deletions | additions       diff --git a/Simu disp maps.tex b/Simu disp maps.tex  index 26c889b..fdddfa1 100644  --- a/Simu disp maps.tex  +++ b/Simu disp maps.tex 
...
To calculate the propagation of the displacement as a function of space and time, we modeled the ablative regime as a point force directed along the Z axis with a depth of 40 $\mu$m and a constant value from -2.5 to 2.5 mm. The magnitude of the force was stored in a matrix, $H_z^{abla}(y,z,t)$. Displacements along the Z axis are again equal to the convolution between $H_z^{abla}$ and $G_{zz}$ \cite{aki1980quantitative}:  \begin{equation}  G_{zz}(r,\theta,t) G_{zz}  = \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\limits_{r/c_p}^{r/c_s}{\tau \delta(t-\tau)d\tau} \end{equation}  with the same notations as presented in equation \ref{eq:Gyz}.