.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "content/user-guide/tutorials/05-dcr/plot_fwd_3_dcr3d.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_05-dcr_plot_fwd_3_dcr3d.py>`
to download the full example code.
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_content_user-guide_tutorials_05-dcr_plot_fwd_3_dcr3d.py:
DC Resistivity Forward Simulation in 3D
=======================================
Here we use the module *simpeg.electromagnetics.static.resistivity* to predict
DC resistivity data on an OcTree mesh. In this tutorial, we focus on the following:
- How to define the survey
- How to definine a tree mesh based on the survey geometry
- How to define the forward simulations
- How to predict DC data for a synthetic conductivity model
- How to include surface topography
- The units of the model and resulting data
- Plotting DC data in 3D
In this case, we simulate dipole-dipole data for three East-West lines and two
North-South lines.
.. GENERATED FROM PYTHON SOURCE LINES 25-29
Import modules
--------------
.. GENERATED FROM PYTHON SOURCE LINES 29-63
.. code-block:: Python
import os
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from discretize import TreeMesh
from discretize.utils import mkvc, refine_tree_xyz, active_from_xyz
from simpeg import maps, data
from simpeg.utils import model_builder
from simpeg.utils.io_utils.io_utils_electromagnetics import write_dcip_xyz
from simpeg.electromagnetics.static import resistivity as dc
from simpeg.electromagnetics.static.utils.static_utils import (
generate_dcip_sources_line,
apparent_resistivity_from_voltage,
)
# To plot DC data in 3D, the user must have the plotly package
try:
import plotly
from simpeg.electromagnetics.static.utils.static_utils import plot_3d_pseudosection
has_plotly = True
except ImportError:
has_plotly = False
pass
mpl.rcParams.update({"font.size": 16})
write_output = False
# sphinx_gallery_thumbnail_number = 2
.. GENERATED FROM PYTHON SOURCE LINES 64-71
Defining Topography
-------------------
Here we define surface topography as an (N, 3) numpy array. Topography could
also be loaded from a file. In our case, our survey takes place within a circular
depression.
.. GENERATED FROM PYTHON SOURCE LINES 71-80
.. code-block:: Python
x_topo, y_topo = np.meshgrid(
np.linspace(-2100, 2100, 141), np.linspace(-2000, 2000, 141)
)
s = np.sqrt(x_topo**2 + y_topo**2)
z_topo = 10 + (1 / np.pi) * 140 * (-np.pi / 2 + np.arctan((s - 600.0) / 160.0))
x_topo, y_topo, z_topo = mkvc(x_topo), mkvc(y_topo), mkvc(z_topo)
topo_xyz = np.c_[x_topo, y_topo, z_topo]
.. GENERATED FROM PYTHON SOURCE LINES 81-92
Construct the DC Survey
-----------------------
Here we define 5 DC lines that use a dipole-dipole electrode configuration;
three lines along the East-West direction and 2 lines along the North-South direction.
For each source, we must define the AB electrode locations. For each receiver
we must define the MN electrode locations. Instead of creating the survey
from scratch (see 1D example), we will use the *generat_dcip_sources_line* utility.
This utility will give us the source list for a given DC/IP line. We can append
the sources for multiple lines to create the survey.
.. GENERATED FROM PYTHON SOURCE LINES 92-122
.. code-block:: Python
# Define the parameters for each survey line
survey_type = "dipole-dipole"
data_type = "volt"
dimension_type = "3D"
end_locations_list = [
np.r_[-1000.0, 1000.0, 0.0, 0.0],
np.r_[-350.0, -350.0, -1000.0, 1000.0],
np.r_[350.0, 350.0, -1000.0, 1000.0],
]
station_separation = 100.0
num_rx_per_src = 8
# The source lists for each line can be appended to create the source
# list for the whole survey.
source_list = []
for ii in range(0, len(end_locations_list)):
source_list += generate_dcip_sources_line(
survey_type,
data_type,
dimension_type,
end_locations_list[ii],
topo_xyz,
num_rx_per_src,
station_separation,
)
# Define the survey
survey = dc.survey.Survey(source_list)
.. GENERATED FROM PYTHON SOURCE LINES 123-129
Create OcTree Mesh
------------------
Here, we create the OcTree mesh that will be used to predict DC data.
