Bruno Giammarinaro

Les ondes de choc de cisaillement dans les solides quasi-incompressibles sont un type d'onde peu exploré car accessible à la mesure seulement depuis une douzaine d'années. Elles se distinguent des ondes de choc de compression par leur non-linéarité cubique au lieu de quadratique. Les faibles vitesses des ondes de cisaillement, de l'ordre du mètre par seconde, permettent notamment d'atteindre des régimes assez fortement non linéaires sur de faibles distances, et de contrebalancer l'absorption relativement importante dans ces milieux. A notre connaissance, ces ondes ont été étudiées presque exclusivement en ondes planes. Or, la focalisation est un phénomène fondamental dans la physique des ondes et ses applications. C'est cette focalisation que l'on s'est attaché à étudier spécifiquement ici, tant du point de vue théorique et numérique, qu'expérimental. L'objectif était de mettre en évidence la focalisation des ondes de choc de cisaillement. Ce travail est en particulier motivé par son application potentielle en biomécanique. On a ici fait l'hypothèse que les ondes de choc de cisaillement pourraient jouer un rôle dans la formation de certaines lésions cérébrales suite à un traumatisme crânien, la géométrie du crâne induisant leur focalisation. Ces considérations nous ont conduits à dimensionner les phénomènes étudiés en conséquence, en termes de fréquence, d'amplitude et de géométrie. La focalisation a ainsi été montrée dans le cas d'un gel simulant un tissu biologique. Les comparaisons avec le modèle théorique et numérique se sont avérées favorables. Pour approfondir l'analyse de l'hypothèse, il resterait à prouver que ces ondes de choc peuvent induire des lésions.

Viscoelastic rods under tension play an important role in medical imaging. The objective is to study longitudinal guided waves in soft viscoelastic rods, for which the wavespeed is directly related to the Young's modulus. The challenge of this work is to reconcile the quantitative estimation of Young's modulus using a conventional tensile test and wave measurements of Young wave velocity. Experiments are conducted using optical elastography. A high-speed camera is used on a rod fabricated with a quasi-incompressible silicone-based material. Wave speed and attenuation are estimated using a combination of transient and modal approaches. The viscoelastic parameters are then extracted using a Zener model, before being compared with tensile tests. The elastic behavior of the material was shown to be linear up to 20% deformation, but it obeys a three-element Zener rheological model, which is relatively complex in the range of frequencies used. The viscoelastic parameters were estimated. Young's modulus was calculated from these parameters and from the tensile tests. Despite the two main pitfalls, nonlinearity and rheology of the material, a good agreement between the static and dynamic measurements is found.

Dynamic elastography uses an imaging system to visualize the propagation of elastic waves, the speed of which is directly related to the elasticity felt by palpation. Very few studies have focused on X-ray elastography because of the technical challenges it poses: a planar image of an integration volume at a very slow sampling rate. We demonstrate that tracking a slow elastic wave guided along a one-dimensional structure could provide a possible solution. The recently discovered flexural pulse wave, which is naturally generated by heartbeats and propagates along arteries, is the perfect candidate for X-ray elastography. As it reflects the cardiovascular health of patients, arterial elasticity is a biomarker of high clinical interest. We first validate the method by measuring the elasticity in artery phantoms using X-ray. We then move on to data obtained in vivo on coronary arteries during a routine angiography examination. During coronary angiography, a catheter is used to inject an X-ray contrast dye into the patient’s aorta. X-rays are then taken as the dye spreads through the coronary arteries. It shows the movement of the coronary arteries for a few seconds and provides an opportunity to follow the natural flexural pulse waves. The obtained Young’s moduli for two patients are E = 38 ± 30 kPa and E = 36 ± 28 kPa, respectively. These preliminary results are expected to pave the way for X-ray elastography.

In the field of ultrasound therapy, the estimation of temperature to monitor treatments is becoming essential. We hypothesize that it is possible to measure temperature directly using a constant acoustic power burst. Under the assumption that the acoustic attenuation does not change significantly with temperature, the thermal strain induced by such bursts presents a linear relation with temperature. A mathematical demonstration is given in the introduction. Then, simulations of ultrasound waves in a canine liver model were conducted at different temperatures (from 20 °C to 90 °C). Finally, experimental measurements on phantom samples were performed over the same temperature range. The simulation and experimental results both showed a linear relation between thermal strain and temperature. This relation may suggest the foundation of a new ultrasound-based thermometry method. The potential and limitations of the method are discussed.

We demonstrate the effectiveness of seismic dense array surface wave focal spot imaging using USArray data from the western‐central United States. We study dispersion in the 60–310 s period range and assess the image quality of fundamental mode Rayleigh wave phase velocity maps. We apply isotropic spatial autocorrelation models to the time domain zero lag noise correlation wavefield data at distances of about one wavelength. Local estimates of the phase velocity, its uncertainty, and the regression quality imply overall better ZZ relative to ZR or RZ results. The extension of the depth resolution compared to passive surface wave tomography is demonstrated by the inversion of three clustered dispersion curves from different tectonic units. We observe anisotropic surface wave energy flux and the influence of body wave energy, but sensitivity tests at 60 s targeting the data range, correlation component, and processing choices show that the ZZ focal spots yield consistent high‐quality images compared to regional tomography results in the 60–150 s period range. In contrast, at 200–300 s the comparatively small scales of the imaged structures and the imperfect agreement with low‐resolution global tomography results highlight the persistent challenge to reconcile imaging results based on different data sources, theories, and techniques. Our study shows that surface wave focal spot imaging is an accurate, robust, local imaging approach. Better control over clean autocorrelation fields can further improve applications of this seismic imaging tool for increased resolution of the elastic structure below dense seismic arrays.

