Reflection seismic imaging usually suffers from a loss of resolution and contrast because of the fluctuations of the wave velocities in the Earth's crust. In the literature, phase distortion issues are generally circumvented by means of a background wave velocity model. However, it requires a prior tomography of the wave velocity distribution in the medium, which is often not possible, especially in depth. In this paper, a matrix approach of seismic imaging is developed to retrieve a three-dimensional image of the subsoil without any prior knowledge of the background wave speed. To do so, passive noise cross-correlations between geophones of a seismic array are investigated under a matrix formalism. They form a reflection matrix that can be leveraged to synthesize virtual sources and detectors at any point in the medium. From this focused reflection matrix, a novel mathematical object is introduced: the distortion matrix. This operator essentially connects any virtual source inside the medium with the distortion that a wavefront, emitted from that point, experiences due to heterogeneities. A time reversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each real geophone at the surface and each virtual geophone in depth. Phase distortions can then be compensated for any point of the underground. Applied to seismic data recorded along the Clark Branch of the San Jacinto Fault Zone, the present method is shown to provide an image of the fault until a depth of 4 km over the frequency range 10-20 Hz with a transverse resolution of 80 m. Strikingly, this resolution is almost one eighth below the diffraction limit imposed by the geophone array aperture. The heterogeneities of the subsoil play the role of a scattering lens which increases drastically the array aperture. The contrast is also optimized since most of the incoherent noise is eliminated by the iterative time reversal process. Beyond the specific case of the San Jacinto Fault Zone, the reported approach can be applied to any scales and areas for which a reflection matrix is available at a spatial sampling satisfying the Nyquist criterion.