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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8"/>
<title>The SEISMIC_CPML software package</title>
<meta name="generator" content="LibreOffice 5.1.6.2 (Linux)"/>
<meta name="created" content="00:00:00"/>
<meta name="changedby" content="Dimitri Komatitsch"/>
<meta name="changed" content="2018-07-12T23:19:48.535278496"/>
</head>
<body lang="en-US" background="data:image/jpeg;base64,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" dir="ltr">
<p><a href="http://komatitsch.free.fr/">Home page of Dimitri
Komatitsch</a></p>
<p align="center"><a name="_x0000_i1025"></a><img src="data:image/png;base64,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" name="graphics1" align="bottom" width="158" height="30" border="0"/>
</p>
<p> </p>
<p><font color="#ff0000"><font size="3" style="font-size: 13pt">SEISMIC_CPML
is a set of </font></font><font color="#ff0000"><font size="3" style="font-size: 13pt">fourteen</font></font><font color="#ff0000">
</font><font color="#ff0000"><font size="3" style="font-size: 13pt">open-source
Fortran90 programs under the GNU GPL version </font></font><font color="#ff0000"><font size="3" style="font-size: 13pt">3</font></font><font color="#ff0000"><font size="3" style="font-size: 13pt">
license</font></font> <font size="3" style="font-size: 13pt">to solve
the two-dimensional or three-dimensional isotropic or anisotropic
acoustic, elastic, viscoelastic or poroelastic wave equation using a
finite-difference method with Convolutional or Auxiliary Perfectly
Matched Layer (C-PML or ADE-PML) conditions, developed by Dimitri
Komatitsch and Roland Martin from CNRS, France. Contributions by
other authors have recently been added.</font>
</p>
<p><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">You
can get the full source code of the programs at the official Web
site: <a href="http://geodynamics.org/cig/software/seismic_cpml">http://geodynamics.org/cig/software/seismic_cpml</a></font></font></p>
<p><font size="3" style="font-size: 13pt">The codes are then
self-explanatory and very easy to use; to understand how to use them
just edit the source codes and read the comments they contain.</font></p>
<p><font size="3" style="font-size: 13pt">The unsplit <b>Convolutional
Perfectly Matched Layer (C-PML) for the 3D elastic wave equation</b>
was introduced and is described in detail in: </font>
</p>
<p><font size="3" style="font-size: 13pt"><b>Dimitri Komatitsch and
Roland Martin,</b></font> <span style="font-variant: normal"><font size="3" style="font-size: 13pt"><span style="font-style: normal">An
unsplit convolutional Perfectly Matched Layer improved at grazing
incidence for the seismic wave equation</span></font></span><font size="3" style="font-size: 13pt"><i>,
Geophysics</i></font><font size="3" style="font-size: 13pt">, vol.
72(5), p SM155-SM167, doi: 10.1190/1.2757586 (2007). <a href="http://komatitsch.free.fr/preprints/geophysics_CPML_2007_elastic_typos_fixed.pdf">Preprint</a>
<a href="http://komatitsch.free.fr/bibtex_komatitsch.bib">BibTeX</a></font></p>
<p><font size="3" style="font-size: 13pt">It was originally developed
for Maxwell's equations by Roden and Gedney (2000) (see reference
below).</font></p>
<p><font size="3" style="font-size: 13pt">An extension to
viscoelastic media is developed in:</font></p>
<p><font size="3" style="font-size: 13pt"><b>Roland Martin and
Dimitri Komatitsch, </b></font><font size="3" style="font-size: 13pt">An
unsplit convolutional perfectly matched layer technique improved at
grazing incidence for the viscoelastic wave equation, </font><font size="3" style="font-size: 13pt"><i>Geophysical
Journal International</i></font><font size="3" style="font-size: 13pt">,
vol. 179(1), p. 333-344, </font><span style="font-variant: normal"><font face="serif"><font size="3" style="font-size: 13pt"><span style="font-style: normal">doi:
10.1111/j.1365-246X.2009.04278.x </span></font></font></span><font size="3" style="font-size: 13pt">(2009).</font>
<font face="serif"><font size="3" style="font-size: 13pt"><a href="http://komatitsch.free.fr/preprints/GJI_CPML_2009_viscoelastic.pdf">Preprint</a>
<a href="http://komatitsch.free.fr/bibtex_komatitsch.bib">BibTeX</a></font></font></p>
<p><font size="3" style="font-size: 13pt">and the viscoelastic
parameters of the Zener body model used to fit a constant-Q model are
computed based upon:</font></p>
<p><font face="serif"><font size="3" style="font-size: 13pt"><b>Émilie
Blanc, Dimitri Komatitsch, Emmanuel Chaljub, Bruno</b></font></font>
<font face="serif"><font size="3" style="font-size: 13pt"><b>Lombard
and Zhinan Xie</b></font></font><font face="serif"><font size="3" style="font-size: 13pt">,
Highly-accurate stability-preserving optimization of the Zener
viscoelastic model, with application to wave propagation in the
presence of strong attenuation, </font></font><font face="serif"><font size="3" style="font-size: 13pt"><i>Geophysical
Journal International,</i></font></font> <span style="font-variant: normal"><font face="serif"><font size="3" style="font-size: 13pt"><span style="font-style: normal">vol.
205(1), p. 427-439, </span></font></font></span><font face="serif"><font size="3" style="font-size: 13pt">doi:
10.1093/gji/ggw024</font></font> <font face="serif"><font size="3" style="font-size: 13pt">(2016).</font></font>
<font face="serif"><font size="3" style="font-size: 13pt"><a href="http://komatitsch.free.fr/preprints/GJI_Lombard_2016.pdf">Preprint</a>
<a href="http://komatitsch.free.fr/bibtex_komatitsch.bib">BibTeX</a></font></font></p>
<p><br/>
<br/>
</p>
<p><font size="3" style="font-size: 13pt">An extension to poroelastic
media is developed in:</font></p>
<p><font size="3" style="font-size: 13pt"><b>Roland Martin, Dimitri
Komatitsch and Abdelaâziz Ezziani</b></font><font size="3" style="font-size: 13pt">,
</font><span style="font-variant: normal"><font size="3" style="font-size: 13pt"><span style="font-style: normal">An
unsplit convolutional Perfectly Matched Layer improved at grazing
incidence for seismic wave propagation in poroelastic media</span></font></span><font size="3" style="font-size: 13pt"><i>,
Geophysics</i></font><font size="3" style="font-size: 13pt">, vol.
73(4), p T51-T61, doi: 10.1190/1.2939484 (2008). <a href="http://komatitsch.free.fr/preprints/geophysics_CPML_2008_poroelastic_typos_fixed.pdf">Preprint</a>
<a href="http://komatitsch.free.fr/bibtex_komatitsch.bib">BibTeX</a></font></p>
<p><font size="3" style="font-size: 13pt">and a variational
formulation is developed in:</font></p>
<p><font size="3" style="font-size: 13pt"><b>Roland Martin, </b></font><font face="serif"><font size="3" style="font-size: 13pt"><b>Dimitri
Komatitsch</b></font></font> <font size="3" style="font-size: 13pt"><b>and
Stephen D. Gedney</b></font><font size="3" style="font-size: 13pt">,
A variational formulation of a stabilized unsplit convolutional
perfectly matched layer for the isotropic or anisotropic seismic wave
equation, </font><font size="3" style="font-size: 13pt"><i>Computer
Modeling in Engineering and Sciences</i></font><font size="3" style="font-size: 13pt">,
vol. 37(3), p. 274-304 (2008). </font><font face="serif"><font size="3" style="font-size: 13pt"><a href="http://komatitsch.free.fr/preprints/CMES_CPML_2008_typos_fixed.pdf">Preprint</a>
<a href="http://komatitsch.free.fr/bibtex_komatitsch.bib">BibTeX</a></font></font></p>
<p><font size="3" style="font-size: 13pt">An extension to
higher-order time schemes, called ADE-PML (Auxiliary Differential
Equation - PML) is developed in:</font></p>
<p><font face="serif"><font size="4" style="font-size: 14pt"><b>Roland
Martin, Dimitri Komatitsch, Stephen D. Gedney and Émilien Bruthiaux</b></font></font><font face="serif"><font size="4" style="font-size: 14pt">,
A high-order time and space formulation of the unsplit perfectly
matched layer for the seismic wave equation using Auxiliary
Differential Equations (ADE-PML), </font></font><font face="serif"><font size="4" style="font-size: 14pt"><i>Computer
Modeling in Engineering and Sciences</i></font></font><font face="serif"><font size="4" style="font-size: 14pt">,
vol. 56(1), p. 17-42 (2010).</font></font> <font size="3" style="font-size: 13pt"><a href="http://komatitsch.free.fr/preprints/CMES_ADE_PML_2010.pdf">Preprint</a>
<a href="http://komatitsch.free.fr/bibtex_komatitsch.bib">BibTeX</a></font></p>
<p><font size="3" style="font-size: 13pt">Note that in the case of an
anisotropic medium the modification made is not strictly speaking
perfectly matched any more, i.e., not a PML, but rather </font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">a
“Modified PML / M-PML” based on Meza-Fajardo and Papageorgiou,
</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><i>Bulletin
of the Seismological Society of America</i></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">,
vol. 98(4), p. 1811-1836 (2008). H</font></font><font size="3" style="font-size: 13pt">owever,
it works well in practice even if it is not perfectly matched any
more from a mathematical point of view.</font></p>
<p><font color="#ff0000"><font size="3" style="font-size: 13pt"><b>IMPORTANT:
all of our codes are written in Fortran; if you have written or if
you write a C or C++ version of some of these codes and want to make
them open source (GNU GPL version 3) and part of the package, please
do not hesitate to send them to us, we will add them to our tar file
and will acknowledge you as the author.</b></font></font></p>
<p><font size="3" style="font-size: 13pt">This software is governed
by the <a href="https://www.gnu.org/licenses/gpl-3.0.en.html">GNU GPL
version </a></font><a href="https://www.gnu.org/licenses/gpl-3.0.en.html"><font size="3" style="font-size: 13pt">3</font><font size="3" style="font-size: 13pt">
license</font></a><font size="3" style="font-size: 13pt">.</font></p>
<p><font size="3" style="font-size: 13pt">If you use this code for
your own research, please cite some (or all) of these articles:</font></p>
<p><font face="Courier 10 Pitch"><font size="3" style="font-size: 13pt">@ARTICLE{BlKoChLoXi16,
