
            t[ii],
            moment="Y",
            fieldType="h",
            mu_r=1,
        )

        hxplt = Hx.reshape(x.size, z.size)
        hzplt = Hz.reshape(x.size, z.size)

        ax[ii] = fig.add_axes([0.1 + 0.28 * ii, 0.1, 0.2, 0.8])
        absH = np.sqrt(Hx**2 + Hy**2 + Hz**2)
        pc[ii] = ax[ii].pcolor(x, z, absH.reshape(x.size, z.size), norm=LogNorm())
        ax[ii].streamplot(x, z, hxplt.real, hzplt.real, color="k", density=1)
        ax[ii].set_xlim([x.min(), x.max()])
        ax[ii].set_ylim([z.min(), z.max()])
        ax[ii].set_title("H at t = {} s".format(t[ii]))
        ax[ii].set_xlabel("x")
        ax[ii].set_ylabel("z")
        cb[ii] = plt.colorbar(pc[ii], ax=ax[ii])
        cb[ii].set_label("H (A/m)")



.. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_004.png
   :alt: H at t = 0.0001 s, H at t = 0.001 s, H at t = 0.01 s
   :srcset: /content/examples/06-tdem/images/sphx_glr_plot_0_tdem_analytic_004.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 10.019 seconds)

**Estimated memory usage:**  170 MB


.. _sphx_glr_download_content_examples_06-tdem_plot_0_tdem_analytic.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_0_tdem_analytic.ipynb <plot_0_tdem_analytic.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_0_tdem_analytic.py <plot_0_tdem_analytic.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_