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P-SV wave propagation in 2D for FWI

Project description


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A Python/C++ package for 2D P-SV wave propagation using finite differences and OpenMP. This package was written to facilitate high-throughput numerical wave simulations for Monte Carlo simulation in Seismology. It uses the velocity-stress formulation on a staggered grid from Virieux's classical 1986 paper. For compilation we require only OpenMP and the git subrepos (header-only): Eigen and inih, however installation can be easily done through pip. Used as a PDE-simulation code for this publication.

Installing the package

There are many ways to install this package. Installing directly from the PyPi archives is arguably the easiest:

pip install psvWave

To check if everything worked correctly, you can run the following in an interactive python shell or notebook:

>>> import psvWave
>>> print(psvWave.__version__)

If this raises an ImportError, the C++ packages have not correctly compiled and you are either on an unsupported system (Windows) or I have made a terrible mistake. Please contact me in any case!

You might also be tempted to install it from tags or another GitHub hash. This has the problem however that submodules are not automatically downloaded. If you still wish to install from the repo, you have to clone it to your machine first, and then also pull all the submodules:

git clone
cd psvWave
git submodule update --init --recursive

Afterwards you can ...

  1. directly install from this directory:

    pip install -e .
  2. create a source distribution (uncompiled) and install it on any machine:

    python sdist
    cd dist
    pip install psvWave-*.tar.gz # this will compile the C++ modules
  3. create a binary wheel in which the compiled code is present and install it on similar machines:

    python bdist_wheel # this will compile the C++ modules
    cd dist
    pip install psvWave-*.whl

The main difference between 2 and 3 is that 2 doesn't compile the C++ code yet at the distribution stage. Option 3 does compile in this stage, and therefore might not work on machines with wildly different architectures.

If you are really at the end of your rope, we can also send a precompiled wheel for the platform you're using.

Working with the configuration files

This section is a must read for anyone wishing to use this package.

An example configuration file is given below. The simulations performed make a few basic assumptions about the medium, wavefield and sources:

1: Physics

All sources propagate waves through the same medium / domain, and are recorded by the same network. The physics is defined in a right-handed coordinate system. However, you are allowed to interpret the simulations in any unit and orientation you like. Just make sure you keep track of the units, and don't use numbers outside the range of either float or double (the package is by default compiled with doubles). And, the physics is for in-plane shear waves.

2: Sources

All sources are normal/reverse faults (with strike parallel to the y-axis) with a Ricker wavelet of all the same frequency as source time function. Every source can have a different dip angle. This source time function can be altered in both the Python and C++ API, the focal mechanism /source type not (yet).

3: Simulations

Simulations are divided in 'shots', i.e. a single time length in which data is recorded and some 'sources' fire. It is thus allowed to have 2 sources in a single shot. This allows for source stacking. The delay_cycles_per_shot variable allows for time staggering, delaying the source time function per source by that many cycles. An example relevant to the given configuration file:

peak_frequency = 50.0

Means all source time functions (STF) are a Ricker wavelet with peak (central) frequency of 50Hz.

delay_cycles_per_shot = 24

Means that if 2 sources are present in a shot, the STF of the second shot is delayed by 24 cycles. For a peak frequency of 50 Hz, this turns out to be 24cycl / 50cycl/s = 0.48s. Every subsequent shot is delayed after the previous by the same amount.

which_source_to_fire_in_which_shot = {{0, 1}}

Means that both source 0 and source 1 (zero-based indexing) are fired in shot 1.

In the below given configuration, total simulation time is 1 second. This means that the second shot is 'fired' at almost half the simulation time. The idea behind source stacking is that without strong reflections, we can take advantage of the position of the wavefields to simulate multiple shots at the same time, with minimal 'cross-talk'.

4: Domain and boundary

The domain is truncated on all 4 sides by absorbing boundary conditions. It's width is variable, but as of yet, the same on all sides. This does not directly allow for free boundary conditions, but this is planned to change. When measuring distance or counting gridpoints, the zero-point is the first points not inside the boundary layer but in the actual simulation medium. When updating medium properties within the domain, the boundary copies the medium properties closest to it, to avoid creating reflectors.

