Matrix Approach of Seismic Imaging: Application to the Erebus Volcano, Antarctica

Volcanoes are among the most challenging media for seismic imaging given their highly localized and abrupt variations in physical parameters, extreme landforms, fractures, and the presence of magma and other fluids. Because of this high level of heterogeneity and the resulting difficulty to access the wave velocity distribution in the medium, reflection seismic imaging of volcanoes usually suffers from a loss of resolution and contrast. Here, we present a passive seismic imaging technique applied to the case of La Soufri&#232;re of Guadeloupe volcano. Inspired by previous works in optics (Badon et al., 2020), in acoustics (Lambert&#160;et al., 2020), and recently introduced in seismology (Touma et al., 2020), this technique relies on a matrix approach of passive reflection imaging, which requires only a rough approximation about the medium background velocity. This makes it robust even applied to extreme environments as volcanoes or fault zones. In this approach, the Green&#8217;s functions between an array of 76 geophones placed at the surface of the volcano are retrieved by cross-correlation of ambient seismic noise. This set of 2850 inter-element impulse responses forms a reflection matrix. Focusing operations are applied to this reflection matrix at emission and reception to project it in&#8211;depth. The focusing process allows to extract body wave components from seismic noise and thus, to retrieve information about reflectivity of in-depth structures. However, at this point, reflectivity images of the subsurface still suffer from phase distortions induced by long-range variations of the seismic velocity. This results in blurred images and hinders appropriate imaging. To overcome these issues, a novel operator is introduced: the distortion matrix. This operator is derived from the focused reflection matrix and connects any point in the medium with the distortion that a wavefront emitted from that point would experience due to heterogeneity. A time-reversal analysis of the distortion matrix allows to retrieve aberrations phase laws and hence to compensate for phase distortions. This correction enables to recover 3D-images of the volcano&#8217;s subsurface for the first 10km below the summit with optimized contrast and with an increased resolution. Interestingly, the restored resolution is even at least one half below the diffraction limit imposed by the geophone array angular aperture at the surface. The obtained gain in resolution and contrast allows to unveil internal structures of La Soufri&#232;re as hypothetical volcanic vents, magma reservoirs and lateral drainage conduits.References[Badon et al., 2020] Badon, A., Barolle, V., Irsch, K., Boccara, A. C., Fink, M., and Aubry, A. (2020). Distortion matrix concept for deep optical imaging in scattering media. Science Advances, 6(30).[Lambert et al., 2020] Lambert, W., Cobus, L. A., Frappart, T., Fink, M., and Aubry, A. (2020). Distortion matrix approach for ultrasound imaging of random scattering media. Proceedings of the National Academy of Sciences, 117(26):14645-14656.[Touma et al., 2020] Touma, R., Blondel, T., Derode, A., Campillo, M., & Aubry, A. (2020). A Distortion Matrix Framework for High-Resolution Passive Seismic 3D Imaging: Application to the San Jacinto Fault Zone, California. arXiv preprint arXiv:2008.01608.

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