SPECFEM SPECFEM2D Seismic Wave Propagation Software User Manual

COMPUTATIONAL INFRASTRUCTURE FOR GEODYNAMICS (CIG)
PRINCETON UNIVERSITY (USA)
CNRS and UNIVERSITY OF MARSEILLE (FRANCE)
SPECFEM 2D
User Manual
Version 7.0
SPECFEM2D
User Manual
© Princeton University (USA) and CNRS / University of Marseille (France)
Version 7.0
January 20, 2015
1
Authors
The SPECFEM2D package was first developed by Dimitri Komatitsch and Jean-Pierre Vilotte at IPG in Paris (France)
from 1995 to 1997 and then by Dimitri Komatitsch at Harvard University (USA), Caltech (USA) and then CNRS and
University of Pau (France) from 1998 to 2005. The story started on April 4, 1995, when Prof. Yvon Maday from
CNRS and University of Paris, France, gave a lecture to Dimitri Komatitsch and Jean-Pierre Vilotte at IPG about
the nice properties of the Legendre spectral-element method with diagonal mass matrix that he had used for other
equations. We are deeply indebted and thankful to him for that. That followed a visit by Dimitri Komatitsch to OGS
(Istituto Nazionale di Oceanografia e di Geofisica Sperimentale) in Trieste, Italy, in February 1995 to meet with Géza
Seriani and Enrico Priolo, who introduced him to their 2D Chebyshev version of the spectral-element method with a
non-diagonal mass matrix. We are deeply indebted and thankful to them for that.
Since then it has been developed and maintained by a development team: in alphabetical order, Paul Cristini, Dimitri Komatitsch, Jesús Labarta, Nicolas Le Goff, Pieyre Le Loher, Qinya Liu, Roland Martin, René Matzen, Christina
Morency, Daniel Peter, Carl Tape, Jeroen Tromp, Jean-Pierre Vilotte, Zhinan Xie.
The code is released open-source under the CeCILL version 2 license, see the license at the end of this manual.
2
Current and past main participants or main sponsors (in no particular order)
Contents
Contents
3
1
Introduction
1.1 Citation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
5
6
2
Getting Started
2.1 Visualizing the subroutine calling tree of the source code . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Becoming a developer of the code, or making small modifications in the source code . . . . . . . . .
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3
Mesh Generation
3.1 How to use SPECFEM2D . . . . . . . . . . . . .
3.2 How to use Gmsh to generate an external mesh .
3.3 Controlling the quality of an external mesh . . .
3.4 Controlling how the mesh samples the wave field
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Running the Solver xspecfem2D
4.1 How to run P-SV or SH (membrane) wave simulations
4.2 How to use anisotropy . . . . . . . . . . . . . . . . .
4.3 How to use poroelasticity . . . . . . . . . . . . . . . .
4.4 How to set plane waves as initial conditions . . . . . .
4.5 How to choose the time step . . . . . . . . . . . . . .
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5
Adjoint Simulations
5.1 How to obtain Finite Sensitivity Kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Remarks about adjoint runs and solving inverse problems . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Caution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Oil and gas industry simulations
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Bibliography
26
A Troubleshooting
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B License
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3
Chapter 1
Introduction
SPECFEM2D facilitates 2D simulations of acoustic, (an)elastic, and poroelastic seismic wave propagation. The 2D
spectral-element solver accommodates regular and unstructured meshes, generated for example by Cubit (http://
cubit.sandia.gov), Gmsh (http://geuz.org/gmsh) or GiD (http://www.gid.cimne.upc.es).
Even mesh creation packages that generate triangles, for instance Delaunay-Voronoi triangulation codes, can be used
because each triangle can then easily be decomposed into three quadrangles by linking the barycenter to the center of
each edge; while this approach does not generate quadrangles of optimal quality, it can ease mesh creation in some
situations and it has been shown that the spectral-element method can very accurately handle distorted mesh elements.
With version 7.0, the 2D spectral-element solver accommodates Convolution PML absorbing layers and well as
higher-order time schemes (4th order Runge-Kutta and LDDRK4-6). Convolution or Auxiliary Differential Equation
Perfectly Matched absorbing Layers (C-PML or ADE-PML) are described in Martin et al. [2008b,c], Martin and
Komatitsch [2009], Martin et al. [2010], Komatitsch and Martin [2007].
The solver has adjoint capabilities and can calculate finite-frequency sensitivity kernels [Tromp et al., 2008, Peter
et al., 2011] for acoustic, (an)elastic, and poroelastic media. The package also considers 2D SH and P-SV wave propagation. Finally, the solver can run both in serial and in parallel. See SPECFEM2D (http://www.geodynamics.
org/cig/software/packages/seismo/specfem2d) for the source code.
The SEM is a continuous Galerkin technique [Tromp et al., 2008, Peter et al., 2011], which can easily be made discontinuous [Bernardi et al., 1994, Chaljub, 2000, Kopriva et al., 2002, Chaljub et al., 2003, Legay et al., 2005, Kopriva,
2006, Wilcox et al., 2010, Acosta Minolia and Kopriva, 2011]; it is then close to a particular case of the discontinuous
Galerkin technique [Reed and Hill, 1973, Lesaint and Raviart, 1974, Arnold, 1982, Johnson and Pitkäranta, 1986,
Bourdel et al., 1991, Falk and Richter, 1999, Hu et al., 1999, Cockburn et al., 2000, Giraldo et al., 2002, Rivière and
Wheeler, 2003, Monk and Richter, 2005, Grote et al., 2006, Ainsworth et al., 2006, Bernacki et al., 2006, Dumbser and
Käser, 2006, De Basabe et al., 2008, de la Puente et al., 2009, Wilcox et al., 2010, De Basabe and Sen, 2010, Étienne
et al., 2010], with optimized efficiency because of its tensorized basis functions [Wilcox et al., 2010, Acosta Minolia
and Kopriva, 2011]. In particular, it can accurately handle very distorted mesh elements [Oliveira and Seriani, 2011].
It has very good accuracy and convergence properties [Maday and Patera, 1989, Seriani and Priolo, 1994, Deville
et al., 2002, Cohen, 2002, De Basabe and Sen, 2007, Seriani and Oliveira, 2008, Ainsworth and Wajid, 2009, 2010,
Melvin et al., 2012]. The spectral element approach admits spectral rates of convergence and allows exploiting hpconvergence schemes. It is also very well suited to parallel implementation on very large supercomputers [Komatitsch
et al., 2003, Tsuboi et al., 2003, Komatitsch et al., 2008, Carrington et al., 2008, Komatitsch et al., 2010b] as well as
on clusters of GPU accelerating graphics cards [Komatitsch, 2011, Michéa and Komatitsch, 2010, Komatitsch et al.,
2009, 2010a]. Tensor products inside each element can be optimized to reach very high efficiency [Deville et al.,
2002], and mesh point and element numbering can be optimized to reduce processor cache misses and improve cache
reuse [Komatitsch et al., 2008]. The SEM can also handle triangular (in 2D) or tetrahedral (in 3D) elements [Wingate
and Boyd, 1996, Taylor and Wingate, 2000, Komatitsch et al., 2001, Cohen, 2002, Mercerat et al., 2006] as well as
mixed meshes, although with increased cost and reduced accuracy in these elements, as in the discontinuous Galerkin
method.
Note that in many geological models in the context of seismic wave propagation studies (except for instance for
fault dynamic rupture studies, in which very high frequencies or supershear rupture need to be modeled near the fault,
see e.g. Benjemaa et al. [2007, 2009], de la Puente et al. [2009], Tago et al. [2010]) a continuous formulation is
4
CHAPTER 1. INTRODUCTION
5
sufficient because material property contrasts are not drastic and thus conforming mesh doubling bricks can efficiently
handle mesh size variations [Komatitsch and Tromp, 2002, Komatitsch et al., 2004, Lee et al., 2008, 2009a,b].
