This repository contains a set of examples and tutorials for seismic modeling and inversion using Devito. These examples use four different wave equations, namely
- The acoustic isotropic wave equation in
seismic/acoustic - The TTI pseudo-acoustic wave equation in
seismic/tti - The elastic isotropic wave equation in
seismic/elastic - The viscoelastic isotropic wave equation in
seismic/elastic
Currently, the acoustic isotropic wave equation solver also contains the propagator associated with the adjoint and linearized (Born) wave-equation solution and the gradient of the FWI objective (application of the Jacobian to data residual)
The majority of these examples can also be found in the Devito examples directory, which is a fork of this repository. These examples for seismic applications have been developed and implemented by Mathias Louboutin at the Georgia Institute of Technology. For additional introductory examples, including tutorials on the Devito compiler, we refer to the Devito example directory on github since these were developed primarily by people from the Devito team at Imperial College London. The contributions by Mathias Louboutin were made as part of actvities at the Georgia Tech's Seismic Laboratory for Imaging and modeling ([SLIM).
To install this set of examples with its dependencies run in your terminal (OSX, Ubuntu):
git clone https://github.com/slimgroup/Devito-Examples
cd Devito-Examples
pip install -e .
This command will install all dependencies including Devito and will allow you to run the examples. To verify your installation you can run:
python seismic/acoustic/acoustic_example.py -nd 1
Some of the examples require velocity models such as the marmousi-ii model. These models can be downloaded at devito-data to be used in the tutorials.
Examples and tutorials are provided in the form of single Python files and as Jupyter
notebooks.Jupyter notebooks are files with extension .ipynb. To execute these, run
jupyter notebook, and then click on the desired notebook in the window that
pops up in your browser.
The seismic examples and tutorials are organized as follows:
seismic/tutorials: A series of Jupyter notebooks of incremental complexity, showing a variety of Devito features in the context of seismic inversion operators. Among the discussed features are modeling, adjoint modeling, computing a gradient and a seismic image, FWI and elastic modeling on a staggered grid.seismic/acoustic: Example implementations of isotropic acoustic forward, adjoint, gradient and born operators, suitable for full-waveform inversion methods (FWI).seismic/tti: Example implementations of several anisotropic acoustic forward operators (TTI).seismic/elastic: Example implementation of an isotropic elastic forward operator.elastic, unlikeacousticandtti, fully exploits the tensorial nature of the Devito symbolic language.seismic/viscoelastic: Example implementation of an isotropic viscoelastic forward operator. Likeelastic,viscoelasticexploits tensor functions for a neat and compact representation of the discretized partial differential equations.
Some of these examples are described in the following papers:
- Devito's symbolic API for a description of the Devito API and symbolic capabilities.
- TTI imaging for small overview of imging in a TTI media (SEG abstract).
- Mathias Louboutin's thesis for Mathias Louboutin's Thesis.
More advanced geophysical application can be found in the JUDI repository. JUDI is a linear algebra DSL built on top of Devito for large scale inverse problems and includes abstractions for source/receivers and handles large SEG-Y datasets with SegyIO. A complete description of JUDI and the related seismic inversion application can be found in Philipp Witte's thesis.