5: Indexing

The location of the sources and receivers is not expressed in distance, but in gridpoint numbering. Because the actual indexing starts within the medium, and not the absorbing boundary, sources and receivers can only be placed inside the medium. However, the nx_inner_boundary and nz_inner_boundary variables determine how many gridpoints are not considered free parameters. The idea behind this is that this allows us to place sources/receivers in regions of the domain that are not inverted for, and are also not inside the boundary. This to avoid near-source and near-receiver effects.

Example file

nt = 4000
nx_inner = 200
nz_inner = 100
nx_inner_boundary = 10
nz_inner_boundary = 20
dx = 1.249
dz = 1.249
dt = 0.00025

np_boundary = 25
np_factor = 0.015

scalar_rho = 1500.0
scalar_vp = 2000.0
scalar_vs = 800.0

peak_frequency = 50.0
n_sources = 2
n_shots = 1
source_timeshift = 0.005
delay_cycles_per_shot = 24
moment_angles = {90, 180}
ix_sources = {25, 175}
iz_sources = {10, 10}
which_source_to_fire_in_which_shot = {{0, 1}}

nr = 19
ix_receivers = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190}
iz_receivers = {90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90, 90}

snapshot_interval = 10

Compiling the C++ interface

Compiling the C++ API into your C++ application is fairly straightforward. One needs an OpenMP enabled compiler, cmake installed and C++11 support. The different targets are defined in the CMakeLists.txt. Assuming your in a local clone of this repo:

mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
make forward_test # or other targets

Compiling the Python interface yourself

Compiling the CMake target psvWave creates a Python module for the current environments' Python version. However, to find the right requirements, we first need to do two things:

  1. Install PyBind, to interface Python to C++, using your favourite package manager;
  2. Set the relevant environment variables.

Before you continue, make sure you are in your desired Python environment, e.g. Conda or PyEnv. Python 3.6 or higher is recommended. Also, the python3-dev or equivalent package is needed for compilation.

Installing development dependencies.

Using your relevant package manager, you need to install all required development dependencies. To at minimum compile the interface, cmake and pybind11 are required:

pip install pybind11
pip install cmake

However, you might want to perform code-formatting and run tests. To install all the dependencies for this, it might be easier to install them using the file. Make sure you are in the cloned repo folder and run the following:

# On Bash / SH
pip install -e .[dev]
# On ZSH
pip install -e .\[dev\]

Setting needed environment variables

The compiler needs three things to work correctly:

  1. the relevant PyBind files (headers);
  2. the relevant Python files (headers);
  3. the appropriate extension for the compiled file.

The CMakeLists.txt file loads these variables from the environment. If you know what you are doing, you can set these yourself. If not, run the following commands in the terminal in which you have activated your relevant Python environment:

export PYBIND_INCLUDES=`python3 -c'import pybind11;print(pybind11.get_include())'`
export PYTHON_INCLUDES=`python3 -c"from sysconfig import get_paths as gp; print(gp()[\"include\"])"`
export SUFFIX=`python3-config --extension-suffix`

Compiling the Python linked C++ code

Compiling the Python interface is done by running CMake in the cloned repo:

mkdir build
cd build
cmake -DCMAKE_BUILD_TYPE=Release ..
make psvWave

Using the Python interface

This interface can be used by having the resulting __psvWave_cpp.*.so file in your working directory or PATH variable, and importing it, e.g.:

import __psvWave_cpp

model = __psvWave_cpp.fdModel(

model.forward_shot(0, verbose=True, store_fields=True)

However, the files in the ./psvWave/ Python module provides an interface that is a little neater with additional functions. Place the .so file in this folder and have this folder in your path.

Compiling the documentation

The documentation for the Python and C++ API requires one extra thing after running pip install -e .[dev]; A locally installed doxygen, to parse the C++ API into a Sphinx readable structure (a bunch of XML files, really. Installing this is a little platform dependent, with a quick install doxygen <platform> typically being enough. On e.g. Ubuntu the command to run would be:

$ sudo apt-get install doxygen

For compiling the total documentation the following needs to be run out of the local git clone:

$ cd docs-source
$ rm build/ -rf
$ make html
$ touch build/html/.nojekyll

The entire content of the docs-source/build/html directory, together with an empty file .nojekyll, is used as the gh-pages branch.

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