For a detailed introduction to the SEM as applied to regional seismic wave propagation, please consult Peter et al.
[2011], Tromp et al. [2008], Komatitsch and Vilotte [1998], Komatitsch and Tromp [1999], Chaljub et al. [2007] and
in particular Lee et al. [2009b,a, 2008], Godinho et al. [2009], van Wijk et al. [2004], Komatitsch et al. [2004]. A
detailed theoretical analysis of the dispersion and stability properties of the SEM is available in Cohen [2002], De
Basabe and Sen [2007], Seriani and Oliveira [2007], Seriani and Oliveira [2008] and Melvin et al. [2012].
The SEM was originally developed in computational fluid dynamics [Patera, 1984, Maday and Patera, 1989] and
has been successfully adapted to address problems in seismic wave propagation. Early seismic wave propagation
applications of the SEM, utilizing Legendre basis functions and a perfectly diagonal mass matrix, include Cohen et al.
[1993], Komatitsch [1997], Faccioli et al. [1997], Casadei and Gabellini [1997], Komatitsch and Vilotte [1998] and
Komatitsch and Tromp [1999], whereas applications involving Chebyshev basis functions and a non-diagonal mass
matrix include Seriani and Priolo [1994], Priolo et al. [1994] and Seriani et al. [1995].
All SPECFEM2D software is written in Fortran2003 with full portability in mind, and conforms strictly to the
Fortran2003 standard. It uses no obsolete or obsolescent features of Fortran. The package uses parallel programming
based upon the Message Passing Interface (MPI) [Gropp et al., 1994, Pacheco, 1997].
The next release of the code will include support for GPU graphics card acceleration [Komatitsch, 2011, Michéa
and Komatitsch, 2010, Komatitsch et al., 2009, 2010a].
The code uses the plane strain convention when the standard P-SV equation case is used, i.e., the off-plane strain
zz is zero by definition of the plane strain convention but the off-plane stress σzz is not equal to zero, one has
σzz = λ(xx +yy ). This implies, as in any plain strain software package, that the P-SV source is a line source along the
direction perpendicular to the plane (see file discussion_of_2D_sources_and_approximations_from_Pilant_1979.pdf
for more details).
1.1
Citation
If you use this code for your own research, please cite at least one article written by the developers of the package, for
instance:
• Tromp et al. [2008],
• Peter et al. [2011],
• Vai et al. [1999],
• Lee et al. [2009a],
• Lee et al. [2008],
• Lee et al. [2009b],
• Komatitsch et al. [2010a],
• Komatitsch et al. [2009],
• Liu et al. [2004],
• Chaljub et al. [2007],
• Komatitsch and Vilotte [1998],
• Komatitsch and Tromp [1999],
• Komatitsch et al. [2004],
• Morency and Tromp [2008],
• and/or other articles from http://komatitsch.free.fr/publications.html.
CHAPTER 1. INTRODUCTION
6
If you use the kernel capabilities of the code, please cite at least one article written by the developers of the package,
for instance:
• Tromp et al. [2008],
• Peter et al. [2011],
• Liu and Tromp [2006],
• Morency et al. [2009].
If you use the SCOTCH / CUBIT non-structured capabilities, please also cite:
• Martin et al. [2008a].
The corresponding BibTEX entries may be found in file doc/USER_MANUAL/bibliography.bib.
1.2
Support
This material is based upon work supported by the USA National Science Foundation under Grants No. EAR-0406751
and EAR-0711177, by the French CNRS, French Inria Sud-Ouest MAGIQUE-3D, French ANR NUMASIS under
Grant No. ANR-05-CIGC-002, and European FP6 Marie Curie International Reintegration Grant No. MIRG-CT2005-017461. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the
authors and do not necessarily reflect the views of the USA National Science Foundation, CNRS, Inria, ANR or the
European Marie Curie program.
Chapter 2
Getting Started
To download the SPECFEM2D software package, type this:
git clone --recursive --branch devel https://github.com/geodynamics/specfem2d.git
We recommend that you add ulimit -S -s unlimited to your .bash_profile file and/or limit
stacksize unlimited to your .cshrc file to suppress any potential limit to the size of the Unix stack.
Then, to configure the software for your system, run the configure shell script. This script will attempt to guess
the appropriate configuration values for your system. However, at a minimum, it is recommended that you explicitly
specify the appropriate command names for your Fortran compiler (another option is to define FC, CC and MPIF90 in
your .bash_profile or your .cshrc file):
./configure FC=ifort
If you want to run in parallel, i.e., using more than one processor core, then you would type
./configure FC=ifort MPIFC=mpif90 --with-mpi
Before running the configure script, you should probably edit file flags.guess to make sure that it contains
the best compiler options for your system. Known issues or things to check are:
Intel ifort compiler See if you need to add -assume byterecl for your machine. In the case of that
compiler, we have noticed that versions dot zero sometimes have bugs or issues that can lead to wrong
results when running the code, thus we strongly recommend using versions dot one or above (for instance
version 13.1 instead of 13.0, version 14.1 instead of 14.0 and so on).
IBM compiler See if you need to add -qsave or -qnosave for your machine.
Mac OS You will probably need to install XCODE.
IBM Blue Gene machines Please refer to the manual of SPECFEM3D_Cartesian, which contains detailed instructions on how to run on Blue Gene.
The SPECFEM2D software package relies on the SCOTCH library to partition meshes. The SCOTCH library
[Pellegrini and Roman, 1996] provides efficient static mapping, graph and mesh partitioning routines. SCOTCH is a
free software package developed by François Pellegrini et al. from LaBRI and Inria in Bordeaux, France, downloadable from the web page https://gforge.inria.fr/projects/scotch/. In case no SCOTCH libraries
can be found on the system, the configuration will bundle the version provided with the source code for compilation.
The path to an existing SCOTCH installation can to be set explicitly with the option --with-scotch-dir. Just as
an example:
./configure FC=ifort MPIFC=mpif90 --with-mpi --with-scotch-dir=/opt/scotch
If you use the Intel ifort compiler to compile the code, we recommend that you use the Intel icc C compiler to compile
Scotch, i.e., use:
7
CHAPTER 2. GETTING STARTED
8
./configure CC=icc FC=ifort MPIFC=mpif90
For further details about the installation of SCOTCH, go to subdirectory scotch_5.1.11/ and read INSTALL.txt.
You may want to download more recent versions of SCOTCH in the future from (http://www.labri.fr/
perso/pelegrin/scotch/scotch_en.html) . Support for the METIS graph partitioner has been discontinued because SCOTCH is more recent and performs better.
When compiling the SCOTCH source code, if you get a message such as: "ld: cannot find -lz", the Zlib compression development library is probably missing on your machine and you will need to install it or ask your system
administrator to do so. On Linux machines the package is often called "zlib1g-dev" or similar. (thus "sudo apt-get
install zlib1g-dev" would install it)
You may edit the Makefile for more specific modifications. Especially, there are several options available:
• -DUSE_MPI compiles with use of an MPI library.
• -DUSE_SCOTCH enables use of graph partitioner SCOTCH.
After these steps, go back to the main directory of SPECFEM2D/ and type
make
to create all executables which will be placed into the folder ./bin/.
By default, the solver runs in single precision. This is fine for most application, but if for some reason you want
to run the solver in double precision, run the configure script with option “--enable-double-precision”.
Keep in mind that this will of course double total memory size and will also make the solver around 20 to 30% slower
on many processors.
If your compiler has problems with the use mpi statements that are used in the code, use the script called
replace_use_mpi_with_include_mpif_dot_h.pl in the root directory to replace all of them with include
‘mpif.h’ automatically.
2.1
Visualizing the subroutine calling tree of the source code
Packages such as doxywizard can be used to visualize the subroutine calling tree of the source code. Doxywizard
is a GUI front-end for configuring and running doxygen.
