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Elastic wave equation

In elastic wave equation, the modulus $ \kappa(\textbf{x})$ corresponds to two Lame parameters: $ \lambda+2\mu=\rho v_p^2$ and $ u=\rho v_s^2$ , in which $ v_p$ and $ v_s$ denote the P- and S-wave velocity. The elastic wave equation can be written as

\begin{equation*}\left\{ \begin{split}\frac{\partial v_x}{\partial t} &=\frac{1}...
...artial x}+\mu\frac{\partial v_z}{\partial z}\\ \end{split}\right.\end{equation*} (9)

where $ \tau_{ij}$ (sometimes $ \sigma_{ij}$ ) is stress, $ v_i$ is particle velocity, $ i,j=x,z$ . We display the 2 components of elastic wave propagation at $ kt=270$ , $ nt=300$ modeled with $ \Delta t=0.001$ in Figure 5, in which the grid size is 200x200, the spatial interval is $ \Delta x=\Delta z=5m$ , and the velocities are chosen to be $ Vp=2km/s$ , $ Vs=Vp/\sqrt {2}$ .

elasticxz
elasticxz
Figure 5.
Two components of elastic wave propagation at $ kt=270$ , $ nt=300$ modeled with $ \Delta t=0.001$ . Grid size=200x200, $ \Delta x=\Delta z=5m$ , $ Vp=2km/s$ , $ Vs=Vp/\sqrt {2}$
[pdf] [png] [scons]


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Next: Forward modeling Up: Basic wave equation Previous: Acoustic wave equation

2021-08-31