[cig-commits] r22784 - in seismo/2D/SPECFEM2D/trunk: doc/USER_MANUAL src/specfem2D
dkomati1 at geodynamics.org
dkomati1 at geodynamics.org
Fri Sep 13 09:50:42 PDT 2013
Author: dkomati1
Date: 2013-09-13 09:50:41 -0700 (Fri, 13 Sep 2013)
New Revision: 22784
Modified:
seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf
seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.tex
seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90
Log:
fixed a comment and the manual regarding the plane strain convention and its impact on the formula to compute pressure; I will fix the code a bit later
Modified: seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf
===================================================================
--- seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf 2013-09-13 14:56:18 UTC (rev 22783)
+++ seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.pdf 2013-09-13 16:50:41 UTC (rev 22784)
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Modified: seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.tex
===================================================================
--- seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.tex 2013-09-13 14:56:18 UTC (rev 22783)
+++ seismo/2D/SPECFEM2D/trunk/doc/USER_MANUAL/manual_SPECFEM2D.tex 2013-09-13 16:50:41 UTC (rev 22784)
@@ -238,6 +238,10 @@
The next release of the code will include support for GPU graphics card acceleration \citep{KoMiEr09,KoErGoMi10,MiKo10,Kom11}.\\
+The code uses the plane strain convention when the standard P-SV equation case is used, i.e.,
+the off-plane strain $\epsilon_{zz}$ is zero by definition of the plane strain convention but thus the off-plane stress $\sigma_{zz}$ is not equal to zero,
+one has $\sigma_{zz} = \lambda (\epsilon_{xx} + \epsilon_{yy})$.
+
%------------------------------------------------------------------------------------------------%
\section{Citation}
%------------------------------------------------------------------------------------------------%
Modified: seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90
===================================================================
--- seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90 2013-09-13 14:56:18 UTC (rev 22783)
+++ seismo/2D/SPECFEM2D/trunk/src/specfem2D/compute_pressure.f90 2013-09-13 16:50:41 UTC (rev 22784)
@@ -217,15 +217,18 @@
! sigma_zz = lambda (epsilon_xx + epsilon_yy + epsilon_zz) + 2 mu epsilon_zz
! pressure = - trace(sigma) / 3 = - (lambda + 2/3 mu) trace(epsilon) = - kappa * trace(epsilon)
!
-! to compute pressure in 2D in an elastic solid, one uses pressure = - trace(sigma) / 2
+! to compute pressure in 2D in an elastic solid in the plane strain convention i.e. in the P-SV case,
+! one still uses pressure = - trace(sigma) / 3 but taking into account that the off-plane strain epsilon_zz is zero
+! by definition of the plane strain convention but thus the off-plane stress sigma_zz is not equal to zero,
+! one has instead: sigma_zz = lambda * (epsilon_xx + epsilon_yy), thus
! sigma_ij = lambda delta_ij trace(epsilon) + 2 mu epsilon_ij
! = lambda (epsilon_xx + epsilon_yy) + 2 mu epsilon_ij
! sigma_xx = lambda (epsilon_xx + epsilon_yy) + 2 mu epsilon_xx
! sigma_yy = lambda (epsilon_xx + epsilon_yy) + 2 mu epsilon_yy
-! pressure = - trace(sigma) / 2 = - (lambda + mu) trace(epsilon)
+! sigma_zz = lambda * (epsilon_xx + epsilon_yy)
+! pressure = - trace(sigma) / 3 = - (lambda + 2*mu/3) (epsilon_xx + epsilon_yy)
!
-
if(elastic(ispec)) then
! get relaxed elastic parameters of current spectral element
@@ -284,10 +287,10 @@
! non-causal rather than causal. We fixed the problem by using equations in Carcione's
! 2004 paper and his 2007 book.
-!J. M. Carcione, H B. Helle, The physics and simulation of wave propagation at the ocean
-! bottom, Geophysics, vol. 69(3), p. 825-839, 2004
-!J. M. Carcione, Wave fields in real media: wave propagation in anisotropic, anelastic
-! and porous media, Elsevier, p. 124-125, 2007
+! J. M. Carcione, H. B. Helle, The physics and simulation of wave propagation at the ocean
+! bottom, Geophysics, vol. 69(3), p. 825-839, 2004
+! J. M. Carcione, Wave fields in real media: wave propagation in anisotropic, anelastic
+! and porous media, Elsevier, p. 124-125, 2007
! compute unrelaxed elastic coefficients from formulas in Carcione 2007 page 125
lambdal_relaxed_viscoelastic = (lambdal_unrelaxed_elastic + mul_unrelaxed_elastic) / Mu_nu1(i,j,ispec) &
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