2.2
Becoming a developer of the code, or making small modifications in the
source code
If you want to develop new features in the code, and/or if you want to make small changes, improvements, or bug
fixes, you are very welcome to contribute. To do so, i.e. to access the development branch of the source code with
read/write access (in a safe way, no need to worry too much about breaking the package, there is a robot called
BuildBot that is in charge of checking and validating all new contributions and changes), please visit this Web page:
https://github.com/geodynamics/specfem2d/wiki/Using-Hub.
Chapter 3
Mesh Generation
3.1
How to use SPECFEM2D
Mesher
CUBIT, Gmsh, GiD
Partitioner
SCOTCH
xmeshfem2D
xmeshfem2D
Databases
Solver
xspecfem2D
Figure 3.1: Schematic workflow for a SPECFEM2D simulation. The executable xmeshfem2D creates the GLL mesh
points and assigns specific model parameters. The executable xspecfem2D solves the seismic wave propagation.
To run the mesher, please follow these steps:
• edit the input file DATA/Par_file, which describes the simulation. The default DATA/Par_file provided
with the code contains detailed comments and should be almost self-explanatory (note that some of the older
DATA/Par_file files provided in the EXAMPLES directory work fine but some of the comments they contain
may be obsolete or even wrong; thus refer to the default DATA/Par_file instead for reliable explanations). If
you need more details we do not have a detailed description of all the parameters for the 2D version in this manual but you can find useful information in the manuals of the 3D versions, since many parameters and the general philosophy is similar. They are available at (https://github.com/geodynamics/specfem3d/
tree/master/doc/USER_MANUAL). To create acoustic (fluid) regions, just set the S wave speed to zero
and the code will see that these elements are fluid and switch to the right equations there automatically, and
automatically match them with the solid regions
• if you are using an external mesher (like GiD or CUBIT / Trelis), you should set read_external_mesh to
.true.:
9
CHAPTER 3. MESH GENERATION
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mesh_file is the file describing the mesh : first line is the number of elements, then a list of 4 nodes (quadrilaterals only) forming each elements on each line.
nodes_coords_file is the file containing the coordinates (x and z) of each node: number of nodes on the
first line, then coordinates x and z on each line.
materials_file is the number of the material for every element : an integer ranging from 1 to nbmodels
on each line.
free_surface_file is the file describing the edges forming the acoustic free surface: number of edges on
the first line, then on each line: number of the element, number of nodes forming the free surface (1 for
a point, 2 for an edge), the nodes forming the free surface for this element. If you do not want any free
surface, just put 0 on the first line.
absorbing_surface_file is the file describing the edges forming the absorbing boundaries: number of
edges on the first line, then on each line: number of the element, number of nodes forming the absorbing
edge (must always be equal to 2), the two nodes forming the absorbing edge for this element, and then the
type of absorbing edge: 1 for BOTTOM, 2 for RIGHT, 3 for TOP and 4 for LEFT. Only two nodes per
element can be listed, i.e., the second parameter of each line must always be equal to 2. If one of your
elements has more than one edge along a given absorbing contour (e.g., if that contour has a corner) then
list it twice, putting the first edge on the first line and the second edge on the second line. Do not list
the same element with the same absorbing edge twice or more, otherwise absorption will not be correct
because the edge integral will be improperly subtracted several times. If one of your elements has a single
point along the absorbing contour rather than a full edge, do NOT list it (it would have no weight in the
contour integral anyway because it would consist of a single point). If you use 9-node elements, list only
the first and last points of the edge and not the intermediate point located around the middle of the edge;
the right 9-node curvature will be restored automatically by the code.
tangential_detection_curve_file contains points describing the envelope, that are used for the
source_normal_to_surface and rec_normal_to_surface. Should be fine grained, and ordered clockwise. Number of points on the first line, then (x,z) coordinates on each line.
• if you have compiled with MPI, you must specify the number of processes.
Then type
./bin/xmeshfem2D
to create the mesh (which will be stored in directory OUTPUT_FILES/). xmeshfem2D is serial; it will output
several files called Database??????, one for each process.
3500
'OUTPUT_FILES.default.M2_UPPA/gridfile.gnu'
3000
2500
2000
1500
1000
500
0
0
500
1000
1500
2000
2500
3000
3500
4000
Figure 3.2: Example of a grid file generated by xmeshfem2D and visualized with gnuplot (within gnuplot, type
‘plot "OUTPUT_FILES/gridfile.gnu" w l’).
Regarding mesh point numbering in the files created by the mesher, we use the classical convention of 4-node and
9-node finite elements:
CHAPTER 3. MESH GENERATION
4 . . . .
.
.
.
8
.
.
.
1 . . . .
11
7 . . . . 3
.
eta
.
|
.
9--xi
6
.
.
.
5 . . . . 2
the local coordinate system being ξ and η (xi and eta). Note that this convention is used to describe the geometry
only. In the solver the wave field is then described based on high-order Lagrange interpolants at Gauss-LobattoLegendre points, as is classical in spectral-element methods.
3.2
How to use Gmsh to generate an external mesh
Gmsh1 is a 3D finite element grid generator which can be used for the generation of quadrangle and hexahedral
meshes. It is therefore a good candidate for generating meshes which can be processed by SPECFEM2D. Only two
modules of Gmsh are of interest for the SPECFEM2D users : the geometry and the mesh modules. An example is
given in directory EXAMPLES/Gmsh_example which illustrates the generation of an external mesh using these two
modules. The model that is considered consists of a homogeneous square containing two circles filled with a different
material.
The geometry is generated by loading file SqrCirc.geo into Gmsh. The end of the .geo file contains several
lines which are required in order to define the sides of the box and the media. This is done using the following
conventions :
Physical Line("Top") = {1}; line corresponding to the top of the box
Physical Line("Left") = {2}; line corresponding to the left side of the box
Physical Line("Bottom") = {3}; line corresponding to the bottom of the box
Physical Line("Right") = {4}; line corresponding to the right side of the box
Physical Surface("M1") = {10}; surrounding medium
Physical Surface("M2") = {11,12}; interior of the two circles
For instance, if you want to fill the two circles with two different materials, you will have to write :
Physical Surface("M1") = {10}; surrounding medium
Physical Surface("M2") = {11}; interior of the big circle
Physical Surface("M3") = {12}; interior of the small circle
and, consequently, you will have to define a new medium numbered 3 in the Par_file.
Then, a 2D mesh can be created and saved after selecting the appropriate options in Gmsh : All quads in
Subdivision algorithm and 1 or 2 in Element order whether you want a 4 or 9 node mesh. This operation
will generate a SqrCirc.msh file which must be processed to get all the files required by SPECFEM2D when using
an external mesh (see previous section). This is done by running a python script called LibGmsh2Specfem.py,
located in directory UTILS/Gmsh:
python LibGmsh2Specfem.py SqrCirc -t A -b A -r A -l A
Where the options -t, -b, -r and -l represent the different sides of the model (top, bottom, right and left) and can
take the values A or F if the corresponding side is respectively absorbing or free. All boundaries are absorbing by
default. The connections of the generated filenames to the filenames indicated in the previous section are :
• Mesh_SqrCirc is the mesh_file
1 freely
available at the following address : http://www.geuz.org/gmsh/
CHAPTER 3. MESH GENERATION
12
Figure 3.3: Geometry and mesh of the two circle model generated with Gmsh
• Material_SqrCirc is the material_file
• Nodes_SqrCirc is the nodes_coords_file
• Surf_abs_SqrCirc is the absorbing_surface_file
• Surf_free_SqrCirc is the free_surface_file
In addition, four files like free_surface_file corresponding to the sides of the model are generated.
