deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index 4629d74..723b87b 100644  --- a/Simu disp maps.tex  +++ b/Simu disp maps.tex 
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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 40 $\mu$m during 100 $\mu$s and of constant value from -2.5 to 2.5 mm. The magnitude of the force is stored in a matrix $H_z^{abla}(y,z,t)$. Propagation as a shear wave was calculated using Green operators $G_{zz}$ \cite{aki1980quantitative}:  \begin{equation}  G_{zz}(r,\theta,t) = \frac{\cos^2 \theta}{4\pi \rho c_p^2 r} \delta(t-\frac{r}{c_p}) + \frac{\sin^2 \theta}{4\pi \rho c_s^2 r} \delta(t-\frac{r}{c_s})\\+ \frac{3\cos^2 \theta-1}{4\pi \rho r^3} \int_{r/c_p}^{r/c_s}{\tau \int\limits_{r/c_p}^{r/c_s}{\tau  \delta(t-\tau)d\tau} \label{eq:Gzz}  \end{equation}  with same notations as in equation \ref{eq:Gyz}.