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We present a method to transmit digital information through a highly scattering medium in a MIMO-MU (multiple input multiple output multiple users) context. It is based on iterations of a time-reversal process, and permits us to focus short pulses, both spatially and temporally, from a base antenna to different users. This iterative technique is shown to be more efficient (lower inter-symbol interference and lower error rate) than classical time-reversal communication, while being computationally light and stable. Experiments are presented: digital information is conveyed from 15 transmitters to 15 receivers by ultrasonic waves propagating through a highly scattering slab. From a theoretical point of view, the iterative technique achieves the inverse filter of propagation in the subspace of non-null singular values of the time-reversal operator. We also investigate the influence of external additive noise, and show that the number of iterations can be optimized to give the lowest error rate.(Some figures in this article are in colour only in the electronic version)

We present a topical review which summarizes the main contributions to 'multiple scattering of acoustic and elastic waves' including the most recent advances. The review is divided into five main parts. In the first part, the effects of multiple scattering on ultrasonic propagation are illustrated on the basis of three experimental examples. In the second and third parts, we present the two possible descriptions for the propagation of an acoustic wave in a random medium. The first one is based on the study of the coherent wave, i.e. the wave amplitude averaged over disorder, whereas the second one deals with the propagation of the incoherent intensity, i.e. the intensity averaged over disorder. We especially insist on the microscopic basis for the phenomenological radiative transfer equation and show how it can be solved in the diffusion approximation. The theory is illustrated with experimental results obtained on a two-dimensional multiple-scattering prototype made of thousands of steel rods randomly distributed and immersed in water. In the fourth part, we present experimental evidence that the diffusion equation fails in describing all the aspects of the propagation of an acoustic wave in a random medium: e.g. the coherent backscattering effect recently observed for ultrasonic waves. We show that this effect arises as a consequence of reciprocity. Finally, in the fifth part, we discuss another property which is not taken into account in the radiative transfer theory: the reversibility of an acoustic wave propagating in a disordered medium.

Multiple scattering of seismic waves is often seen as a nightmare for conventional migration techniques that generally rely on a ballistic or a single‐scattering assumption. In heterogeneous areas such as volcanoes, the multiple‐scattering contribution limits the imaging‐depth to one scattering mean free path, the mean distance between two successive scattering events for body waves. In this Letter, we propose a matrix approach of passive seismic imaging that pushes back this fundamental limit by making an efficient use of scattered body waves drowned into a noisy seismic coda. As a proof of concept, the case of the Erebus volcano in Antarctica is considered. The Green's functions between a set of geophones placed on top of the volcano are first retrieved by the cross correlation of coda waves induced by multiple icequakes. This set of impulse responses forms a reflection matrix. By combining a matrix discrimination of singly scattered waves with iterative time reversal, we are able to push back the multiple scattering limit beyond 10 scattering mean free paths. The matrix approach reveals the internal structure of the Erebus volcano: A chimney‐shaped structure at shallow depths, a magma reservoir at 2,500 m and several cavities at sea level and below it. The matrix approach paves the way toward a greatly improved monitoring of volcanic structures at depth. Beyond this specific case, the matrix approach of seismic imaging can generally be applied to all scales and areas where multiple scattering events undergone by body waves prevent in‐depth imaging of the Earth's crust. Matrix approach of passive seismic bulk wave imaging is proposed to overcome the fundamental multiple‐scattering limitCross correlations of coda waves induced by multiple icequakes on Erebus form a reflection matrix of impulse responses between geophonesMatrix discrimination of singly scattered bulk waves combined with iterative time reversal reveal the internal structure of Erebus