If you use CPML, an additional file listing the CPML elements is needed. Its first line is the total number of CPML
elements, and then a list of all the CPML elements, one per line. The format of these lines is: in the first column the
CPML element number, and in the second column a flag as follows:
Table 3.1: Definition of flags for CPML elements
Flag
1
2
3
Meaning
element belongs to a X CPML layer only (either in Xmin or in Xmax)
element belongs to a Y CPML layer only (either in Ymin or in Ymax)
element belongs to both a X and a Y CPML layer (i.e., to a CPML corner)
In order to see how to add PML layers to a mesh / model created with an external mesher such as ‘Gmsh’, see the
examples in directory EXAMPLES/CPML_absorbing_layers.
If you use PML, the mesh elements that belong to the PML layers can be acoustic or elastic, but not viscoelastic nor
poroelastic. Then, when defining your model, you should define these absorbing elements as either acoustic or elastic.
In you forget to do that, the code will fix the problem by automatically converting the viscoelastic or poroelastic PML
elements to elastic. This means that strictly speaking the PML layer will not be perfectly matched any more, since the
physical model will change from viscoelastic or poroelastic to elastic at the entrance of the PML, but in practice this
is sufficient and produces only tiny / negligible spurious reflections.
If you use PML and an external velocity and density model (e.g., setting flag “READ_EXTERNAL_SEP_FILE”
to .true.), you should be careful because mathematically a PML cannot handle heterogeneities along the normal
to the PML edge inside the PML layer. This comes from the fact that the damping profile that is defined assumes a
constant velocity and density model along the normal direction. Thus, you need to modify your velocity and density
model in order for it to be 1D inside the PML, as shown in Figure 3.4. This applies to the bottom layer as well; there
you should make sure that your model is 1D and thus constant along the vertical direction. To summarize, only use a
2D velocity and density model inside the physical region, and in all the PML layers extend it by continuity from its
values along the inner PML edge.
CHAPTER 3. MESH GENERATION
13
Use a
horizontally
1D velocity
model here
PML
Use a vertically-1D velocity model here
PML
Figure 3.4: How to modify your external 2D velocity and density model in order to use PML. Such a modification is
not needed when using Stacey absorbing boundary conditions (but such conditions are significantly less efficient).
3.3
Controlling the quality of an external mesh
To examine the quality of the elements in your externally build mesh, type
./bin/xcheck_quality_external_mesh
(and answer "3" to the first question asked). This code will tell you which element in the whole mesh has the worst
quality (maximum skewness, i.e. maximum deformation of the element angles) and it should be enough to modify
this element with the external software package used for the meshing, and to repeat the operation until the maximum
skewness of the whole mesh is less or equal to about 0.75 (above is dangerous: from 0.75 to 0.80 could still work, but
if there is a single element above 0.80 the mesh should be improved).
The code also shows a histogram of 20 classes of skewness which tells how many element are above the skewness
= 0.75, and to which percentage of the total this amounts. To see this histogram, you could type:
gnuplot plot_mesh_quality_histogram.gnu
This tool is useful to estimate the mesh quality and to see it evolve along the successive corrections.
3.4
Controlling how the mesh samples the wave field
To examine (using Gnuplot) how the mesh samples the wave field, type
gnuplot plot_points_per_wavelength_histogram.gnu
and also check the following histogram printed on the screen or in the output file:
histogram of min number of points per S wavelength (P wavelength in
acoustic regions)
(too small: poor resolution of calculations - too big = wasting
memory and CPU time)
(threshold value is around 4.5 points per wavelength in elastic media
and 5.5 in acoustic media)
If you see that you have a significant number of mesh elements below the threshold indicated, then your simulations
will not be accurate and you should create a denser mesh. Conversely, if you have a significant number of mesh
elements above the threshold indicated, the mesh your created is too dense, it will be extremely accurate but the
simulations will be slow; using a coarser mesh would be sufficient and would lead to faster simulations.
Chapter 4
Running the Solver xspecfem2D
To run the solver, type:
./bin/xspecfem2D
to run the main solver (use mpirun or equivalent if you compiled with parallel support). This will output the seismograms and snapshots of the wave fronts at different time steps in directory OUTPUT_FILES/. To visualize them,
type "gs OUTPUT_FILES/vect*.ps" to see the Postscript files (in which the wave field is represented with small
arrows, fluid/solid matching interfaces with a thick pink line, and absorbing edges with a thick green line) and "gimp
OUTPUT_FILES/image*.gif" to see the colour snapshot showing a pixelized image of one of the two components of the wave field (or pressure, depending on what you have selected for the output in DATA/Par_file).
Figure 4.1: Wavefield snapshots of the default example generated by xspecfem2D when parameter
output_color_image is set to .true.. To create smaller (subsampled) images you can change double precision parameter factor_subsample_image = 1.0 to a higher value in file DATA/Par_file. This can be
useful in the case of very large models. The number of pixels of the image in each direction must be smaller than
parameter NX_NZ_IMAGE_MAX defined in file SETUP/constants.h.in, again to avoid creating huge images in
the case of very large models.
Please consider these following points, when running the solver:
• the DATA/Par_file given with the code works fine, you can use it without any modification to test the code
• the seismograms OUTPUT_FILES/*.sem* are simple ASCII files with two columns: time in the first column
and amplitude in the second, therefore they can be visualized with any tool you like, for instance “gnuplot”; if
you prefer to output binary seismograms in Seismic Unix format (which is a simple binary array dump) you can
use parameter SU_FORMAT, in which case all the seismograms will be written to a single file with the extension
*.bin. Depending on your installation of the Seismic Unix package you can use one of these two commands:
surange < Uz_file_single.bin
suoldtonew < Uz_file_single.bin | surange
14
CHAPTER 4. RUNNING THE SOLVER XSPECFEM2D
15
to see the header info. Replace surange with suxwigb to see wiggle plots for the seismograms.
• if you set flag assign_external_model to .true. in DATA/Par_file, the velocity and density model
that is given at the end of DATA/Par_file is then ignored and overwritten by the external velocity and density
model that you define yourself in define_external_model.f90
• when compiling with Intel ifort, use “-assume byterecl” option to create binary PNM images displaying
the wave field
• there are a few useful scripts and Fortran routines in directory UTILS/.
• you can find a Fortran code to compute the analytical solution for simple media that we use as a reference in
benchmarks in many of our articles at (http://www.spice-rtn.org/library/software/EX2DDIR).
That code is described in: Berg et al. [1994]
The SOURCE file located in the DATA/ directory should be edited in the following way:
source_surf Set this flag to .true. to force the source to be located at the surface of the model, otherwise the
sol be placed inside the medium
xs source location x in meters
zs source location z in meters
source_type Set this value equal to 1 for elastic forces or acoustic pressure, set this to 2 for moment tensor
sources. For a plane wave including converted and reflected waves at the free surface, P wave = 1, S wave = 2,
Rayleigh wave = 3; for a plane wave without converted nor reflected waves at the free surface, i.e. the incident
wave only, P wave = 4, S wave = 5. (incident plane waves are turned on by parameter initialfield in
DATA/Par_file).
time_function_type Choose a source-time function: set this value to 1 to use a Ricker, 2 the first derivative, 3
a Gaussian, 4 a Dirac or 5 a Heaviside source-time function.
f0 Set this to the dominant frequency of the source. For point-source simulations using a Heaviside source-time
function (time_function_type = 5), we recommend setting the source frequency parameter f0 equal to
a high value, which corresponds to simulating a step source-time function, i.e., a moment-rate function that is a
delta function.
The half duration of a source is obtained by 1/f0. If the code will use a Gaussian source-time function
(time_function_type = 3) (i.e., a signal with a shape similar to a ‘smoothed triangle’, as explained
in Komatitsch and Tromp [2002] and shown in Fig 4.2), the source-time function uses a half-width of half
duration. We prefer to run the solver with half duration set to zero and convolve the resulting synthetic
seismograms in post-processing after the run, because this way it is easy to use a variety of source-time functions.
