[cig-commits] [commit] devel: doc: Turn Carcione reference into a real quotation. (82b08d5)

[cig_noreply at geodynamics.org]

Repository : ssh://geoshell/specfem2d

On branch  : devel
Link       : https://github.com/geodynamics/specfem2d/compare/24dca31bf087ee51d2d1db912640d58ade2df07c...a3880316a04510a6c88ed36ceee2fab3c0169f6e

>---------------------------------------------------------------

commit 82b08d57d8881306d9baadac11438de221e47d96
Author: Elliott Sales de Andrade <esalesde at physics.utoronto.ca>
Date:   Fri Jan 24 01:52:59 2014 -0500

    doc: Turn Carcione reference into a real quotation.
    
    The only modification I made is where to wrap the last set of equations,
    as I think the same number on each line looks better.


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82b08d57d8881306d9baadac11438de221e47d96
 .../figures/Carcione_et_al_aniso_1988_image.pdf    | Bin 206646 -> 0 bytes
 doc/USER_MANUAL/manual_SPECFEM2D.pdf               | Bin 3313326 -> 3118752 bytes
 doc/USER_MANUAL/manual_SPECFEM2D.tex               |  34 ++++++++++++++++++---
 3 files changed, 29 insertions(+), 5 deletions(-)

diff --git a/doc/USER_MANUAL/figures/Carcione_et_al_aniso_1988_image.pdf b/doc/USER_MANUAL/figures/Carcione_et_al_aniso_1988_image.pdf
deleted file mode 100644
index 1f2b4d4..0000000
Binary files a/doc/USER_MANUAL/figures/Carcione_et_al_aniso_1988_image.pdf and /dev/null differ
diff --git a/doc/USER_MANUAL/manual_SPECFEM2D.pdf b/doc/USER_MANUAL/manual_SPECFEM2D.pdf
index c0c5a0a..4369ea5 100644
Binary files a/doc/USER_MANUAL/manual_SPECFEM2D.pdf and b/doc/USER_MANUAL/manual_SPECFEM2D.pdf differ
diff --git a/doc/USER_MANUAL/manual_SPECFEM2D.tex b/doc/USER_MANUAL/manual_SPECFEM2D.tex
index 6e98bad..4c488a3 100644
--- a/doc/USER_MANUAL/manual_SPECFEM2D.tex
+++ b/doc/USER_MANUAL/manual_SPECFEM2D.tex
@@ -869,13 +869,37 @@ It allows one to automatically save all the parameters and results of a given si
 %------------------------------------------------------------------------------------------------%
 
 \begin{flushleft}
-Following \cite{CaKoKo88}, we use the classical reduced Voigt notation \citep{Hel94,Car07}:
+Following \cite{CaKoKo88}, we use the classical reduced Voigt notation to represent symmetric
+tensors \citep{Hel94,Car07}:
 \end{flushleft}
 %%%
-\begin{center}
-\includegraphics[width=4.2in,trim=0 2.6cm 0 2.6cm]{figures/Carcione_et_al_aniso_1988_image.pdf}
-\end{center}
-%%%
+\begin{quotation}
+The constitutive relation of a heterogeneous anisotropic and elastic solid
+is expressed by the generalized Hooke's law, which can be written as
+%
+\begin{equation*}
+\sigma_{ij} = c_{ijkl} \varepsilon_{kl}, \qquad i, j, k = 1, \dots, 3,
+\end{equation*}
+%
+where $t$ is the time, $\mathbf{x}$ is the position vector, $\sigma_{ij}(\mathbf{x}, t)$ and $\varepsilon_{ij}(\mathbf{x}, t)$ are the
+Cartesian components of the stress and strain tensors respectively, and
+$c_{ijkl}(\mathbf{x})$ 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:
+%
+\begin{align*}
+(11) \rightarrow 1, &&
+(22) \rightarrow 2, &&
+(33) \rightarrow 3, \\
+(23) = (32) \rightarrow 4, &&
+(31) = (13) \rightarrow 5, &&
+(12) = (21) \rightarrow 6.
+\end{align*}
+\end{quotation}
 
 \noindent
 Thus in the most general 2D case we have the following convention for the stress-strain relationship: