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Pol Grasland-Mongrain edited Simu disp maps.tex
over 8 years ago
Commit id: f17c9ebc607a42fe48782f9a560e98f704b9c8fd
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diff --git a/Simu disp maps.tex b/Simu disp maps.tex
index dd2ce48..1a82ad9 100644
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To calculate the propagation of the displacement along space and time, we modeled the ablation regime as a point force directed along Z direction with a depth of 50 $\mu$m and increasing linearly from -2.5 to 0 mm and decreasing symmetrically from 0 to 2.5 mm. Propagation as a shear wave was calculated using Green operators $G_{zz}$ \cite{aki1980quantitative}:
\begin{equation}
G_{zz}(r,\theta,z,t) = \frac{\cos^2 \theta}{4\pi \rho c_p^2 r} f(t-\frac{r}{c_p}) + \frac{\sin^2 \theta}{4\pi \rho c_s^2 r} f(t-\frac{r}{c_s}) + \frac{3\cos^2 \theta-1}{4\pi \rho r^3} \int_{r/c_p}^{r/c_s}{\tau
f_{NF}} f_{NF}(t)dt}
\label{eq:Gzz}
\end{equation}
with same notations as in equation \ref{eq:Gyz}.