Komatitsch and Tromp [2002] determined that the noise generated in the simulation by using a step source time
function may be safely filtered out afterward based upon a convolution with the desired source time function
and/or low-pass filtering. Use the serial code convolve_source_timefunction.f90 and the script
convolve_source_timefunction.sh for this purpose, or alternatively use signal-processing software
packages such as SAC (www.llnl.gov/sac). Type
make xconvolve_source_timefunction
to compile the code and then set the parameter hdur in convolve_source_timefunction.sh to the
desired half-duration.
t0 For single sources, we recommend to set the time shift parameter t0 equal to 0.0. The time shift parameter would
simply apply an overall time shift to the synthetics (according to the time shift of the first source), something
that can be done in the post-processing. This time shift parameter can be non-zero when using multiple sources.
anglesource angle of the source (for a force only); for a plane wave, this is the incidence angle. For moment
tensor sources this parameter is unused.
CHAPTER 4. RUNNING THE SOLVER XSPECFEM2D
16
- source decay rate
- half duration
half duration
tCMT
Figure 4.2: Comparison of the shape of a triangle and the Gaussian function actually used.
Mxx,Mzz,Mxz Moment tensor components (valid only for moment tensor sources, source_type = 2). Note
that the units for the components of a moment tensor source are different in SPECFEM2D and in SPECFEM3D:
SPECFEM3D: in SPECFEM3D the moment tensor components are in dyne*cm
SPECFEM2D: in SPECFEM2D the moment tensor components are in N*m
To go from strike / dip / slip to CMTSOLUTION moment-tensor format using the classical formulas (of e.g.
Aki and Richards [1980] you can use these two small C programs from SPECFEM3D_GLOBE:
./utils/strike_dip_rake_to_CMTSOLUTION.c
./utils/CMTSOLUTION_to_AkiRichards.c
but then it is another story to make a good 2D approximation of that, because in plain-strain P-SV what you get
is the equivalent of a line source in the third direction (orthogonal to the plane) rather than a 3D point source
For more details on this see e.g. Section 7.3 "Two-dimensional point sources" of the book of Pilant [1979]. That
book being hard to find, we scanned the related pages in file
discussion_of_2D_sources_and_approximations_from_Pilant_1979.pdf in the same directory as this users manual. Another very useful reference addressing that is Helmberger and Vidale [1988]
and its recent extension (Global synthetic seismograms using a 2D finite-difference method, Dunzhu Li, Don
Helmberger, Robert W. Clayton and Daoyuan Sun, submitted to Geophys. J. Int, 2014).
factor amplification factor
Note, the zero time of the simulation corresponds to the center of the triangle/Gaussian, or the centroid time of
the earthquake. The start time of the simulation is t = −1.2 ∗ half duration + t0 (the factor 1.2 is to make sure
the moment rate function is very close to zero when starting the simulation; Heaviside functions use a factor 2.0), the
half duration is obtained by 1/f0. If you prefer, you can fix this start time by setting the parameter USER_T0 in the
constants.h file to a positive, non-zero value. The simulation in that case would start at a starting time equal to
-USER_T0.
Coupled Simulations
The code supports acoustic/elastic, acoustic/poroelastic, elastic/poroelastic, and acoustic, elastic/poroelastic simulations. Elastic/poroelastic coupling supports anisotropy, but not attenuation for the elastic material.
CHAPTER 4. RUNNING THE SOLVER XSPECFEM2D
4.1
17
How to run P-SV or SH (membrane) wave simulations
For elastic materials, you have these additional options:
P-SV: To run a P-SV waves calculation propagating in the x-z plane, set p_sv = .true. in the Par_file.
SH: To run a SH (membrane) waves calculation travelling in the x-z plane with a y-component of motion, set p_sv
= .false.
This feature is only implemented for elastic materials and sensitivity kernels can be calculated (see Tape et al. [2007]
for details on membrane surface waves).
A useful Python script called SEM_save_dir.py, written by Paul Cristini from Laboratoire de Mecanique et
d’Acoustique, CNRS, Marseille, France, is provided. It allows one to automatically save all the parameters and results
of a given simulation.
4.2
How to use anisotropy
Following Carcione et al. [1988], we use the classical reduced Voigt notation to represent symmetric tensors [Helbig,
1994, Carcione, 2007]:
The constitutive relation of a heterogeneous anisotropic and elastic solid is expressed by the generalized Hooke’s law, which can be written as
σij = cijkl εkl ,
i, j, k = 1, . . . , 3,
where t is the time, x is the position vector, σij (x, t) and εij (x, t) are the Cartesian components of the
stress and strain tensors respectively, and cijkl (x) are the components of a fourth-order tensor called the
elasticites of the medium. The Einstein convention for repeated indices is used.
To express the stress-strain relation for a transversely isotropic medium we introduce a shortened
matrix notation commonly used in the literature. With this convention, pairs of subscripts concerning the
elasticities are replaced by a single number according to the following correspondence:
(11) → 1,
(22) → 2,
(33) → 3,
(23) = (32) → 4,
(31) = (13) → 5,
(12) = (21) → 6.
Thus in the most general 2D case we have the following convention for the stress-strain relationship:
! implement anisotropy in 2D
sigma_xx = c11*dux_dx + c13*duz_dz + c15*(duz_dx + dux_dz)
sigma_zz = c13*dux_dx + c33*duz_dz + c35*(duz_dx + dux_dz)
sigma_xz = c15*dux_dx + c35*duz_dz + c55*(duz_dx + dux_dz)
! sigma_yy is not equal to zero in the plane strain formulation
! but is used only in post-processing if needed,
! to compute pressure for display or seismogram recording purposes
sigma_yy = c12*dux_dx + c23*duz_dz + c25*(duz_dx + dux_dz)
where the notations are for instance duz_dx = d(Uz) / dx.
4.3
How to use poroelasticity
Check the following new inputs in Par_file:
In section "# geometry of model and mesh description":
TURN_VISCATTENUATION_ON, Q0, and FREQ0 deal with viscous damping in a poroelastic medium. Q0 is
the quality factor set at the central frequency FREQ0. For more details see Morency and Tromp [2008].
CHAPTER 4. RUNNING THE SOLVER XSPECFEM2D
18
In section "# time step parameters":
SIMULATION_TYPE defines the type of simulation
(1) forward simulation
(2) UNUSED (purposely, for compatibility with the numbering convention used in our 3D codes)
(3) adjoint method and kernels calculation
In section "# source parameters":
The code now support multiple sources. NSOURCE is the number of sources. Parameters of the sources are
displayed in the file SOURCE, which must be in the directory DATA/. The components of a moment tensor
source must be given in N.m, not in dyne.cm as in the DATA/CMTSOLUTION source file of the 3D version of
the code.
Figure 4.3: Example of timing for three sources. The center of the first source triangle is defined to be time zero. Note
that this is NOT in general the hypocentral time, or the start time of the source (marked as tstart). The time shift
parameter t0 in the SOURCE file would be t1(= 0), t2, t3 in this case, and the half-duration parameter, f0, would be
hdur1 = 1/f01 , hdur2 = 1/f02 , hdur3 = 1/f03 for the sources 1, 2, 3 respectively.
In section "# receiver line parameters for seismograms":
SAVE_FORWARD determines if the last frame of a forward simulation is saved (.true.) or not (.false)
In section "# define models....":
There are three possible types of models:
I: (model_number 1 rho Vp Vs 0 0 QKappa Qmu 0 0 0 0 0 0) or
II: (model_number 2 rho c11 c13 c15 c33 c35 c55 c12 c23 c25 0 0 0) or
III: (model_number 3 rhos rhof phi c kxx kxz kzz Ks Kf Kfr etaf mufr Qmu).
For isotropic elastic/acoustic material use I and set Vs to zero to make a given model acoustic, for anisotropic
elastic use II, and for isotropic poroelastic material use III. The mesh can contain acoustic, elastic, and
poroelastic models simultaneously.
