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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: (i) determine the transmission matrix between the Earth's surface and any point in the subsurface; (ii) 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 (DANA) 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 NAFZ 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., Comment: 44 pages, 9 figures

Fault zones are associated with multi-scale heterogeneities of rock properties. Large scale variations may be imaged with conventional seismic reflection methods that detect offsets in geological units, and tomographic techniques that provide average seismic velocities in resolved volumes. However, characterizing elementary localized inhomogeneities of fault zones, such as cracks and fractures, constitutes a challenge for conventional techniques. Resolving these small-scale heterogeneities can provide detailed information for structural and mechanical models of fault zones. Recently, the reflection matrix approach utilizing body wave reflections in ambient noise cross-correlations was extended with the introduction of aberration corrections to handle the actual lateral velocity variations in the fault zone [Touma et al., Geophys. J. Int. 226, 780-794, 2021]. Here this method is applied further to analyze the distribution of scatterers in the first few kilometers of the crust in the San Jacinto Fault Zone at the Sage Brush Flat (SGB) site, southeast of Anza, California. The matrix approach allows us to image not only specular reflectors but also to resolve the presence, location and intensity of scatterers of seismic waves starting with a simple homogeneous background velocity model of the medium. The derived three-dimensional image of the fault zone resolves lateral variations of scattering properties in the region within and around the surface fault traces, as well as differences between the Northwest (NW) and the Southeast (SE) parts of the study area. A localized intense damage zone at depth is observed in the SE section, suggesting that a geometrical complexity of the fault zone at depth induces ongoing generation of rock damage., Comment: 15 pages, 8 figures

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, 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. More precisely, 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 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 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 and of a transverse wave guide which increase drastically the array aperture., Comment: 24 pages, 12 figures