.. GENERATED FROM PYTHON SOURCE LINES 129-163
.. code-block:: Python
# Defining domain side and minimum cell size
dh = 25.0 # base cell width
dom_width_x = 6000.0 # domain width x
dom_width_y = 6000.0 # domain width y
dom_width_z = 4000.0 # domain width z
nbcx = 2 ** int(np.round(np.log(dom_width_x / dh) / np.log(2.0))) # num. base cells x
nbcy = 2 ** int(np.round(np.log(dom_width_y / dh) / np.log(2.0))) # num. base cells y
nbcz = 2 ** int(np.round(np.log(dom_width_z / dh) / np.log(2.0))) # num. base cells z
# Define the base mesh
hx = [(dh, nbcx)]
hy = [(dh, nbcy)]
hz = [(dh, nbcz)]
mesh = TreeMesh([hx, hy, hz], x0="CCN")
# Mesh refinement based on topography
k = np.sqrt(np.sum(topo_xyz[:, 0:2] ** 2, axis=1)) < 1200
mesh = refine_tree_xyz(
mesh, topo_xyz[k, :], octree_levels=[0, 6, 8], method="surface", finalize=False
)
# Mesh refinement near sources and receivers.
electrode_locations = np.r_[
survey.locations_a, survey.locations_b, survey.locations_m, survey.locations_n
]
unique_locations = np.unique(electrode_locations, axis=0)
mesh = refine_tree_xyz(
mesh, unique_locations, octree_levels=[4, 6, 4], method="radial", finalize=False
)
# Finalize the mesh
mesh.finalize()
.. rst-class:: sphx-glr-script-out
.. code-block:: none
/home/vsts/work/1/s/tutorials/05-dcr/plot_fwd_3_dcr3d.py:143: FutureWarning:
In discretize v1.0 the TreeMesh will change the default value of diagonal_balance to True, which will likely slightly change meshes you have previously created. If you need to keep the current behavior, explicitly set diagonal_balance=False.
/home/vsts/work/1/s/tutorials/05-dcr/plot_fwd_3_dcr3d.py:147: DeprecationWarning:
The surface option is deprecated as of `0.9.0` please update your code to use the `TreeMesh.refine_surface` functionality. It will be removed in a future version of discretize.
/home/vsts/work/1/s/tutorials/05-dcr/plot_fwd_3_dcr3d.py:156: DeprecationWarning:
The radial option is deprecated as of `0.9.0` please update your code to use the `TreeMesh.refine_points` functionality. It will be removed in a future version of discretize.
.. GENERATED FROM PYTHON SOURCE LINES 164-172
Create Conductivity Model and Mapping for OcTree Mesh
-----------------------------------------------------
Here we define the conductivity model that will be used to predict DC
resistivity data. The model consists of a conductive sphere and a
resistive sphere within a moderately conductive background. Note that
you can carry through this work flow with a resistivity model if desired.
