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Additionally to the experiments, a three dimensional simulation of the experiments was performed using Matlab (Matlab 2010, The MathWorks, Natick, MA, USA). The numerical study was performed by (1) calculating the electrical current induced by the coil, (2) simulating the magnetic field created by the permanent magnet, (3) computing the resulting Lorentz force inside the medium, and finally (4) computing the propagation along space and time of the displacement due to the Lorentz force.   Using Equation \ref{Equation1} with two 75 mm diameter coils crossed by a 149.10$^6$ A.s$^{-1}$ electrical current, representing the TMS coil used in the experiment, electrical field $E$ was calculated in a 20x10x20 cm$^3$ volume (see \cite{Grandori_1991} for details on mathematical solving). Using Ohm's law, the electrical current $\mathbf{j}$ was estimated assuming an electrical conductivity $\sigma$ = 5 S.m$^{-1}$. No border effect has been taken into account. Induced electrical current in a XY plane at a depth of 2 cm with 2x2 mm$^2$ pixels is illustrated in Figure \ref{Figure3}-(A), with colors indicating the absolute magnitude and arrows the direction. Electrical current reached a density of 3 4  kA.m$^{-2}$ at the medium location. A finite element software (Finite Element Magnetic Method \cite{FEMM}) was used to produce a two dimensional simulation of the magnetic field $\mathbf{B}$. The magnetic field was supposed to be approximately constant in the sample along the Y axis. Magnetostatic problem was solved from equations $\nabla \times H = \nabla \times M$, $\nabla B = 0$ and $B=\mu_p H$, with $H$ magnetic field intensity, $M$ magnetization of the medium, and $\mu_p$ medium permeability. Medium was considered as linear, and space was meshed with approximately 0.5 cm$^2$ triangles. The software simulated a N48 NdFeB permanent magnet of 5x5 cm$^2$ placed in a 30x30 cm$^2$ surface of air. Resulting magnetic field in a XZ plane is illustrated in Figure \ref{Figure3}-(B), with colors indicating the absolute magnitude and arrows the direction. The magnetic field ranged from 100 to 200 mT at the medium location.  Body Lorentz force $\mathbf{f}$ was computed from the cross-product of $\mathbf{j}$ and $\mathbf{B}$. The resulting Lorentz force in a XZ plane with 2x2 mm$^2$ pixels is illustrated in Figure \ref{Figure3}-C, with arrows indicating the Lorentz force vector and color its amplitude along Z - as the electrical current is induced in the XY plane and the magnetic field essentially along X direction, Lorentz force is mainly along Z direction. Lorentz force reached a magnitude of 500 600  N.m$^{−3}$ in the medium location. Finally, displacement $\mathbf{u}(\mathbf{r},t)$ was determined analytically along space (pixels of 2x2 mm$^2$) and time (steps of 1 ms) by solving Equation \ref{Equation3} with the Green operator \cite{aki1980quantitative}. It used a medium density $\rho$ of 1000 kg.m$^{-3}$, a bulk modulus $K$ of 2.3 GPa and a shear modulus $\mu$ of 16 kPa, corresponding to a shear wave speed of 4 m.s$^{-1}$.