<br/>
title = {Highly accurate stability-preserving optimization of
the {Z}ener viscoelastic model, with application to wave propagation
in the presence of strong attenuation}, <br/>
author = {\'Emilie
Blanc and Dimitri Komatitsch and Emmanuel Chaljub and Bruno Lombard
and Zhinan Xie}, <br/>
journal = {Geophysical Journal
International},<br/>
year = {2016}, <br/>
number = {1}, <br/>
pages =
{427-439}, <br/>
volume = {205}, <br/>
doi = {10.1093/gji/ggw024}} </font></font>
</p>
<p><font face="Courier 10 Pitch"><font size="3" style="font-size: 13pt">@ARTICLE{MaKo09,<br/>
author
= {Roland Martin and Dimitri Komatitsch},<br/>
title = {An unsplit
convolutional perfectly matched layer technique improved at grazing
incidence for the viscoelastic wave equation},<br/>
journal =
{Geophysical Journal International},<br/>
year = {2009},<br/>
volume
= {179},<br/>
number = {1},<br/>
pages = {333-344},<br/>
doi =
{10.1111/j.1365-246X.2009.04278.x}}<br/>
<br/>
@ARTICLE{MaKoEz08,<br/>
author
= {Roland Martin and Dimitri Komatitsch and Abdelaaziz
Ezziani},<br/>
title = {An unsplit convolutional perfectly matched
layer improved at grazing incidence for seismic wave equation in
poroelastic media},<br/>
journal = {Geophysics},<br/>
year =
{2008},<br/>
volume = {73},<br/>
pages = {T51-T61},<br/>
number =
{4},<br/>
doi = {10.1190/1.2939484}}<br/>
<br/>
@ARTICLE{MaKoGe08,<br/>
author
= {Roland Martin and Dimitri Komatitsch and Stephen D. Gedney},<br/>
title
= {A variational formulation of a stabilized unsplit convolutional
perfectly matched layer for the isotropic or anisotropic seismic wave
equation},<br/>
journal = {Computer Modeling in Engineering and
Sciences},<br/>
year = {2008},<br/>
volume = {37},<br/>
pages =
{274-304},<br/>
number = {3}}</font></font></p>
<p><font face="Courier 10 Pitch"><font size="3" style="font-size: 13pt">@ARTICLE{MaKoGeBr10,<br/>
author
= {Roland Martin and Dimitri Komatitsch and Stephen D. Gedney and
Emilien Bruthiaux},<br/>
title = {A high-order time and space
formulation of the unsplit perfectly matched layer for the seismic
wave equation using {Auxiliary Differential Equations
(ADE-PML)}},<br/>
journal = {Computer Modeling in Engineering and
Sciences},<br/>
year = {2010},<br/>
volume = {56},<br/>
pages =
{17-42},<br/>
number = {1}}</font></font></p>
<p><font face="Courier 10 Pitch"><font size="3" style="font-size: 13pt">@ARTICLE{KoMa07,<br/>
author
= {Dimitri Komatitsch and Roland Martin},<br/>
title = {An unsplit
convolutional {P}erfectly {M}atched {L}ayer improved at grazing
incidence for the seismic wave equation},<br/>
journal =
{Geophysics},<br/>
year = {2007},<br/>
volume = {72},<br/>
number =
{5},<br/>
pages = {SM155-SM167},<br/>
doi = {10.1190/1.2757586}}</font></font></p>
<p><br/>
<br/>
</p>
<p><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">Roden
and Gedney's original article for Maxwell's equations
is:</font></font><font face="Liberation Serif, serif"><font size="1" style="font-size: 6pt"><br/>
<br/>
<br/>
</font></font><font face="Courier 10 Pitch"><font size="3" style="font-size: 13pt">@ARTICLE{RoGe00,<br/>
author
= {J. A. Roden and S. D. Gedney},<br/>
title = {Convolution {PML}
({CPML}): {A}n Efficient {FDTD} Implementation of the {CFS}-{PML} for
Arbitrary Media},<br/>
journal = {Microwave and Optical Technology
Letters},<br/>
year = {2000},<br/>
volume = {27},<br/>
number =
{5},<br/>
pages = {334-339},<br/>
doi =
{10.1002/1098-2760(20001205)27:5<334::AID-MOP14>3.0.CO;2-A}}</font></font><font face="Courier New, monospace"><font size="3" style="font-size: 13pt"><br/>
</font></font><a href="http://www.geodynamics.org/cig/software/"><font face="Liberation Serif, serif"><font size="1" style="font-size: 6pt"><b><br/>
<br/>
</b></font></font></a><font size="3" style="font-size: 13pt">The
package is composed of the following </font><font size="3" style="font-size: 13pt">fourteen</font><font size="3" style="font-size: 13pt">
programs:</font></p>
<p><br/>
<br/>
</p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_2D_pressure_second_order.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D C-PML program for an acoustic</font></font> <font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">medium
using a second-order finite-difference spatial operator </font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">for
the pressure equation written as a second-order system in time</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_2D_pressure_and_velocity_second_order_viscoacoustic.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D C-PML program for a </font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">visco</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">acoustic
medium using a second-order finite-difference spatial operator </font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">for
the velocity and pressure equation written as a split first-order