We investigate the lateral resolution power of the seismic Rayleigh wave focal spot imaging technique. We use two-dimensional acoustics simulations in a closed cavity for the passive Green’s function and focal spot reconstruction. Four different velocity distributions target different resolution aspects. The finite data range that is necessary to constrain the Bessel function model controls the lateral spreading of material contrasts, the distinction of two objects on sub-wavelength scales, and the image quality of complex random media. Good data quality from dense networks supports short range estimates and super-resolution.

We investigate the lateral resolution power of the seismic Rayleigh wave focal spot imaging technique. We use two-dimensional acoustics simulations in a closed cavity for the passive Green's function and focal spot reconstruction. Four different velocity distribution configurations target different resolution aspects. The finite data range that is necessary to constrain the Bessel function model controls the lateral spreading of material contrasts, the distinction of two objects on sub-wavelength scales, and the image quality of complex random media. Good data quality from dense networks supports short range estimates and super-resolution.

Numerical experiments of seismic wave propagation in a laterally homogeneous layered medium explore subsurface imaging at subwavelength distances for dense seismic arrays. We choose a time-reversal approach to simulate fundamental mode Rayleigh surface wavefields that are equivalent to the cross-correlation results of three-component ambient seismic field records. We demonstrate that the synthesized 2-D spatial autocorrelation fields in the time domain support local or so-called focal spot imaging. Systematic tests involving clean isotropic surface wavefields but also interfering body wave components and anisotropic incidence assess the accuracy of the phase velocity and dispersion estimates obtained from focal spot properties. The results suggest that data collected within half a wavelength around the origin is usually sufficient to constrain the used Bessel functions models. Generally, the cleaner the surface wavefield the smaller the fitting distances that can be used to accurately estimate the local Rayleigh wave speed. Using models based on isotropic surface wave propagation we find that phase velocity estimates from vertical–radial component data are less biased by P-wave energy compared to estimates obtained from vertical–vertical component data, that even strong anisotropic surface wave incidence yields phase velocity estimates with an accuracy of 1 per cent or better, and that dispersion can be studied in the presence of noise. Estimates using a model to resolve potential medium anisotropy are significantly biased by anisotropic surface wave incidence. The overall accurate results obtained from near-field measurements using isotropic medium assumptions imply that dense array seismic Rayleigh wave focal spot imaging can increase the depth sensitivity compared to ambient noise surface wave tomography. The analogy to elastography focal spot medical imaging implies that a high station density and clean surface wavefields support subwavelength resolution of lateral medium variations.

The spatial zero-lag amplitude distribution of correlations obtained from vertical component dense array records of diffuse seismic wave fields is characterized by a large-amplitude feature around the origin referred to as focal spot. In the context of time-reversed surface waves it can be understood as the collapse of a converging wavefront. The analogy to the SPAC method implies that the nine-component solutions that describe the spectral features can readily be applied to the time-domain focal spot shape to estimate local phase velocity, which connects this method to established elastographic medical imaging. In contrast to sparse SPAC arrays, modern dense arrays allow a properly resolved focal spot at near-field distances for an inversion-free sensor-by-sensor image compilation, with intriguing implications for vertical and lateral resolution enhancement. We demonstrate the applicability of this method on the basis of Rayleigh wave focal spots in the 60 s to 200 s period range that are obtained from ambient field correlations using USArray data between -125 and -90 degrees west. The 1000 s long noise correlations are computed using standard techniques, Gaussian filtered around the central target frequency, and the spatial zero-lag distribution fitted with the SPAC Bessel functions model to distances of 1.2 wavelengths. The effectiveness and accuracy of this approach is demonstrated by the impressive similarity between the obtained “instantaneous image” at 60 s and surface wave tomography results from the literature. The stark velocity contrast between the western and central U.S. is clearly resolved, but the similarity extends to well resolved details including the Sierra Nevada, the Snake River Plain feature, the circular low-velocity rim around the Colorado Plateau, and part of the Mississippi Embayment. Based on this benchmark result obtained with vertical-component data we explore the internal consistency of the obtained maps towards longer periods and the associated extension of dispersion measurements; we probe the limits of the near-field approach by systematically lowering the fitting distance to sub-wavelength scales; and we quantify the similarity of vertical-radial results. The zero-lag amplitude distributions in the wavenumber domain show signatures of near-vertically incident energy associated with global body wave reverberations. We mute this energy by neglecting time windows from the correlation data after global large earthquakes. Systematic tests of the window length, and again the comparison to the benchmark observations, inform about the efficiency of this approach. We conclude that time-domain dense array near-field imaging yields accurate distributions of the velocity structure. We emphasize the disadvantageous low randomization of the long period ambient field, and the sub-array shapes resulting from the rolling USArray deployment. Imaging on smaller scales should therefore work better.