.. GENERATED FROM PYTHON SOURCE LINES 172-230
.. code-block:: Python
# Define conductivity model in S/m (or resistivity model in Ohm m)
air_value = 1e-8
background_value = 1e-2
conductor_value = 1e-1
resistor_value = 1e-3
# Find active cells in forward modeling (cell below surface)
ind_active = active_from_xyz(mesh, topo_xyz)
# Define mapping from model to active cells
nC = int(ind_active.sum())
conductivity_map = maps.InjectActiveCells(mesh, ind_active, air_value)
# Define model
conductivity_model = background_value * np.ones(nC)
ind_conductor = model_builder.get_indices_sphere(
np.r_[-350.0, 0.0, -300.0], 160.0, mesh.cell_centers[ind_active, :]
)
conductivity_model[ind_conductor] = conductor_value
ind_resistor = model_builder.get_indices_sphere(
np.r_[350.0, 0.0, -300.0], 160.0, mesh.cell_centers[ind_active, :]
)
conductivity_model[ind_resistor] = resistor_value
# Plot Conductivity Model
fig = plt.figure(figsize=(10, 4))
plotting_map = maps.InjectActiveCells(mesh, ind_active, np.nan)
log_mod = np.log10(conductivity_model)
ax1 = fig.add_axes([0.15, 0.15, 0.68, 0.75])
mesh.plot_slice(
plotting_map * log_mod,
ax=ax1,
normal="Y",
ind=int(len(mesh.h[1]) / 2),
grid=True,
clim=(np.log10(resistor_value), np.log10(conductor_value)),
pcolor_opts={"cmap": mpl.cm.viridis},
)
ax1.set_title("Conductivity Model")
ax1.set_xlabel("x (m)")
ax1.set_ylabel("z (m)")
ax1.set_xlim([-1000, 1000])
ax1.set_ylim([-1000, 0])
ax2 = fig.add_axes([0.84, 0.15, 0.03, 0.75])
norm = mpl.colors.Normalize(
vmin=np.log10(resistor_value), vmax=np.log10(conductor_value)
)
cbar = mpl.colorbar.ColorbarBase(
ax2, cmap=mpl.cm.viridis, norm=norm, orientation="vertical", format="$10^{%.1f}$"
)
cbar.set_label("Conductivity [S/m]", rotation=270, labelpad=15, size=12)
.. image-sg:: /content/user-guide/tutorials/05-dcr/images/sphx_glr_plot_fwd_3_dcr3d_001.png
:alt: Conductivity Model
:srcset: /content/user-guide/tutorials/05-dcr/images/sphx_glr_plot_fwd_3_dcr3d_001.png
:class: sphx-glr-single-img
.. GENERATED FROM PYTHON SOURCE LINES 231-240
Project Survey to Discretized Topography
----------------------------------------
It is important that electrodes are not modeled as being in the air. Even if the
electrodes are properly located along surface topography, they may lie above
the *discretized* topography. This step is carried out to ensure all electrodes
lie on the discretized surface.
.. GENERATED FROM PYTHON SOURCE LINES 240-243
.. code-block:: Python
survey.drape_electrodes_on_topography(mesh, ind_active, option="top")
.. GENERATED FROM PYTHON SOURCE LINES 244-253
Predict DC Resistivity Data
---------------------------
Here we predict DC resistivity data. If the keyword argument *sigmaMap* is
defined, the simulation will expect a conductivity model. If the keyword
argument *rhoMap* is defined, the simulation will expect a resistivity model.
.. GENERATED FROM PYTHON SOURCE LINES 253-265
.. code-block:: Python
# Define the DC simulation
simulation = dc.simulation.Simulation3DNodal(
mesh,
survey=survey,
sigmaMap=conductivity_map,
)
# Predict the data by running the simulation. The data are the measured voltage
# normalized by the source current in units of V/A.
dpred = simulation.dpred(conductivity_model)
.. rst-class:: sphx-glr-script-out
.. code-block:: none
/home/vsts/work/1/s/simpeg/base/pde_simulation.py:490: DefaultSolverWarning:
Using the default solver: Pardiso.
If you would like to suppress this notification, add
warnings.filterwarnings('ignore', simpeg.utils.solver_utils.DefaultSolverWarning)
to your script.
.. GENERATED FROM PYTHON SOURCE LINES 266-277
Plot DC Data in 3D Pseudosection
--------------------------------
Here we demonstrate how 3D DC resistivity data can be represented on a 3D
pseudosection plot. To use this utility, you must have Python's *plotly*
package. Here, we represent the data as apparent conductivities.
The *plot_3d_pseudosection* utility allows the user to plot all pseudosection
points, or plot the pseudosection plots that lie within some distance of
one or more planes.