For anisotropic elastic media the last three parameters, c12 c23 c25, are used only when the user asks
the code to compute pressure for display or seismogram recording purposes. Thus, if you do not know these
parameters for your anisotropic material and/or if you do not plan to display or record pressure you can ignore
them and set them to zero. When pressure is used these three parameters are needed because the code needs to
compute σyy , which is not equal to zero in the plane strain formulation.
rho_s = solid density
CHAPTER 4. RUNNING THE SOLVER XSPECFEM2D
19
rho_f = fluid density
phi = porosity
tort = tortuosity
permxx = xx component of permeability tensor
permxz = xz,zx components of permeability tensor
permzz = zz component of permeability tensor
kappa_s = solid bulk modulus
kappa_f = fluid bulk modulus
kappa_fr = frame bulk modulus
eta_f = fluid viscosity
mu_fr = frame shear modulus
Qmu = shear quality factor
Note: for the poroelastic case, mu_s is irrelevant. For details on the poroelastic theory see Morency and Tromp
[2008].
get_poroelastic_velocities.f90 allows to compute cpI, cpII, and cs function of the source dominant
frequency. Notice that for this calculation we use permxx and the dominant frequency of the first source, f0(1).
Caution if you use several sources with different frequencies and if you consider anistropic permeability.
4.4
How to set plane waves as initial conditions
To simulate propagation of incoming plane waves in the simulation domain, initial conditions based on analytical
formulae of plane waves in homogeneous model need to be set. No additional body or boundary forces are required.
To set up this scenario:
Par_file:
• switch on initialfield = .true.
• at this point setting add_bielak_condition does not seem to help with absorbing boundaries, therefore, it should be turned off.
SOURCE:
• zs has to be the same as the height of the simulation domain defined in interfacesfile.
• xs is the x-coordinate of the intersection of the initial plane wave front with the free surface.
• source_type = 1 for a plane P wave, 2 for a plane SV wave, 3 for a Rayleigh wave.
• angleforce can be negative to indicate a plane wave incident from the right (instead of the left)
4.5
How to choose the time step
Three different explicit conditionally-stable time schemes can be used for elastic, acoustic (fluid) or coupled elastic/acoustic media: the Newmark method, the low-dissipation and low-dispersion fourth-order six-stage Runge-Kutta
method (LDDRK4-6) presented in Berland et al. [2006], and the classical fourth-order four-stage Runge-Kutta (RK4)
method. Currently the last two methods are not implemented for poroelastic media. According to De Basabe and Sen
[2010] and Berland et al. [2006], with different degrees N = N GLLX −1 of the GLL basis functions the CFL bounds
are given in the following tables. Note that by default the SPECFEM solver uses N GLLX = 5 and thus a degree N =
4, which is thus the value you should use in most cases in the following tables. You can directly compare these values
with the value given in sentence ‘Max stability for P wave velocity’ in file output_solver.txt to see whether you
set the correct ∆t in Par_file or not. For elastic simulation, the CFL value given in output_solver.txt does
CHAPTER 4. RUNNING THE SOLVER XSPECFEM2D
20
not consider the Vp /Vs ratio, but the CFL limit slight decreases when Vp /Vs increases. In viscoelastic simulations the
CFL limit does not change compared to the elastic case because we use a rational approximation of a constant quality
factor Q, which has no attenuation effect on zero-frequency waves. Additionally, if you use C-PML absorbing layers in
your simulations, which are implemented for the Newmark and LDDRK4-6 techniques but not for the classical RK4),
the CFL upper limit decreases to approximately 95% of the limit without absorbing layers in the case of Newmark and
to 85% in the case of LDDRK4-6.
Table 4.1: CFL upper bound for an acoustic (fluid) simulation.
Degree N Newmark LDDRK4-6 RK4
1
0.709
1.349
1.003
2
0.577
1.098
0.816
3
0.593
1.129
0.839
4
0.604
1.150
0.854
5
0.608
1.157
0.860
6
0.608
1.157
0.860
7
0.608
1.157
0.860
8
0.607
1.155
0.858
9
0.607
1.155
0.858
10
0.607
1.155
0.858
Table 4.2: CFL upper bound for an elastic simulation with Vp /Vs =
Degree N Newmark LDDRK4-6 RK4
1
0.816
1.553
1.154
2
0.666
1.268
0.942
3
0.684
1.302
0.967
4
0.697
1.327
0.986
5
0.700
1.332
0.990
6
0.700
1.332
0.990
7
0.700
1.332
0.990
8
0.699
1.330
0.989
9
0.698
1.328
0.987
10
0.698
1.328
0.987
√
2.
Chapter 5
Adjoint Simulations
5.1
How to obtain Finite Sensitivity Kernels
1. Run a forward simulation:
• SIMULATION_TYPE = 1
• SAVE_FORWARD = .true.
• seismotype = 1 (we need to save the displacement fields to later on derive the adjoint source. Note: if
the user forgets it, the program corrects it when reading the proper SIMULATION_TYPE and SAVE_FORWARD
combination and a warning message appears in the output file)
Important output files (for example, for the elastic case, P-SV waves):
• absorb_elastic_bottom*****.bin
• absorb_elastic_left*****.bin
• absorb_elastic_right*****.bin
• absorb_elastic_top*****.bin
• lastframe_elastic*****.bin
• S****.AA.BXX.semd
• S****.AA.BXZ.semd
2. Define the adjoint source:
• Use adj_seismogram.f90
• Edit to update NSTEP, nrec, t0, deltat, and the position of the cut to pick any given phase if needed
(tstart,tend), add the right number of stations, and put one component of the source to zero if needed.
• The output files of adj_seismogram.f90 are S****.AA.BXX.adj and S****.AA.BXZ.adj,
for P-SV waves (and S****.AA.BXY.adj, for SH (membrane) waves). Note that you will need these
three files (S****.AA.BXX.adj, S****.AA.BXY.adj and S****.AA.BXZ.adj) to be present in
the SEM/ directory together with the absorb_elastic_****.bin and lastframe_elastic.bin
files to be read when running the adjoint simulation.
3. Run the adjoint simulation:
• Make sure that the adjoint source files absorbing boundaries and last frame files are in the OUTPUT_FILES/
directory.
• SIMULATION_TYPE = 3
• SAVE_FORWARD = .false.
21
CHAPTER 5. ADJOINT SIMULATIONS
22
Output files (for example for the elastic case):
• snapshot_rho_kappa_mu*****
• snapshot_rhop_alpha_beta*****
which are the primary moduli kernels and the phase velocities kernels respectively, in ascii format and at the
local level, that is as “kernels(i,j,ispec)”.
5.2
Remarks about adjoint runs and solving inverse problems
SPECFEM2D can produce the gradient of the misfit function for a tomographic inversion, but options for using the
gradient within an iterative inversion are left to the user (e.g., conjugate-gradient, steepest descent). The plan is to
include some examples in the future.
The algorithm is simple:
1. calculate the forward wave field s(x, t)
2. calculate the adjoint wave field s† (x, t)
3. calculate their interaction s(x, t) · s† (x, T − t) (these symbolic, temporal and spatial derivatives should be
included)
4. integrate the interactions, which is summation in the code.
That is all. Step 3 has some tricks in implementation, but which can be skipped by regular users.
If you look into SPECFEM2D, besides “rhop_ac_kl” and “rho_ac_kl”, there are more variables such as
“kappa_ac_kl” and “rho_el_kl” etc. “rho” denotes density ρ (“kappa” for bulk modulus κ etc.), “ac”
denotes acoustic (“el” for elastic), “kl” means kernel (and you may find “k” as well, which is the interaction at each
time step, i.e., before doing time integration).
5.3
Caution
Please note that:
• at the moment, adjoint simulations do not support anisotropy, attenuation, and viscous damping.
• you will need S****.AA.BXX.adj, S****.AA.BXY.adj and S****.AA.BXZ.adj to be present in
directory SEM/ even if you are just running an acoustic or poroelastic adjoint simulation.
