mirror of
https://github.com/wassname/simpeg.git
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organizing the docs - put the content in a content folder. put the SimPEG core api docs in core_api
This commit is contained in:
Lindsey Heagy
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.. _examples_DC_Analytic_Dipole:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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DC Analytic Dipole
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==================
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.. plot::
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from SimPEG import Examples
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Examples.DC_Analytic_Dipole.run()
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.. literalinclude:: ../../SimPEG/Examples/DC_Analytic_Dipole.py
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:language: python
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:linenos:
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.. _examples_DC_Forward_PseudoSection:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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DC Forward Simulation
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=====================
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Forward model two conductive spheres in a half-space and plot a
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pseudo-section. Assumes an infinite line source and measures along the
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center of the spheres.
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INPUT:
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loc = Location of spheres [[x1,y1,z1],[x2,y2,z2]]
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radi = Radius of spheres [r1,r2]
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param = Conductivity of background and two spheres [m0,m1,m2]
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surveyType = survey type 'pole-dipole' or 'dipole-dipole'
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unitType = Data type "appResistivity" | "appConductivity" | "volt"
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Created by @fourndo
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.. plot::
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from SimPEG import Examples
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Examples.DC_Forward_PseudoSection.run()
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.. literalinclude:: ../../SimPEG/Examples/DC_Forward_PseudoSection.py
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:language: python
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:linenos:
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.. _examples_EM_FDEM_1D_Inversion:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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EM: FDEM: 1D: Inversion
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=======================
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Here we will create and run a FDEM 1D inversion.
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.. plot::
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from SimPEG import Examples
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Examples.EM_FDEM_1D_Inversion.run()
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.. literalinclude:: ../../SimPEG/Examples/EM_FDEM_1D_Inversion.py
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:language: python
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:linenos:
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.. _examples_EM_FDEM_Analytic_MagDipoleWholespace:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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EM: Magnetic Dipole in a Whole-Space
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====================================
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Here we plot the magnetic flux density from a harmonic dipole in a wholespace.
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.. plot::
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from SimPEG import Examples
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Examples.EM_FDEM_Analytic_MagDipoleWholespace.run()
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.. literalinclude:: ../../SimPEG/Examples/EM_FDEM_Analytic_MagDipoleWholespace.py
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:language: python
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:linenos:
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.. _examples_EM_Schenkel_Morrison_Casing:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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EM: Schenkel and Morrison Casing Model
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======================================
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Here we create and run a FDEM forward simulation to calculate the vertical
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current inside a steel-cased. The model is based on the Schenkel and
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Morrison Casing Model, and the results are used in a 2016 SEG abstract by
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Yang et al.
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.. code-block:: text
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Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
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The model consists of:
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- Air: Conductivity 1e-8 S/m, above z = 0
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- Background: conductivity 1e-2 S/m, below z = 0
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- Casing: conductivity 1e6 S/m
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- 300m long
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- radius of 0.1m
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- thickness of 6e-3m
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Inside the casing, we take the same conductivity as the background.
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We are using an EM code to simulate DC, so we use frequency low enough
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that the skin depth inside the casing is longer than the casing length (f
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= 1e-6 Hz). The plot produced is of the current inside the casing.
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These results are shown in the SEG abstract by Yang et al., 2016: 3D DC
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resistivity modeling of steel casing for reservoir monitoring using
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equivalent resistor network. The solver used to produce these results and
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achieve the CPU time of ~30s is Mumps, which was installed using pymatsolver_
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.. _pymatsolver: https://github.com/rowanc1/pymatsolver
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This example is on figshare: https://dx.doi.org/10.6084/m9.figshare.3126961.v1
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If you would use this example for a code comparison, or build upon it, a
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citation would be much appreciated!
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.. plot::
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from SimPEG import Examples
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Examples.EM_Schenkel_Morrison_Casing.run()
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.. literalinclude:: ../../SimPEG/Examples/EM_Schenkel_Morrison_Casing.py
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:language: python
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:linenos:
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.. _examples_EM_TDEM_1D_Inversion:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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EM: TDEM: 1D: Inversion
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=======================
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Here we will create and run a TDEM 1D inversion.
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.. plot::
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from SimPEG import Examples
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Examples.EM_TDEM_1D_Inversion.run()
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.. literalinclude:: ../../SimPEG/Examples/EM_TDEM_1D_Inversion.py
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:language: python
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:linenos:
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.. _examples_FLOW_Richards_1D_Celia1990:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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FLOW: Richards: 1D: Celia1990
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=============================
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There are two different forms of Richards equation that differ
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on how they deal with the non-linearity in the time-stepping term.
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The most fundamental form, referred to as the
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'mixed'-form of Richards Equation Celia1990_
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.. math::
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\frac{\partial \theta(\psi)}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0
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\quad \psi \in \Omega
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where \\(\\theta\\) is water content, and \\(\\psi\\) is pressure head.
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This formulation of Richards equation is called the
|
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'mixed'-form because the equation is parameterized in \\(\\psi\\)
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but the time-stepping is in terms of \\(\\theta\\).
