Many of today's fundamental questions about the Earth and facing modern society (hazard assessment, energy, nuclear monitoring) depend on accurate images of the Earth's interior. Due to technical limitations in drilling deeply and densely, we need to rely on indirect means of imaging. Seismology is by far the most prominent approach to do this, drawing equally from quantitative sciences, observations, and interpretation. We develop state-of-the-art numerical methodologies for seismic wave propagation and imaging, and apply this to scales ranging from Earth's crust to inner core, from the interior of other planets to the Sun. We are also interested in uncertainty quantification by probabilistic modeling, source processes such as complex earthquakes with their associated hazard, and natural ambient noise generated by ocean-continent interactions. Our multi-disciplinary and collaborative research connects geophysics, applied and numerical mathematics, high-performance computing, mechanics, control theory, signal processing, machine learning, statistics, psychology, and involves to a variety of links to industry and public outreach.