Passive seismic matrix imaging of La Soufrière of Guadeloupe volcano

<p>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 Soufrière of Guadeloupe volcano. Inspired by previous works in optics (Badon <em>et al</em>., 2020), in acoustics (Lambert <em>et al</em>., 2020), and recently introduced in seismology (Touma <em>et al</em>., 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’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–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’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 Soufrière as hypothetical volcanic vents, magma reservoirs and lateral drainage conduits.</p><p><strong>References</strong></p><p>[Badon <em>et al</em>., 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. <em>Science Advances,</em> 6(30).</p><p>[Lambert <em>et al.</em>, 2020] Lambert, W., Cobus, L. A., Frappart, T., Fink, M., and Aubry, A. (2020). Distortion matrix approach for ultrasound imaging of random scattering media. <em>Proceedings of the National Academy of Sciences,</em> 117(26):14645-14656.</p><p>[Touma<em> et al.</em>, 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.<em> arXiv preprint arXiv</em>:2008.01608.</p>

Distortion matrix concept for deep optical imaging in scattering media

In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sample-induced aberrations and multiple scattering can strongly degrade the image resolution and contrast. On the basis of a dynamic correction of the incident and/or reflected wavefronts, adaptive optics has been used to compensate for those aberrations. However, it only applies to spatially invariant aberrations or to thin aberrating layers. Here, we propose a global and noninvasive approach based on the distortion matrix concept. This matrix basically connects any focusing point of the image with the distorted part of its wavefront in reflection. A singular value decomposition of the distortion matrix allows to correct for high-order aberrations and forward multiple scattering over multiple isoplanatic modes. Proof-of-concept experiments are performed through biological tissues including a turbid cornea. We demonstrate a Strehl ratio enhancement up to 2500 and recover a diffraction-limited resolution until a depth of 10 scattering mean free paths.

Distortion matrix approach for ultrasound imaging of random scattering media

Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wave fronts and degrade image quality. Adaptive focusing can compensate for such aberration but is only effective over a restricted field of view. Here, we introduce a full-field approach to wave imaging based on the concept of the distortion matrix. This operator essentially connects any focal point inside the medium with the distortion that a wave front, 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 sensor and image voxel. Phase aberrations can then be unscrambled for any point, providing a full-field image of the medium with diffraction-limited resolution. Importantly, this process is particularly efficient in random scattering media, where traditional approaches such as adaptive focusing fail. Here, we first present an experimental proof of concept on a tissue-mimicking phantom and then, apply the method to in vivo imaging of human soft tissues. While introduced here in the context of acoustics, this approach can also be extended to optical microscopy, radar, or seismic imaging.

Passive Reflection Seismic Imaging of the North Anatolian Fault at crustal-scale: A Matrix Framework for Aberrations Correction

<p>To understand fault systems, it is required to identify the structure of the crust and upper mantle. Seismic investigations have long been relying on active sources generating an incident wave-field from the Earth surface. The reflected wave-field is then recorded by sensors deployed at the surface. Nowadays, passive imaging has been adopted as an alternative of this source-receiver configuration by computing the correlations of ambient noise. This process allows to estimate the Green’s function between two receivers. We here present a passive imaging technique applied to data recorded with the Dense Array of North Anatolia [1], which was deployed in western Turkey during 16 months. The array consists of 73 stations covering the two major fault branches of the North Anatolian Fault (NAF). Inspired by previous works in optics and acoustics, we introduce a matrix approach of seismic imaging based on seismic noise cross correlations. Our method applies focusing operations at emission and reception (Blondel et al.,2019) allowing to project the reflection matrix recorded at the surface to depth (redatuming). Although seismic noise is dominated by surface waves, focusing operations allow to extract the body wave components that carry information about the reflectivity of in-depth structures. However, complex velocity distribution of the Earth’s crust results in phase distortions, referred to as aberrations in the imaging process. Phase distortions prevent the imaging of the true reflectivity of the subsurface leading to unphysical features and blurry images. To overcome these issues, we introduce a new operator: the so-called distortion matrix. It connects any virtual source induced by focusing at emission with the distorted part of the reflected wave-front in the spatial Fourier domain. A time-reversal analysis of the distortion matrix allows to correct for high-order aberrations. Crustal-scale 3D images of the fault structure of the North Anatolian Fault are revealed with optimal resolution and contrast.</p><p>(1) DANA. Dense array for north anatolia. International Federation of Digital Seismograph Networks doi:10.7914/SN/YH2012, 2012.</p>

Thermomass Theory in the Framework of GENERIC

Thermomass theory was developed to deal with the non-Fourier heat conduction phenomena involving the influence of heat inertia. However, its structure, derived from an analogy to fluid mechanics, requires further mathematical verification. In this paper, General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, which is a geometrical and mathematical structure in nonequilibrium thermodynamics, was employed to verify the thermomass theory. At first, the thermomass theory was introduced briefly; then, the GENERIC framework was applied in the thermomass gas system with state variables, thermomass gas density ρh and thermomass momentum mh, and the time evolution equations obtained from GENERIC framework were compared with those in thermomass theory. It was demonstrated that the equations generated by GENERIC theory were the same as the continuity and momentum equations in thermomass theory with proper potentials and eta-function. Thermomass theory gives a physical interpretation to the GENERIC theory in non-Fourier heat conduction phenomena. By combining these two theories, it was found that the Hamiltonian energy in reversible process and the dissipation potential in irreversible process could be unified into one formulation, i.e., the thermomass energy. Furthermore, via the framework of GENERIC, thermomass theory could be extended to involve more state variables, such as internal source term and distortion matrix term. Numerical simulations investigated the influences of the convective term and distortion matrix term in the equations. It was found that the convective term changed the shape of thermal energy distribution and enhanced the spreading behaviors of thermal energy. The distortion matrix implies the elasticity and viscosity of the thermomass gas.

The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants

The crystallography of displacive/martensitic phase transformations can be described with three types of matrix: the lattice distortion matrix, the orientation relationship matrix and the correspondence matrix. Given here are some formulae to express them in crystallographic, orthonormal and reciprocal bases, and an explanation is offered of how to deduce the matrices of inverse transformation. In the case of the hard-sphere assumption, a continuous form of distortion matrix can be determined, and its derivative is identified to the velocity gradient used in continuum mechanics. The distortion, orientation and correspondence variants are determined by coset decomposition with intersection groups that depend on the point groups of the phases and on the type of transformation matrix. The stretch variants required in the phenomenological theory of martensitic transformation should be distinguished from the correspondence variants. The orientation and correspondence variants are also different; they are defined from the geometric symmetries and algebraic symmetries, respectively. The concept of orientation (ir)reversibility during thermal cycling is briefly and partially treated by generalizing the orientation variants with n-cosets and graphs. Some simple examples are given to show that there is no general relation between the numbers of distortion, orientation and correspondence variants, and to illustrate the concept of orientation variants formed by thermal cycling.