.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "content/user-guide/tutorials/10-vrm/plot_fwd_1_vrm_layer.py"
.. LINE NUMBERS ARE GIVEN BELOW.
.. only:: html
.. note::
:class: sphx-glr-download-link-note
:ref:`Go to the end <sphx_glr_download_content_user-guide_tutorials_10-vrm_plot_fwd_1_vrm_layer.py>`
to download the full example code.
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_content_user-guide_tutorials_10-vrm_plot_fwd_1_vrm_layer.py:
Response from a Homogeneous Layer for Different Waveforms
=========================================================
Here we use the module *simpeg.electromagnetics.viscous_remanent_magnetization*
to predict the characteristic VRM response over magnetically viscous layer.
We consider a small-loop, ground-based survey which uses a coincident loop
geometry. For this tutorial, we focus on the following:
- How to define the transmitters and receivers
- How to define the survey
- How to define a diagnostic physical property
- How to define the physics for the linear potential fields formulation
- How the VRM response depends on the transmitter waveform
Note that for this tutorial, we are only modeling the VRM response. A separate
tutorial have been developed for modeling both the inductive and VRM responses.
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Import Modules
--------------
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.. code-block:: Python
import simpeg.electromagnetics.viscous_remanent_magnetization as vrm
from discretize import TensorMesh
from discretize.utils import mkvc
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
# sphinx_gallery_thumbnail_number = 2
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Define Waveforms
----------------
Under *simpeg.electromagnetic.viscous_remanent_magnetization.waveform*
there are a multitude of waveforms that can be defined (Step-off, square-pulse,
piecewise linear, ...). Here we define a specific waveform for each transmitter.
Each waveform is defined with a diferent set of parameters.
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.. code-block:: Python
waveform_list = []
# Step-off waveform
waveform_list.append(vrm.waveforms.StepOff(t0=0))
# 20 ms square pulse with off-time at t = 0 s.
waveform_list.append(vrm.waveforms.SquarePulse(t0=0, delt=0.02))
# 30 ms trapezoidal waveform with off-time at t = 0 s.
t_wave = np.r_[-0.03, -0.02, -0.01, 0]
I_wave = np.r_[0.0, 1.0, 1.0, 0]
waveform_list.append(vrm.waveforms.ArbitraryPiecewise(t_wave=t_wave, I_wave=I_wave))
# 40 ms triangular waveform with off-time at t = 0 s.
t_wave = np.r_[-0.04, -0.02, 0]
I_wave = np.r_[0.0, 1.0, 0]
waveform_list.append(vrm.waveforms.ArbitraryPiecewise(t_wave=t_wave, I_wave=I_wave))
# Plot waveforms
fig = plt.figure(figsize=(8, 4))
mpl.rcParams.update({"font.size": 12})
ax1 = fig.add_axes([0.1, 0.1, 0.85, 0.85])
ax1.plot(np.r_[-0.04, 0.0, 0.0, 0.02], np.r_[1, 1, 0, 0], "b", lw=2)
ax1.plot(np.r_[-0.04, -0.02, -0.02, 0.0, 0.0, 0.04], np.r_[0, 0, 1, 1, 0, 0], "r", lw=2)
ax1.plot(np.r_[-0.04, -0.03, -0.02, -0.01, 0, 0.04], np.r_[0, 0, 1, 1, 0, 0], "k", lw=2)
ax1.plot(np.r_[-0.04, -0.02, 0, 0.04], np.r_[0, 1, 0, 0], "g", lw=2)
ax1.set_xlim((-0.04, 0.04))
ax1.set_ylim((-0.01, 1.1))
ax1.set_xlabel("time [s]")
ax1.set_ylabel("current [A]")
ax1.set_title("Waveforms")
ax1.legend(
["step-off", "20 ms square pulse", "30 ms trapezoidal", "40 ms triangular"],
loc="upper right",
)
.. image-sg:: /content/user-guide/tutorials/10-vrm/images/sphx_glr_plot_fwd_1_vrm_layer_001.png
:alt: Waveforms
:srcset: /content/user-guide/tutorials/10-vrm/images/sphx_glr_plot_fwd_1_vrm_layer_001.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
<matplotlib.legend.Legend object at 0x7fd3ef201f00>
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Survey
------
Here we define the sources, the receivers and the survey. For this exercise,
we are modeling the response for single transmitter-receiver pair with
different transmitter waveforms.
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.. code-block:: Python
# Define the observation times for the receivers. It is VERY important to
# define the first time channel AFTER the off-time.
time_channels = np.logspace(-4, -1, 31)
# Define the location of the coincident loop transmitter and receiver.
# In general, you can define the receiver locations as an (N, 3) numpy array.
xyz = np.c_[0.0, 0.0, 0.5]
# There are 4 parameters needed to define a receiver.
dbdt_receivers = [
vrm.receivers.Point(xyz, times=time_channels, field_type="dbdt", orientation="z")
]
# Define sources
source_list = []
dipole_moment = [0.0, 0.0, 1]
for pp in range(0, len(waveform_list)):
# Define the transmitter-receiver pair for each waveform
source_list.append(
vrm.sources.MagDipole(
dbdt_receivers, mkvc(xyz), dipole_moment, waveform_list[pp]
)
)
# Define the survey
survey = vrm.Survey(source_list)
.. GENERATED FROM PYTHON SOURCE LINES 124-132
Defining the Mesh
-----------------
Here we create the tensor mesh that will be used for this tutorial example.
