Mechanical Compliance of Individual Fractures in a Heterogeneous Rock Mass From Production‐Type Full‐Waveform Sonic Data

The mechanical fracture compliance is of interest in a number of geoscientific applications. Seismic borehole methods, especially full-waveform sonic (FWS) data, have indicated their potential to infer the compliance of macroscopic fractures under in situ conditions. These approaches rely on the assumption of a homogeneous background embedding the fractures and, as of yet, compliance estimates for individual fractures are limited to static FWS measurements. In this work, we assess the potential of inferring the compliance of individual fractures from standard, production-type FWS data in the presence of background heterogeneity. We first perform a comparative test on synthetic data to evaluate three approaches known as the transmission, phase, and group time delay methods. The results indicate that the former two produce adequate compliance estimates for scenarios with a strongly heterogeneous background or a damage zone around the fracture. These two methods are then applied to two FWS data sets acquired before and after a hydraulic stimulation campaign in a crystalline rock, which allows to test them on natural and man-made fractures. The transmission method turned out to be unsuitable for the considered data due to its reliance on amplitudes. Conversely, the travel time behavior remained stable and the phase time delay method produced robust and consistent estimates. The results for a newly created hydro-fracture imply the capability of resolving remarkably small compliance values of the order of 10−14 m/Pa. This estimate is one order-of-magnitude smaller than that for the natural fracture, which may help to distinguish between these two fracture types

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled

Caractérisation des discontinuités dans le massif rocheux par combinaison de mesures de diagraphies soniques et électriques

La présence de discontinuités dans un massif rocheux a un impact significatif sur la stabilité et la résistance mécanique de ce dernier, ainsi que sur la sécurité et la conception de projets impliquant la roche. Dans cette thèse, nous chercherons à caractériser les propriétés des discontinuités, directement dans le massif, par l’utilisation de mesures diagraphiques classiques, avec les sondes Fullwave (FWS) et sonde électrique normale (DN). Le but ultime est de mieux comprendre leur impact sur le comportement du massif et de prendre des décisions éclairées en matière de construction, d'exploitation minière et de gestion des risques géologiques. Dans cette optique, cette thèse propose une nouvelle méthodologie de caractérisation des propriétés géométriques (ouverture, longueur) et physiques (vitesse de compression, vitesse de cisaillement, masse volumique, résistivité) des discontinuités en combinant les réponses de deux techniques. Les deux outils ont montré leur potentiel de détecter les discontinuités, ainsi que leurs limites à caractériser ces propriétés. La complémentarité des données électriques (DN) et acoustiques (FWS) est exploitée pour surmonter les limites de chaque méthode et bénéficier de leurs caractéristiques distinctes en termes de volume d'investigation, de propriétés détectées et de résolution. Pour cela, les réponses des deux outils sont combinées dans le but de caractériser les propriétés des discontinuités de manière non destructive. Cette thèse repose sur une première approche numérique qui consiste à modéliser la réponse de deux outils de diagraphie (FWS et DN) face à la présence d'une discontinuité idéale et isolée dans un massif rocheux. Sur la base de l’étude de sensibilité réalisée, cette approche a permis de définir des facteurs de perte acoustique (liés à l'atténuation et au retard des ondes de compression et de cisaillement) et électrique (liés à la diminution de la résistivité). Une base de données numériques de 880 cas issue de l’étude paramétrique, est construite. Des techniques de régressions multiples non linéaires et de réseaux de neurones ont été comparées pour créer des modèles prédictifs visant à diagnostiquer les différentes propriétés de la discontinuité. Les résultats sont ensuite confrontés à une validation expérimentale sur des données réelles réalisées sur un site de calibration à Bells Corners (Ottawa, Ontario, Canada). Les résultats attestent du potentiel de l’approche pour évaluer l’ouverture de la discontinuité à un niveau de précision d’ordre centimétrique.Abstract : The presence of discontinuities in a rock mass has a significant impact on its stability, mechanical resistance, as well as stability of structures laid on hard rock. The purpose of this research is to investigate these discontinuities with borehole logging techniques in an attempt to better understand their impact on the behavior of the rock mass and to propose an appropriate guideline for construction, mining operations, and geological risk management. In this regard, this thesis proposes a new methodology to characterize the geometric (opening, length) and physical (compression velocity, shear velocity, density, resistivity) properties of discontinuities by combining the responses of two wireline logging techniques, namely [Fullwave Sonic (FWS) and Normal Electrical Resistivity (DN) probes]. These two tools have shown potential in detecting discontinuities, as well as their limitations in characterizing these properties. Therefore, the objective is to combine the response of both tools to overcome the limitations of each method and benefit from their distinct characteristics in terms of investigation volume, detected properties, and resolution, to accurately characterize the properties of discontinuities. The thesis is based on a numerical approach that models the response of two logging tools (FWS and DN) in the presence of an ideal and isolated discontinuity in a rock mass. This approach defines acoustic loss factors (related to the attenuation and delay of compression and shear waves) and electrical loss factors (related to the decrease in resistivity) and evaluates their sensitivity to the geometric, mechanical, and electrical properties of a filled discontinuity. By conducting a parametric study, a numerical database of 880 cases was built, and techniques such as multiple nonlinear regression and neural networks were used to create predictive models aimed to characterize various properties of the discontinuity. Real FWS and DN log measurements from the Bells Corners calibration site (in Ottawa, Ontario, Canada) were used to validate the developed method. These promising results demonstrate a high potential for identifying discontinuity aperture with centimeter precision