  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
2500 m and several cavities at sea level and below it. The matrix approach
paves the way towards 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.
