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Imaging the structure of major fault zones is essential for our understanding of crustal deformations and their implications on seismic hazards. Investigating such complex regions presents several issues, including the variation of seismic velocity due to the diversity of geological units and the cumulative damage caused by earthquakes. Conventional migration techniques are in general strongly sensitive to the available velocity model. Here we apply a passive matrix imaging approach which is robust to the mismatch between this model and the real seismic velocity distribution. This method relies on the cross‐correlation of ambient noise recorded by a geophone array. The resulting set of impulse responses form a reflection matrix that contains all the information about the subsurface. In particular, the reflected body waves can be leveraged to: (a) determine the transmission matrix between the Earth's surface and any point in the subsurface; (b) build a confocal image of the subsurface reflectivity with a transverse resolution only limited by diffraction. As a study case, we consider seismic noise (0.1–0.5 Hz) recorded by the Dense Array for Northern Anatolia that consists of 73 stations deployed for 18 months in the region of the 1999 Izmit earthquake. Passive matrix imaging reveals the scattering structure of the crust and upper mantle around the North Anatolian Fault zone over a depth range of 60 km. The results show that most of the scattering is associated with the Northern branch that passes throughout the crust and penetrates into the upper mantle. Plain Language Summary: Investigating the structure of major fault zones is important to understand the deformations of the Earth's crust and their potential impact on future earthquakes. However, the large variations of seismic velocity between different geological units drastically hampers the ability to image those areas. The North Anatolian Fault is no exception since it splits into two branches separating three major geological blocks in the region of the 1999 Izmit earthquake. To image the deep structure of this fault, seismic noise is here exploited to retrieve information on the body waves reflected by the underground heterogeneities. A three‐dimensional map of the subsurface reflectivity is then built by applying methods originally developed in optical microscopy and ultrasound for deep imaging inside complex media. The inner structure of the Earth around the North Anatolian Fault is revealed. In particular, the Northern branch is shown to exhibit a strong damage pattern and a deep penetration inside the upper mantle. Key Points: A matrix approach of passive seismology provides 3D imaging of the North Anatolian Fault, Turkey, over a depth range of 60 kmTransmission matrix between the Earth surface and the underground is extracted by means of spatio‐temporal correlations of seismic noiseTime reversal of this transmission matrix enables a sharp compensation of the seismic velocity variations in the fault area [ABSTRACT FROM AUTHOR]

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 3-D image of the subsoil, despite a rough knowledge of the background wave velocity. 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 contains all the information available on the medium. A set of matrix operations can then be applied in order to extract the relevant information as a function of the problem considered. On the one hand, the background seismic wave velocity can be estimated and its fluctuations quantified by projecting the reflection matrix in a focused basis. It consists in investigating the response between virtual sources and detectors synthesized at any point in the medium. The minimization of their cross-talk can then be used as a guide star for approaching the actual wave velocity distribution. On the other hand, the detrimental effect of wave velocity fluctuations on imaging is overcome by introducing a novel mathematical object: 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 passive seismic data recorded along the Clark branch of the San Jacinto fault zone (SJFZ), the present method is shown to provide an image of the fault until a depth of 4 km over the frequency range 10–20Hz with an horizontal 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 and of a transverse waveguide which increase 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 SJFZ, 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. [ABSTRACT FROM AUTHOR]