– S****.AA.BXX.adj is the only relevant component for an acoustic case.
– S****.AA.BXX.adj and S****.AA.BXZ.adj are the only relevant components for a poroelastic
case.
Chapter 6
Oil and gas industry simulations
The SPECFEM2D package provides compatibility with industrial (oil and gas industry) types of simulations. These
features include importing Seismic Unix (SU) format wavespeed models into SPECFEM2D, output of seismograms
in SU format with a few key parameters defined in the trace headers and reading adjoint sources in SU format etc.
There is one example given in EXAMPLES/INDUSTRIAL_FORMAT, which you can follow.
We also changed the relationship between adjoint potential and adjoint displacement in fluid region (the relationship between forward potential and forward displacement remains the same as previously defined). The new definition
is critical when there are adjoint sources (in other words, receivers) in the acoustic domain, and is the direct consequence of the optimization problem.
1
∇φ
ρ
p ≡ −κ (∇ · s) = −∂t2 φ
s≡
1
∂t2 s† ≡ − ∇φ†
ρ
p† ≡ −κ ∇ · s† = φ†
23
Acknowledgments
The Gauss-Lobatto-Legendre subroutines in gll_library.f90 are based in part on software libraries from the
Massachusetts Institute of Technology, Department of Mechanical Engineering (Cambridge, Massachusetts, USA).
The non-structured global numbering software was provided by Paul F. Fischer (Brown University, Providence, Rhode
Island, USA, now at Argonne National Laboratory, USA).
Please e-mail your feedback, bug reports, questions, comments, and suggestions to the CIG Computational Seismology Mailing List ([email protected]).
24
Copyright
Main historical authors: Dimitri Komatitsch and Jeroen Tromp
Princeton University, USA, and CNRS / University of Marseille, France
© Princeton University and CNRS / University of Marseille, July 2012
25
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Appendix A
Troubleshooting
FAQ
Regarding the structure of some of the database files
Question: Can anyone tell me what the columns of the SPECFEM2D boundary condition files in SPECFEM2D/DATA/
Mesh_canyon are?
SPECFEM2D/DATA/Mesh_canyon/canyon_absorbing_surface_file
SPECFEM2D/DATA/Mesh_canyon/canyon_free_surface_file
Answer: canyon_absorbing_surface_file refers to parameters related to the absorbing conditions: The
first number (180) is the number of absorbing elements (nelemabs in the code). Then the columns are:
column 1: the element number
column 2: the number of nodes of this element that form the absorbing surface
column 3: the first node
column 4: the second node
canyon_free_surface_file refers to the elements of the free surface (relevant for enforcing free surface
condition for acoustic media): The first number (160) is the number of elements of the free surface. Then the columns
are (similar to the absorbing case):
column 1: the element number
column 2: the number of nodes of this element that form the absorbing surface
column 3: the first node
column 4: the second node
Concerning the free surface description file, nodes/edges pertaining to elastic elements are discarded when the file
is read (if for whatever reason it was simpler to include all the nodes/edges on one side of a studied area and that there
are among them some elements that are elastic elements, only the nodes/edges of acoustic elements are kept).
These files are opened and read in meshfem2D.F90 using subroutines read_abs_surface() and read_
acoustic_surface(), which are in part_unstruct.F90
32
Appendix B
License
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3.1 The Licensee shall be deemed as having accepted the terms and conditions of this Agreement upon the occurrence of the first of the following events:
(i) loading the Software by any or all means, notably, by downloading from a remote server, or by loading from a
physical medium;
(ii) the first time the Licensee exercises any of the rights granted hereunder. 3.2 One copy of the Agreement,
containing a notice relating to the characteristics of the Software, to the limited warranty, and to the fact that its use
is restricted to experienced users has been provided to the Licensee prior to its acceptance as set forth in Article 3.1
hereinabove, and the Licensee hereby acknowledges that it has read and understood it.
Article 4 - EFFECTIVE DATE AND TERM
4.1 EFFECTIVE DATE
The Agreement shall become effective on the date when it is accepted by the Licensee as set forth in Article 3.1.
4.2 TERM
The Agreement shall remain in force for the entire legal term of protection of the economic rights over the Software.
Article 5 - SCOPE OF RIGHTS GRANTED
The Licensor hereby grants to the Licensee, who accepts, the following rights over the Software for any or all use,
and for the term of the Agreement, on the basis of the terms and conditions set forth hereinafter.
Besides, if the Licensor owns or comes to own one or more patents protecting all or part of the functions of the
Software or of its components, the Licensor undertakes not to enforce the rights granted by these patents against successive Licensees using, exploiting or modifying the Software. If these patents are transferred, the Licensor undertakes
to have the transferees subscribe to the obligations set forth in this paragraph.
5.1 RIGHT OF USE
The Licensee is authorized to use the Software, without any limitation as to its fields of application, with it being
hereinafter specified that this comprises:
permanent or temporary reproduction of all or part of the Software by any or all means and in any or all form.
APPENDIX B. LICENSE
35
loading, displaying, running, or storing the Software on any or all medium.
entitlement to observe, study or test its operation so as to determine the ideas and principles behind any or all
constituent elements of said Software. This shall apply when the Licensee carries out any or all loading, displaying,
running, transmission or storage operation as regards the Software, that it is entitled to carry out hereunder.
5.2 ENTITLEMENT TO MAKE CONTRIBUTIONS
The right to make Contributions includes the right to translate, adapt, arrange, or make any or all modifications to
the Software, and the right to reproduce the resulting software.
The Licensee is authorized to make any or all Contributions to the Software provided that it includes an explicit
notice that it is the author of said Contribution and indicates the date of the creation thereof.
5.3 RIGHT OF DISTRIBUTION
In particular, the right of distribution includes the right to publish, transmit and communicate the Software to the
general public on any or all medium, and by any or all means, and the right to market, either in consideration of a fee,
or free of charge, one or more copies of the Software by any means.
The Licensee is further authorized to distribute copies of the modified or unmodified Software to third parties
according to the terms and conditions set forth hereinafter.
5.3.1 DISTRIBUTION OF SOFTWARE WITHOUT MODIFICATION
The Licensee is authorized to distribute true copies of the Software in Source Code or Object Code form, provided
that said distribution complies with all the provisions of the Agreement and is accompanied by:
a copy of the Agreement,
a notice relating to the limitation of both the Licensor’s warranty and liability as set forth in Articles 8 and 9,
and that, in the event that only the Object Code of the Software is redistributed, the Licensee allows future Licensees unhindered access to the full Source Code of the Software by indicating how to access it, it being understood
that the additional cost of acquiring the Source Code shall not exceed the cost of transferring the data.
5.3.2 DISTRIBUTION OF MODIFIED SOFTWARE
When the Licensee makes a Contribution to the Software, the terms and conditions for the distribution of the
resulting Modified Software become subject to all the provisions of this Agreement.
The Licensee is authorized to distribute the Modified Software, in source code or object code form, provided that
said distribution complies with all the provisions of the Agreement and is accompanied by:
a copy of the Agreement,
a notice relating to the limitation of both the Licensor’s warranty and liability as set forth in Articles 8 and 9,
and that, in the event that only the object code of the Modified Software is redistributed, the Licensee allows future
Licensees unhindered access to the full source code of the Modified Software by indicating how to access it, it being
understood that the additional cost of acquiring the source code shall not exceed the cost of transferring the data.
5.3.3 DISTRIBUTION OF EXTERNAL MODULES
When the Licensee has developed an External Module, the terms and conditions of this Agreement do not apply
to said External Module, that may be distributed under a separate license agreement.
5.3.4 COMPATIBILITY WITH THE GNU GPL
The Licensee can include a code that is subject to the provisions of one of the versions of the GNU GPL in the
Modified or unmodified Software, and distribute that entire code under the terms of the same version of the GNU GPL.