.. GENERATED FROM PYTHON SOURCE LINES 277-330
.. code-block:: Python
# Since the data are normalized voltage, we must convert predicted
# to apparent conductivities.
apparent_conductivity = 1 / apparent_resistivity_from_voltage(
survey,
dpred,
)
# For large datasets or for surveys with unconventional electrode geometry,
# interpretation can be challenging if we plot every datum. Here, we plot
# 3 out of the 5 survey lines to better image anomalous structures.
# To plot ALL of the data, simply remove the keyword argument *plane_points*
# when calling *plot_3d_pseudosection*.
plane_points = []
p1, p2, p3 = np.array([-1000, 0, 0]), np.array([1000, 0, 0]), np.array([0, 0, -1000])
plane_points.append([p1, p2, p3])
p1, p2, p3 = (
np.array([-350, -1000, 0]),
np.array([-350, 1000, 0]),
np.array([-350, 0, -1000]),
)
plane_points.append([p1, p2, p3])
p1, p2, p3 = (
np.array([350, -1000, 0]),
np.array([350, 1000, 0]),
np.array([350, 0, -1000]),
)
plane_points.append([p1, p2, p3])
if has_plotly:
fig = plot_3d_pseudosection(
survey,
apparent_conductivity,
scale="log",
units="S/m",
plane_points=plane_points,
plane_distance=15,
)
fig.update_layout(
title_text="Apparent Conductivity",
title_x=0.5,
title_font_size=24,
width=650,
height=500,
scene_camera=dict(center=dict(x=0.05, y=0, z=-0.4)),
)
plotly.io.show(fig)
else:
print("INSTALL 'PLOTLY' TO VISUALIZE 3D PSEUDOSECTIONS")
.. raw:: html
:file: images/sphx_glr_plot_fwd_3_dcr3d_002.html
.. GENERATED FROM PYTHON SOURCE LINES 331-336
Optional: Write Predicted DC Data
---------------------------------
Write DC resistivity data, topography and true model
.. GENERATED FROM PYTHON SOURCE LINES 336-385
.. code-block:: Python
if write_output:
dir_path = os.path.dirname(__file__).split(os.path.sep)
dir_path.extend(["outputs"])
dir_path = os.path.sep.join(dir_path) + os.path.sep
if not os.path.exists(dir_path):
os.mkdir(dir_path)
# Add 5% Gaussian noise to each datum
np.random.seed(433)
std = 0.1 * np.abs(dpred)
noise = std * np.random.randn(len(dpred))
dobs = dpred + noise
# Create dictionary that stores line IDs
N = int(survey.nD / len(end_locations_list))
lineID = np.r_[np.ones(N), 2 * np.ones(N), 3 * np.ones(N)]
out_dict = {"LINEID": lineID}
# Create a survey with the original electrode locations
# and not the shifted ones
source_list = []
for ii in range(0, len(end_locations_list)):
source_list += generate_dcip_sources_line(
survey_type,
data_type,
dimension_type,
end_locations_list[ii],
topo_xyz,
num_rx_per_src,
station_separation,
)
survey_original = dc.survey.Survey(source_list)
# Write out data at their original electrode locations (not shifted)
data_obj = data.Data(survey_original, dobs=dobs, standard_deviation=std)
fname = dir_path + "dc_data.xyz"
write_dcip_xyz(
fname,
data_obj,
data_header="V/A",
uncertainties_header="UNCERT",
out_dict=out_dict,
)
fname = dir_path + "topo_xyz.txt"
np.savetxt(fname, topo_xyz, fmt="%.4e")
.. rst-class:: sphx-glr-timing
**Total running time of the script:** (0 minutes 16.957 seconds)
**Estimated memory usage:** 288 MB
.. _sphx_glr_download_content_user-guide_tutorials_05-dcr_plot_fwd_3_dcr3d.py:
.. only:: html
.. container:: sphx-glr-footer sphx-glr-footer-example
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_fwd_3_dcr3d.ipynb <plot_fwd_3_dcr3d.ipynb>`
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_fwd_3_dcr3d.py <plot_fwd_3_dcr3d.py>`
.. container:: sphx-glr-download sphx-glr-download-zip
:download:`Download zipped: plot_fwd_3_dcr3d.zip <plot_fwd_3_dcr3d.zip>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_