system in time</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_2D_pressure_and_velocity_fourth_order_viscoacoustic.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D C-PML program for a</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">
visco</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">acoustic
medium using a </font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">fourth</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">-order
finite-difference spatial operator </font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">for
the velocity and pressure equation written as a split first-order
system in time</font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_2D_isotropic_second_order.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D C-PML program for an elastic isotropic medium using a second-order
finite-difference spatial operator.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_2D_isotropic_fourth_order.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D C-PML program for an elastic isotropic medium using a fourth-order
finite-difference spatial operator.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_2D_anisotropic.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D C-PML program for an elastic anisotropic medium using a
second-order finite-difference spatial operator. More precisely we
implement a “Modified PML / M-PML” based on Meza-Fajardo and
Papageorgiou, </font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><i>Bulletin
of the Seismological Society of America</i></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">,
vol. 98(4), p. 1811-1836 (2008). Strictly speaking the layers are not
perfectly matched any more from a mathematical point of view, but the
code works well in practice.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_2D_poroelastic_fourth_order.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D C-PML program for a poroelastic medium using a fourth-order
finite-difference spatial operator.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_ADEPML_2D_elastic_RK4_eighth_order.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D ADE-PML program for an isotropic elastic medium using an
eighth-order finite-difference spatial operator and fourth-order
Runge-Kutta implicit, semi implicit or explicit time scheme.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_ADEPML_2D_viscoelastic_RK4_eighth_order.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D ADE-PML program for an isotropic viscoelastic medium using an
eighth-order finite-difference spatial operator and fourth-order
Runge-Kutta implicit, semi implicit or explicit time scheme.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_PML_Collino_2D_isotropic.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D classical split PML program for an isotropic medium using a
second-order finite-difference spatial operator, for comparison.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_PML_Collino_2D_anisotropic_fourth.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
2D classical split PML program for an anisotropic medium using a
fourth-order finite-difference spatial operator, for comparison.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_3D_isotropic_MPI_OpenMP.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
3D C-PML program for an isotropic medium using a second-order
finite-difference spatial operator. Parallel implementation based on
both MPI and OpenMP.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_PML_Collino_3D_isotropic_OpenMP.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
3D classical split PML program for an isotropic medium using a
second-order finite-difference spatial operator, for comparison.
Parallel implementation based on OpenMP.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>seismic_CPML_3D_viscoelastic_MPI.f90</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
3D C-PML program for a viscoelastic medium using a fourth-order
finite-difference spatial operator. Parallel implementation based on
MPI.</font></font></p>
<p><font color="#ff0000"><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt"><b>Makefile</b></font></font></font><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">:
a standard Makefile. You can type “make all” to compile all the
codes.</font></font></p>
<p><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">For
more details about the classical PML, see for instance <a href="http://en.wikipedia.org/wiki/Perfectly_Matched_Layer">Wikipedia
about PML</a>.</font></font></p>
<p><font face="Liberation Serif, serif"><font size="3" style="font-size: 13pt">For
more details about finite differences in the time domain (FDTD), see
for instance <a href="http://en.wikipedia.org/wiki/Finite-difference_time-domain_method">Wikipedia
about FDTD</a>.</font></font></p>
<p><a href="http://komatitsch.free.fr/"><font size="3" style="font-size: 13pt">Home
page of Dimitri Komatitsch</font></a></p>
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