The Licensee can include the Modified or unmodified Software in a code that is subject to the provisions of one of
the versions of the GNU GPL, and distribute that entire code under the terms of the same version of the GNU GPL.
Article 6 - INTELLECTUAL PROPERTY
6.1 OVER THE INITIAL SOFTWARE
The Holder owns the economic rights over the Initial Software. Any or all use of the Initial Software is subject to
compliance with the terms and conditions under which the Holder has elected to distribute its work and no one shall
be entitled to modify the terms and conditions for the distribution of said Initial Software.
The Holder undertakes that the Initial Software will remain ruled at least by this Agreement, for the duration set
forth in Article 4.2.
6.2 OVER THE CONTRIBUTIONS
The Licensee who develops a Contribution is the owner of the intellectual property rights over this Contribution as
defined by applicable law.
6.3 OVER THE EXTERNAL MODULES
The Licensee who develops an External Module is the owner of the intellectual property rights over this External
Module as defined by applicable law and is free to choose the type of agreement that shall govern its distribution.
APPENDIX B. LICENSE
36
6.4 JOINT PROVISIONS
The Licensee expressly undertakes:
not to remove, or modify, in any manner, the intellectual property notices attached to the Software;
to reproduce said notices, in an identical manner, in the copies of the Software modified or not.
The Licensee undertakes not to directly or indirectly infringe the intellectual property rights of the Holder and/or
Contributors on the Software and to take, where applicable, vis-a-vis its staff, any and all measures required to ensure
respect of said intellectual property rights of the Holder and/or Contributors.
Article 7 - RELATED SERVICES
7.1 Under no circumstances shall the Agreement oblige the Licensor to provide technical assistance or maintenance
services for the Software.
However, the Licensor is entitled to offer this type of services. The terms and conditions of such technical assistance, and/or such maintenance, shall be set forth in a separate instrument. Only the Licensor offering said maintenance
and/or technical assistance services shall incur liability therefor.
7.2 Similarly, any Licensor is entitled to offer to its licensees, under its sole responsibility, a warranty, that shall
only be binding upon itself, for the redistribution of the Software and/or the Modified Software, under terms and
conditions that it is free to decide. Said warranty, and the financial terms and conditions of its application, shall be
subject of a separate instrument executed between the Licensor and the Licensee.
Article 8 - LIABILITY
8.1 Subject to the provisions of Article 8.2, the Licensee shall be entitled to claim compensation for any direct loss
it may have suffered from the Software as a result of a fault on the part of the relevant Licensor, subject to providing
evidence thereof.
8.2 The Licensor’s liability is limited to the commitments made under this Agreement and shall not be incurred
as a result of in particular: (i) loss due the Licensee’s total or partial failure to fulfill its obligations, (ii) direct or
consequential loss that is suffered by the Licensee due to the use or performance of the Software, and (iii) more
generally, any consequential loss. In particular the Parties expressly agree that any or all pecuniary or business loss
(i.e. loss of data, loss of profits, operating loss, loss of customers or orders, opportunity cost, any disturbance to
business activities) or any or all legal proceedings instituted against the Licensee by a third party, shall constitute
consequential loss and shall not provide entitlement to any or all compensation from the Licensor.
Article 9 - WARRANTY
9.1 The Licensee acknowledges that the scientific and technical state-of-the-art when the Software was distributed
did not enable all possible uses to be tested and verified, nor for the presence of possible defects to be detected. In
this respect, the Licensee’s attention has been drawn to the risks associated with loading, using, modifying and/or
developing and reproducing the Software which are reserved for experienced users.
The Licensee shall be responsible for verifying, by any or all means, the suitability of the product for its requirements, its good working order, and for ensuring that it shall not cause damage to either persons or properties.
9.2 The Licensor hereby represents, in good faith, that it is entitled to grant all the rights over the Software
(including in particular the rights set forth in Article 5).
9.3 The Licensee acknowledges that the Software is supplied "as is" by the Licensor without any other express or
tacit warranty, other than that provided for in Article 9.2 and, in particular, without any warranty as to its commercial
value, its secured, safe, innovative or relevant nature.
Specifically, the Licensor does not warrant that the Software is free from any error, that it will operate without
interruption, that it will be compatible with the Licensee’s own equipment and software configuration, nor that it will
meet the Licensee’s requirements.
9.4 The Licensor does not either expressly or tacitly warrant that the Software does not infringe any third party
intellectual property right relating to a patent, software or any other property right. Therefore, the Licensor disclaims
any and all liability towards the Licensee arising out of any or all proceedings for infringement that may be instituted in
respect of the use, modification and redistribution of the Software. Nevertheless, should such proceedings be instituted
against the Licensee, the Licensor shall provide it with technical and legal assistance for its defense. Such technical
and legal assistance shall be decided on a case-by-case basis between the relevant Licensor and the Licensee pursuant
to a memorandum of understanding. The Licensor disclaims any and all liability as regards the Licensee’s use of the
name of the Software. No warranty is given as regards the existence of prior rights over the name of the Software or
as regards the existence of a trademark.
Article 10 - TERMINATION
APPENDIX B. LICENSE
37
10.1 In the event of a breach by the Licensee of its obligations hereunder, the Licensor may automatically terminate
this Agreement thirty (30) days after notice has been sent to the Licensee and has remained ineffective.
10.2 A Licensee whose Agreement is terminated shall no longer be authorized to use, modify or distribute the
Software. However, any licenses that it may have granted prior to termination of the Agreement shall remain valid
subject to their having been granted in compliance with the terms and conditions hereof.
Article 11 - MISCELLANEOUS
11.1 EXCUSABLE EVENTS
Neither Party shall be liable for any or all delay, or failure to perform the Agreement, that may be attributable
to an event of force majeure, an act of God or an outside cause, such as defective functioning or interruptions of the
electricity or telecommunications networks, network paralysis following a virus attack, intervention by government
authorities, natural disasters, water damage, earthquakes, fire, explosions, strikes and labor unrest, war, etc.
11.2 Any failure by either Party, on one or more occasions, to invoke one or more of the provisions hereof, shall
under no circumstances be interpreted as being a waiver by the interested Party of its right to invoke said provision(s)
subsequently.
11.3 The Agreement cancels and replaces any or all previous agreements, whether written or oral, between the
Parties and having the same purpose, and constitutes the entirety of the agreement between said Parties concerning
said purpose. No supplement or modification to the terms and conditions hereof shall be effective as between the
Parties unless it is made in writing and signed by their duly authorized representatives.
11.4 In the event that one or more of the provisions hereof were to conflict with a current or future applicable act or
legislative text, said act or legislative text shall prevail, and the Parties shall make the necessary amendments so as to
comply with said act or legislative text. All other provisions shall remain effective. Similarly, invalidity of a provision
of the Agreement, for any reason whatsoever, shall not cause the Agreement as a whole to be invalid.
11.5 LANGUAGE
The Agreement is drafted in both French and English and both versions are deemed authentic.
Article 12 - NEW VERSIONS OF THE AGREEMENT
12.1 Any person is authorized to duplicate and distribute copies of this Agreement.
12.2 So as to ensure coherence, the wording of this Agreement is protected and may only be modified by the
authors of the License, who reserve the right to periodically publish updates or new versions of the Agreement, each
with a separate number. These subsequent versions may address new issues encountered by Free Software.
12.3 Any Software distributed under a given version of the Agreement may only be subsequently distributed under
the same version of the Agreement or a subsequent version, subject to the provisions of Article 5.3.4.
Article 13 - GOVERNING LAW AND JURISDICTION
13.1 The Agreement is governed by French law. The Parties agree to endeavor to seek an amicable solution to any
disagreements or disputes that may arise during the performance of the Agreement.
13.2 Failing an amicable solution within two (2) months as from their occurrence, and unless emergency proceedings are necessary, the disagreements or disputes shall be referred to the Paris Courts having jurisdiction, by the more
diligent Party.
Version 2.0 dated 2006-09-05.
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