# Annotation of /trunk/doc/user/slip.tex

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Mon Sep 7 03:39:45 2009 UTC (11 years, 4 months ago) by jfenwick
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Fixed latex compile error.
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 1 gross 2647 \section{Slip on a Fault} 2 \label{Slip CHAP} 3 4 In this next example we want to calculate the displacement field $u\hackscore{i}$ for any time $t>0$ by solving the wave equation: 5 \index{wave equation} 6 jfenwick 2651 \begin{eqnarray}\label{WAVE general problem fault} 7 gross 2647 \rho u\hackscore{i,tt} - \sigma\hackscore{ij,j}=0 8 \end{eqnarray} 9 in a three dimensional block of length $L$ in $x\hackscore{0}$ 10 and $x\hackscore{1}$ direction and height $H$ 11 in $x\hackscore{2}$ direction. $\rho$ is the known density which may be a function of its location. 12 $\sigma\hackscore{ij}$ is the stress field \index{stress} which in case of an isotropic, linear elastic material is given by 13 jfenwick 2651 \begin{eqnarray} \label{WAVE stress fault} 14 gross 2647 \sigma\hackscore{ij} & = & \lambda u\hackscore{k,k} \delta\hackscore{ij} + \mu ( u\hackscore{i,j} + u\hackscore{j,i}) 15 \end{eqnarray} 16 where $\lambda$ and $\mu$ are the Lame coefficients 17 \index{Lame coefficients} and $\delta\hackscore{ij}$ denotes the Kronecker symbol\index{Kronecker symbol}. 18 On the boundary the normal stress is given by 19 jfenwick 2651 \begin{eqnarray} \label{WAVE natural fault} 20 gross 2647 \sigma\hackscore{ij}n\hackscore{j}=0 21 \end{eqnarray} 22 for all time $t>0$.