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\section{Material and methods}
In the experimental setup, pictured in Figure \ref{Figure1}-(B), the electrical current was induced by a TMS device using a 2x75 mm diameter
butterfly coil (MagPro R100 device with C-B60 Butterfly coil, MagVenture, Farum, Danemark). The coil was placed 1 cm away from the medium, without any contact, and fixed to an independent support. The electrical current in the coil was in "monophasic" mode, i.e., a half cycle of 0.4 ms, as illustrated in Figure \ref{InducedElectricalCurrent}-(A). Alternatively, "biphasic" mode, i.e., a full sinus cycle of 0.4 ms could be used, as illustrated in Figure \ref{InducedElectricalCurrent}-(B). According to the manufacturer's specifications, at 100\% amplitude, current reached a magnitude of 149.10$^6$ A.s$^{-1}$ in the coil, leading to a peak transient magnetic field of 2 T at the surface of the coil and of 0.74 T at 20 mm in depth.
The magnetic field was induced by a 5x5x5 cm$^3$ N48 NdFeB magnet (model BY0Y0Y0, K\&J Magnetics, Pipersville, PA, USA). The magnet was placed 1 cm away from the medium, without any contact, and fixed to a second independent support. The magnetic field intensity ranged from 100 to 200 mT at the medium location, as measured by a gaussmeter (Model GM2, AlphaLab, Salt Lake City, UT, USA).
Main tested sample was a 4x8x8 cm$^3$ water-based tissue-mimicking phantom made with 5\% polyvinyl alcohol (PVA), 0.1 \% graphite powder and 5\% salt, giving an electrical conductivity of 5 S.m$^{-1}$. Three freezing/thawing cycles were applied to stiffen the material \cite{fromageau2007estimation}. The graphite powder (\#282863 product, Sigma-Aldrich, Saint-Louis, MO, USA) was made of submillimeter particles, which presented a speckle pattern on ultrasound images. The sample was placed in a rigid plastic box of 2 mm thick layers with an opening on a side to introduce the ultrasound probe. The rigid box simulated a solid interface such as a
skull. It was also used to skull and ensure
also that any observed movement was not due to surrounding displacement of air. Alternatively, we used a similar phantom made of 5\%
polyvinyl alcohol (PVA), PVA, 0.1 \% graphite powder and 0.9\% salt, giving an electrical conductivity of 1.8 S.m$^{-1}$. A biological tissue sample was also tested. This tissue was
an approximately 3x5x5 cm$^3$ a chicken breast
sample, placed sample bought in
the plastic box previously described, immersed local grocery of approximately 3x5x5 cm$^3$. It was degassed in
a 20$^o$C saline water (0.9 \% NaCl)
at 20$^o$C and degassed during two
hours. hours prior to the experiment.
Each sample was observed with a 5 MHz ultrasonic probe made of 128 elements (ATL L7-4, Philips, Amsterdam, Netherlands) coupled to a Verasonics scanner (Verasonics V-1, Redmond, WA, USA). The probe was in contact with the sample with an ultrasound coupling gel but was fixed on a third independent support. It was used in ultrafast mode \cite{bercoff2004supersonic}, to acquire 1000 frames per second using plane waves and Stolt's fk migration algorithm \cite{garcia2013stolt}. The Z component of the displacement in the sample was observed by performing cross-correlations between radiofrequency images with a speckle-tracking technique \cite{montagnon2012real}. Noise was partly reduced
thanks to using a low-pass frequency filter. Time $t$ = 0 ms was defined as the electrical burst emission.
Great care was taken to ensure that the three supports were not in contact and fixed separately. It could ensure that any vibration of one of the element could not be transmitted to the medium.