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As noted in Celia1990_ the 'head'-based form of Richards
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equation can be written in the continuous form as:
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.. math::
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\frac{\partial \theta}{\partial \psi}\frac{\partial \psi}{\partial t} - \nabla \cdot k(\psi) \nabla \psi - \frac{\partial k(\psi)}{\partial z} = 0 \quad \psi \in \Omega
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However, it can be shown that this does not conserve mass in the discrete formulation.
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Here we reproduce the results from Celia1990_ demonstrating the head-based formulation and the mixed-formulation.
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.. _Celia1990: http://www.webpages.uidaho.edu/ch/papers/Celia.pdf
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.. plot::
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from SimPEG import Examples
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Examples.FLOW_Richards_1D_Celia1990.run()
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.. literalinclude:: ../../SimPEG/Examples/FLOW_Richards_1D_Celia1990.py
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:language: python
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:linenos:
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.. _examples_Inversion_Linear:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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Inversion: Linear Problem
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=========================
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Here we go over the basics of creating a linear problem and inversion.
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.. plot::
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from SimPEG import Examples
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Examples.Inversion_Linear.run()
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.. literalinclude:: ../../SimPEG/Examples/Inversion_Linear.py
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:language: python
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:linenos:
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.. _examples_MT_1D_ForwardAndInversion:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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|
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MT: 1D: Inversion
|
||||
=================
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||||
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Forward model 1D MT data.
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Setup and run a MT 1D inversion.
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||||
|
||||
|
||||
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.. plot::
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||||
|
||||
from SimPEG import Examples
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||||
Examples.MT_1D_ForwardAndInversion.run()
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||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/MT_1D_ForwardAndInversion.py
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:language: python
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:linenos:
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.. _examples_MT_3D_Foward:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
|
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.. ..
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.. --------------------------------- ..
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|
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|
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MT: 3D: Forward
|
||||
===============
|
||||
|
||||
Forward model 3D MT data.
|
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|
||||
|
||||
|
||||
.. plot::
|
||||
|
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from SimPEG import Examples
|
||||
Examples.MT_3D_Foward.run()
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||||
|
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.. literalinclude:: ../../SimPEG/Examples/MT_3D_Foward.py
|
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:language: python
|
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:linenos:
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.. _examples_Mesh_Basic_ForwardDC:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
|
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.. ..
|
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.. --------------------------------- ..
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|
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|
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Mesh: Basic Forward 2D DC Resistivity
|
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=====================================
|
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|
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2D DC forward modeling example with Tensor and Curvilinear Meshes
|
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|
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|
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.. plot::
|
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|
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from SimPEG import Examples
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Examples.Mesh_Basic_ForwardDC.run()
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.. literalinclude:: ../../SimPEG/Examples/Mesh_Basic_ForwardDC.py
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:language: python
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:linenos:
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.. _examples_Mesh_Basic_PlotImage:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
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.. ..
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.. --------------------------------- ..
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|
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|
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Mesh: Basic: PlotImage
|
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======================
|
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|
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You can use M.PlotImage to plot images on all of the Meshes.
|
||||
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
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from SimPEG import Examples
|
||||
Examples.Mesh_Basic_PlotImage.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Mesh_Basic_PlotImage.py
|
||||
:language: python
|
||||
:linenos:
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.. _examples_Mesh_Basic_Types:
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.. --------------------------------- ..
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
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.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
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.. --------------------------------- ..
|
||||
|
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|
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Mesh: Basic: Types
|
||||
==================
|
||||
|
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Here we show SimPEG used to create three different types of meshes.
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Mesh_Basic_Types.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Mesh_Basic_Types.py
|
||||
:language: python
|
||||
:linenos:
|
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.. _examples_Mesh_Operators_CahnHilliard:
|
||||
|
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.. --------------------------------- ..
|
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.. ..
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.. THIS FILE IS AUTO GENEREATED ..
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.. ..
|
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.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
Mesh: Operators: Cahn Hilliard
|
||||
==============================
|
||||
|
||||
This example is based on the example in the FiPy_ library.
|
||||
Please see their documentation for more information about the Cahn-Hilliard equation.
|
||||
|
||||
The "Cahn-Hilliard" equation separates a field \\( \\phi \\) into 0 and 1 with smooth transitions.
|
||||
|
||||
.. math::
|
||||
|
||||
\frac{\partial \phi}{\partial t} = \nabla \cdot D \nabla \left( \frac{\partial f}{\partial \phi} - \epsilon^2 \nabla^2 \phi \right)
|
||||
|
||||
Where \\( f \\) is the energy function \\( f = ( a^2 / 2 )\\phi^2(1 - \\phi)^2 \\)
|
||||
which drives \\( \\phi \\) towards either 0 or 1, this competes with the term
|
||||
\\(\\epsilon^2 \\nabla^2 \\phi \\) which is a diffusion term that creates smooth changes in \\( \\phi \\).
