Josselin Garnier receives the Grand Prix Scientifique of the Simone and Cino Del Duca Foundation

What do an earthquake, a sonar at sea and a laser shot into the atmosphere have in common? All three emit waves which, as they travel through these complex media, interact with microscopic constituents (molecules, rock grains, etc.) and are re-emitted in random directions. Understanding this scattering phenomenon and exploiting it for imaging purposes is at the heart of the work of Josselin Garnier, a researcher at the Centre for Applied Mathematics (CMAP*) and professor at the École Polytechnique, who has just been awarded the Grand Prix Scientifique 2021 by the Simone and Cino Del Duca Foundation.

Extract information

“In the classical approach to imaging, these multiple scatters are considered as noise that blurs the signal,” explains Josselin Garnier. But this noise actually contains a lot of useful information, provided that we know how to extract it. "This researcher, a probabilist trained at the Ecole Normale Supérieure and the École Polytechnique, is tackling this physics-related problem with mathematics. "I was first confronted with this type of question as a contingent scientist in a laser physics department at the CEA. I asked myself: as a mathematician, what can I do? "

He therefore combines methods of partial differential equation analysis and stochastic analysis to build toolkits adapted to the questions he encounters. "A wave, whether acoustic, electromagnetic or elastic, is still a wave that can be described by a mathematical object obeying a wave equation, a partial differential equation. "Stochastic analysis is then used to describe the complex medium in which the wave propagates. The earth's crust or concrete are examples of such media that cannot be described in great detail because of the large number of small-scale components over which the wave scatters. "We consider these media as a random mixture of different components with different statistics, for example rocks of different sizes distributed according to well-understood random processes," continues the mathematician. The aim is then to try to reconstruct an image of the medium that allows macroscopic structures such as a crack in a concrete block to be identified. If we analyse the waves recorded separately by the detectors, we only see noise caused by multiple scattering. "But my work, conducted with George Papanicolaou at Stanford University, Knut Sølna at the University of California, Irvine, and Liliana Borcea at the University of Michigan, among others, has shown that the useful information is actually in the cross-correlations between the signals received at different locations." By doing so, cracks in the concrete or geological structures in the ground can be seen emerging from noise.

Opportunistic sources and applications in imaging

This work has also led Josselin Garnier to participate in the development of a new type of imaging, known as "opportunistic" source imaging. To make an image, you need a sufficiently powerful wave source to illuminate the desired area. But to probe deep into the Earth's interior, for instance, only powerful earthquakes can serve as sources. Fortunately, these are fairly rare and unevenly distributed. However, seismometers constantly record background noise generated by human or natural activities. "For example, the slight seismic noise generated by waves on the ocean is perceptible everywhere, even in Tibet! And we can use it to reconstruct images of the Earth's interior. "

These mathematical methods for imaging therefore have multiple applications for the Earth sciences, underground prospecting or the monitoring of certain non-explosive volcanoes such as the Piton de la Fournaise on Reunion Island, but also for the non-destructive testing of buildings such as bridges or tunnels. Josselin Garnier is also the founder of the start-up company Sivienn, which specialises in this field and in passive underwater imaging.

The study of these diffusion phenomena is not the only focus of his research. The management of uncertainties in numerical codes is another. "Numerical codes are used everywhere in industry today, for the development of systems, to guarantee their performance, or even to carry out crash tests. How can we quantify the quality of the predictions made by the models and digital simulations? "In addition to the work carried out with industrial groups such as EDF and Airbus, the researcher has been studying Covid-19's epidemiological models for the past year, to try to understand and reduce their uncertainties. Nevertheless, he intends to continue studying the propagation of waves in complex environments. "There are still many theoretical questions to be clarified, particularly on the coupling of the different types of elastic waves, volume or surface waves, that can propagate in the earth's crust, for example. This scientific prize will also enable him to finance future research on the subject.

About the Grand Prix scientifique of the Simone and Cino Del Duca Foundation

Created in 1975, the Simone and Cino Del Duca Foundation has been housed at the Institut de France since 2005. It works in France and abroad in the field of arts, letters and sciences through grants and prizes awarded each year on the proposal of the academies. The Foundation awards four Grand Prix each year. The Grand Prix scientifique is awarded to a French or European researcher and his/her team, presenting an ambitious research project on a promising theme specified each year.

*CMAP: a joint research unit CNRS, École Polytechnique - Institut Polytechnique de Paris