Merge pull request devitocodes#1231 from devitocodes/ssa_iso_implemen…

…tation

ssa iso implementation

examples/seismic/skew_self_adjoint/README.md

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+# Devito Skew Self Adjoint modeling operators
+
+## These operators are contributed by Chevron Energy Technology Company (2020)
+
+These operators are based on simplfications of the systems presented in:
+<br>**Self-adjoint, energy-conserving second-order pseudoacoustic systems for VTI and TTI media for reverse time migration and full-waveform inversion** (2016)
+<br>Kenneth Bube, John Washbourne, Raymond Ergas, and Tamas Nemeth
+<br>SEG Technical Program Expanded Abstracts
+<br>https://library.seg.org/doi/10.1190/segam2016-13878451.1
+
+## Tutorial goal
+
+The goal of this series of tutorials is to generate -- and then test for correctness -- the modeling and inversion capability in Devito for variable density visco- acoustics. We use an energy conserving form of the wave equation that is *skew self adjoint*, which allows the same modeling system to be used for all for all phases of finite difference evolution required for quasi-Newton optimization:
+- **nonlinear forward**, nonlinear with respect to the model parameters
+- **Jacobian forward**, linearized with respect to the model parameters 
+- **Jacobian adjoint**, linearized with respect to the model parameters
+
+These notebooks first implement and then test for correctness for three types of modeling physics.
+
+| Physics         | Goal                          | Notebook                           |
+|:----------------|:----------------------------------|:-------------------------------------|
+| Isotropic       | Implementation, nonlinear ops | [ssa_01_iso_implementation1.ipynb] |
+| Isotropic       | Implementation, Jacobian ops  | [ssa_02_iso_implementation2.ipynb] |
+| Isotropic       | Correctness tests             | [ssa_03_iso_correctness.ipynb]     |
+|-----------------|-----------------------------------|--------------------------------------|
+| VTI Anisotropic | Implementation, nonlinear ops | [ssa_11_vti_implementation1.ipynb] |
+| VTI Anisotropic | Implementation, Jacobian ops  | [ssa_12_vti_implementation2.ipynb] |
+| VTI Anisotropic | Correctness tests             | [ssa_13_vti_correctness.ipynb]     |
+|-----------------|-----------------------------------|--------------------------------------|
+| TTI Anisotropic | Implementation, nonlinear ops | [ssa_21_tti_implementation1.ipynb] |
+| TTI Anisotropic | Implementation, Jacobian ops  | [ssa_22_tti_implementation2.ipynb] |
+| TTI Anisotropic | Correctness tests             | [ssa_23_tti_correctness.ipynb]     |
+|:----------------|:----------------------------------|:-------------------------------------|
+
+[ssa_01_iso_implementation1.ipynb]: ssa_01_iso_implementation1.ipynb
+[ssa_02_iso_implementation2.ipynb]: ssa_02_iso_implementation2.ipynb
+[ssa_03_iso_correctness.ipynb]:     ssa_03_iso_correctness.ipynb
+[ssa_11_vti_implementation1.ipynb]: ssa_11_vti_implementation1.ipynb
+[ssa_12_vti_implementation2.ipynb]: ssa_12_vti_implementation2.ipynb
+[ssa_13_vti_correctness.ipynb]:     ssa_13_vti_correctness.ipynb
+[ssa_21_tti_implementation1.ipynb]: ssa_21_tti_implementation1.ipynb
+[ssa_22_tti_implementation2.ipynb]: ssa_22_tti_implementation2.ipynb
+[ssa_23_tti_correctness.ipynb]:     ssa_23_tti_correctness.ipynb
+
+## Running unit tests
+- if you would like to see stdout when running the tests, use
+```py.test -c testUtils.py```

examples/seismic/skew_self_adjoint/__init__.py

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+from .utils import *  # noqa