We are modeling the response from a magnetically viscous layer. As a result,
we do not need to model the Earth at depth. For this example the layer is
10 m thick.
.. GENERATED FROM PYTHON SOURCE LINES 132-139
.. code-block:: Python
cs, ncx, ncy, ncz, npad = 2.0, 35, 35, 5, 5
hx = [(cs, npad, -1.3), (cs, ncx), (cs, npad, 1.3)]
hy = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)]
hz = [(cs, ncz)]
mesh = TensorMesh([hx, hy, hz], "CCN")
.. GENERATED FROM PYTHON SOURCE LINES 140-149
Defining an Amalgamated Magnetic Property Model
-----------------------------------------------
For the linear potential field formulation, the magnetic viscosity
characterizing each cell can be defined by an "amalgamated magnetic property"
(see Cowan, 2016). Here we define an amalgamated magnetic property model.
For other formulations of the forward simulation, you may define the parameters
assuming a log-uniform or log-normal distribution of time-relaxation constants.
.. GENERATED FROM PYTHON SOURCE LINES 149-158
.. code-block:: Python
# Amalgamated magnetic property for the layer
model_value = 0.0001
model = model_value * np.ones(mesh.nC)
# Define the active cells. These are the cells that exhibit magnetic viscosity
# and/or lie below the surface topography.
ind_active = np.ones(mesh.nC, dtype="bool")
.. GENERATED FROM PYTHON SOURCE LINES 159-168
Define the Simulation
---------------------
Here we define the formulation for solving Maxwell's equations. We have chosen
to model the off-time VRM response. There are two important keyword arguments,
*refinement_factor* and *refinement_distance*. These are used to refine the
sensitivities of the cells near the transmitters. This improves the accuracy
of the forward simulation without having to refine the mesh near transmitters.
.. GENERATED FROM PYTHON SOURCE LINES 168-181
.. code-block:: Python
# For this example, cells lying within 2 m of a transmitter will be modeled
# as if they are comprised of 4^3 equal smaller cells. Cells within 4 m of a
# transmitter will be modeled as if they are comprised of 2^3 equal smaller
# cells.
simulation = vrm.Simulation3DLinear(
mesh,
survey=survey,
active_cells=ind_active,
refinement_factor=2,
refinement_distance=[2.0, 4.0],
)
.. GENERATED FROM PYTHON SOURCE LINES 182-185
Predict Data and Plot
---------------------
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.. code-block:: Python
# Predict VRM response
dpred = simulation.dpred(model)
# Reshape for plotting
n_times = len(time_channels)
n_waveforms = len(waveform_list)
dpred = np.reshape(dpred, (n_waveforms, n_times)).T
# Characteristic VRM decay for several waveforms.
fig = plt.figure(figsize=(6, 7))
ax1 = fig.add_axes([0.15, 0.1, 0.8, 0.85])
ax1.loglog(time_channels, -dpred[:, 0], "b", lw=2)
ax1.loglog(time_channels, -dpred[:, 1], "r", lw=2)
ax1.loglog(time_channels, -dpred[:, 2], "k", lw=2)
ax1.loglog(time_channels, -dpred[:, 3], "g", lw=2)
ax1.set_xlim((np.min(time_channels), np.max(time_channels)))
ax1.set_xlabel("time [s]")
ax1.set_ylabel("-dBz/dt [T/s]")
ax1.set_title("Characteristic Decay")
ax1.legend(
["step-off", "20 ms square pulse", "30 ms trapezoidal", "40 ms triangular"],
loc="upper right",
)
.. image-sg:: /content/user-guide/tutorials/10-vrm/images/sphx_glr_plot_fwd_1_vrm_layer_002.png
:alt: Characteristic Decay
:srcset: /content/user-guide/tutorials/10-vrm/images/sphx_glr_plot_fwd_1_vrm_layer_002.png
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
.. code-block:: none
CREATING T MATRIX
CREATING A MATRIX
<matplotlib.legend.Legend object at 0x7fd3ee242bc0>
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (0 minutes 4.093 seconds)
**Estimated memory usage:** 295 MB
.. _sphx_glr_download_content_user-guide_tutorials_10-vrm_plot_fwd_1_vrm_layer.py:
.. only:: html
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.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_fwd_1_vrm_layer.ipynb <plot_fwd_1_vrm_layer.ipynb>`
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_fwd_1_vrm_layer.py <plot_fwd_1_vrm_layer.py>`
.. container:: sphx-glr-download sphx-glr-download-zip
:download:`Download zipped: plot_fwd_1_vrm_layer.zip <plot_fwd_1_vrm_layer.zip>`
.. only:: html
.. rst-class:: sphx-glr-signature
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