|
||||
The equation can be factored:
|
||||
|
||||
.. math::
|
||||
|
||||
\frac{\partial \phi}{\partial t} = \nabla \cdot D \nabla \psi \\
|
||||
\psi = \frac{\partial^2 f}{\partial \phi^2} (\phi - \phi^{\text{old}}) + \frac{\partial f}{\partial \phi} - \epsilon^2 \nabla^2 \phi
|
||||
|
||||
Here we will need the derivatives of \\( f \\):
|
||||
|
||||
.. math::
|
||||
|
||||
\frac{\partial f}{\partial \phi} = (a^2/2)2\phi(1-\phi)(1-2\phi)
|
||||
\frac{\partial^2 f}{\partial \phi^2} = (a^2/2)2[1-6\phi(1-\phi)]
|
||||
|
||||
The implementation below uses backwards Euler in time with an exponentially increasing time step.
|
||||
The initial \\( \\phi \\) is a normally distributed field with a standard deviation of 0.1 and mean of 0.5.
|
||||
The grid is 60x60 and takes a few seconds to solve ~130 times. The results are seen below, and you can see the
|
||||
field separating as the time increases.
|
||||
|
||||
.. _FiPy: http://www.ctcms.nist.gov/fipy/examples/cahnHilliard/generated/examples.cahnHilliard.mesh2DCoupled.html
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Mesh_Operators_CahnHilliard.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Mesh_Operators_CahnHilliard.py
|
||||
:language: python
|
||||
:linenos:
|
||||
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|
||||
.. _examples_Mesh_QuadTree_Creation:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
.. THIS FILE IS AUTO GENEREATED ..
|
||||
.. ..
|
||||
.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
Mesh: QuadTree: Creation
|
||||
========================
|
||||
|
||||
You can give the refine method a function, which is evaluated on every cell
|
||||
of the TreeMesh.
|
||||
|
||||
Occasionally it is useful to initially refine to a constant level
|
||||
(e.g. 3 in this 32x32 mesh). This means the function is first evaluated
|
||||
on an 8x8 mesh (2^3).
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Mesh_QuadTree_Creation.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Mesh_QuadTree_Creation.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -0,0 +1,26 @@
|
||||
.. _examples_Mesh_QuadTree_FaceDiv:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
.. THIS FILE IS AUTO GENEREATED ..
|
||||
.. ..
|
||||
.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
Mesh: QuadTree: FaceDiv
|
||||
=======================
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Mesh_QuadTree_FaceDiv.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Mesh_QuadTree_FaceDiv.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -0,0 +1,31 @@
|
||||
.. _examples_Mesh_QuadTree_HangingNodes:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
.. THIS FILE IS AUTO GENEREATED ..
|
||||
.. ..
|
||||
.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
Mesh: QuadTree: Hanging Nodes
|
||||
=============================
|
||||
|
||||
You can give the refine method a function, which is evaluated on every cell
|
||||
of the TreeMesh.
|
||||
|
||||
Occasionally it is useful to initially refine to a constant level
|
||||
(e.g. 3 in this 32x32 mesh). This means the function is first evaluated
|
||||
on an 8x8 mesh (2^3).
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Mesh_QuadTree_HangingNodes.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Mesh_QuadTree_HangingNodes.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -0,0 +1,43 @@
|
||||
.. _examples_Mesh_Tensor_Creation:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
.. THIS FILE IS AUTO GENEREATED ..
|
||||
.. ..
|
||||
.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
|
||||
Mesh: Tensor: Creation
|
||||
======================
|
||||
|
||||
For tensor meshes, there are some functions that can come
|
||||
in handy. For example, creating mesh tensors can be a bit time
|
||||
consuming, these can be created speedily by just giving numbers
|
||||
and sizes of padding. See the example below, that follows this
|
||||
notation::
|
||||
|
||||
h1 = (
|
||||
(cellSize, numPad, [, increaseFactor]),
|
||||
(cellSize, numCore),
|
||||
(cellSize, numPad, [, increaseFactor])
|
||||
)
|
||||
|
||||
.. note::
|
||||
|
||||
You can center your mesh by passing a 'C' for the x0[i] position.
|
||||
A 'N' will make the entire mesh negative, and a '0' (or a 0) will
|
||||
make the mesh start at zero.
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Mesh_Tensor_Creation.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Mesh_Tensor_Creation.py
|
||||
:language: python
|
||||
:linenos:
|
||||
@@ -0,0 +1,28 @@
|
||||
.. _examples_Utils_surface2ind_topo:
|
||||
|
||||
.. --------------------------------- ..
|
||||
.. ..
|
||||
.. THIS FILE IS AUTO GENEREATED ..
|
||||
.. ..
|
||||
.. SimPEG/Examples/__init__.py ..
|
||||
.. ..
|
||||
.. --------------------------------- ..
|
||||
|
||||
|
||||
|
||||
Utils: surface2ind_topo
|
||||
=======================
|
||||
|
||||
Here we show how to use :code:`Utils.surface2ind_topo` to identify cells below
|
||||
a topographic surface.
|
||||
|
||||
|
||||
|
||||
.. plot::
|
||||
|
||||
from SimPEG import Examples
|
||||
Examples.Utils_surface2ind_topo.run()
|
||||
|
||||
.. literalinclude:: ../../SimPEG/Examples/Utils_surface2ind_topo.py
|
||||
:language: python
|
||||
:linenos:
|
||||
Reference in New Issue
Block a user