Title: The source process of Greek earthquakes Author: Dana K ížová Department: Department of Geophysics Supervisor of the doctoral thesis: Prof. RNDr. Ji í Zahradník DrSc., Department of Geophysics Abstract: Investigations of moment tensor (MT) and its uncertainty are topical. This thesis is focused on isotropic component of three shallow earthquakes: Event A in Cretan Sea (Mw 5.3) and two events near Santorini island, B (Mw 4.9) and C (Mw 4.7). MT is inverted from full waveforms in an assumed 1D velocity model. The inverse problem is non-linear in centroid depth and time, and linear in six MT parameters, one is the MT-trace. Uncertainty of isotropic component is studied by a new approach (K ížová et al., 2013). The trace is systematically varied, and remaining parameters are optimized. The method reveals tradeoffs between the isotropic component, depth, time, and focal mechanism. From two existing velocity models, we prefer the one with lower condition number, in which a (positive) isotropic component is indicated for event B. To rapidly assess a likely existence of isotropic component, an empirical method is proposed (K ížová et al., 2016). It is based on comparison between depth- dependences of waveform correlation in full and deviatoric modes. Based on extensive synthetic tests, the method confirms a...

The ever-expanding need for energy, including those related to fossil fuels, is behind the drive to explore more complicated regions, such as salt and subsalt provinces. This exploration quest relies heavily on recorded surface seismic data to provide precise and detailed subsurface properties. However, conventional seismic processing algorithms including the state-of-the-art full-waveform inversion (FWI) fail to recover those features in many areas of salt provinces. Even the industrial solution with substantial involvement of manual human-interpretation has faced challenges in many regions. In this thesis, I attempt to replace those manual, and somewhat erroneous, steps to the velocity building in salt provinces with a mathematically robust algorithm under the FWI machinery. I, specifically, regularize FWI by penalizing the velocity drops with depth with a new more flexible function. Although promising, FWI is computationally very expensive, especially for large 3D seismic data. It updates an initial guess of the model iteratively using the gradient of the misfit function, which requires lengthy computations and large memory space/disc storage. Based on the adjoint state method, gradient computation usually requires us to store the source wavefield, or include an additional extrapolation step to propagate the source wavefield from its temporary storage at the boundary. To mitigate this computational overburden, I propose an amplitude excitation gradient calculation based on representing the source wavefield history by a single, specifically the most energetic arrival. In this thesis, I also propose a novel-multiscale scheme based on ux-corrected transport (FCT) to reduce artifacts in the gradient direction due to the noise present in seismic data. FCT comprises of two finite difference schemes: a transport and a diffusion to compute the flux at a grid point. I observe a couple of benefits in FCT-based FWI. First, it yields a smooth gradient at the earlier iterations of FWI by promoting the lower frequency content of the seismic data. Second, it is easily compatible with the existing FWI code, and with any objective function. The multiscale strategy starts with a large smoothing parameter and relaxes it progressively to zero to achieve the final inverted model from traditional FWI.

Dans cette thèse, un algorithme d'inversion de formes d'ondes (FWI) est développé pour l'imagerie 3D des paramètres élastiques de la lithosphère à partir des enregistrements télésismiques dans le but d'accroître la résolution des images lithosphériques. La modélisation sismique est effectuée par un méthode hybride d'injection de champ d'ondes. Une première modélisation est effectuée dans une Terre globale avec le logiciel AxiSEM pour déterminer les champs d’ondes aux bords de la cible lithosphérique. Ces solutions sont ensuite propagées dans cette cible par une méthode aux éléments finis spectraux. Le problème inverse est résolu avec un algorithme d’optimisation locale de type quasi-Newton (l-BFGS). La sensibilité de la méthode à la configuration expérimentale (paramétrisation du milieu, modèle initial, géométrie et échantillonnage du dispositif de capteurs) est tout d’abord analysée avec un modèle synthétique réaliste des Alpes Occidentales. L’algorithme est finalement appliqué à neuf événements de la campagne CIFALPS dans les Alpes occidentales jusqu’à une fréquence de 0.2Hz. Les modèles de vitesses P et S et de densité révèlent les grandes structures lithosphériques de la chaîne alpine, en particulier le corps d’Ivrée et la géométrie des Moho européen et adriatique. Plus profondément, deux anomalies de vitesses lentes sont imagées dans le manteau et sont interprétées comme la signature d’une remontée asthénosphérique et la localisation du détachement du panneau plongeant européen. Ces résultats corroborent l’hypothèse d’une subduction continentale de la croûte européenne et d’une éventuelle déchirure du panneau plongeant européen lors de la phase de collision. / In this thesis, a full-waveform inversion (FWI) algorithm is developed with the aim to image the elastic properties (Vp, Vs and density) of 3D lithospheric models from teleseismic recordings with a spatial resolution of the order of the wavelength. Seismic modeling is performed with a wavefield injection hybrid approach. A first simulation is performed in a global radially symmetric Earth with the AxiSEM code to compute the wavefields on the borders of the lithospheric target. Then, these wavefields are propagated in the target with the spectral finite-element method. After linearization, the inverse problem is solved with a quasi-Newton (1-BFGS) optimization algorithm. The sensitivity of the teleseismic FWI to the experimental setup (subsurface parameterization, initial model, sampling and geometry of the station layout) is first assessed with a realistic synthetic model of the Western Alps. The method is finally applied to nine events of the CIFALPS experiment carried out in the Western Alps, up to a frequency of 0.2Hz. Reliable models of P and S wave speeds and density reveal with an unprecedented resolution the crustal and lithospheric structures of the Alpine Belt, in particular the geometry of the Ivrea body, and the European and Adriatic Mohos. Deeper, two slow velocity anomalies beneath the Western Alps are imaged in the mantle. The first, to the west of the chain, is interpreted as the signature of an asthenospheric upwelling, the second near the location of the Ivrea body indicates the European slab break-off. The study supports the hypothesis of the European continental crust subduction and confirms the possible tearing of the European slab.

Maintenance of aging buried infrastructure and reinforced concrete are critical issues in the United States. Inexpensive non-destructive techniques for mapping and imaging infrastructure and defects are an integral component of maintenance. Ground penetrating radar (GPR) is a widely-used non-destructive tool for locating buried infrastructure and for imaging rebar and other features of interest to civil engineers. Conventional acquisition and interpretation of GPR profiles is based on the arrival times of strong reflected/diffracted returns, and qualitative interpretation of return amplitudes. Features are thereby generally well located, but their material properties are only qualitatively assessed. For example, in the typical imaging of buried pipes, the average radar wave velocity through the overlying soil is estimated, but the properties of the pipe itself are not quantitatively resolved. For pipes on the order of the radar wavelength (<5-35 cm), pipe dimensions and infilling material remain ambiguous. Full waveform inversion (FWI) methods exploit the entire radar return rather than the time and peak amplitude. FWI can generate better quantitative estimates of subsurface properties. In recent decades FWI methods, developed for seismic oil exploration, have been adapted and advanced for GPR with encouraging results. To date, however, FWI methods for GPR data have not been specifically tuned and applied on surface collected common offset GPR data, which are the most common type of GPR data for engineering applications. I present an effective FWI method specifically tailored for common-offset GPR data. This method is composed of three main components, the forward modeling, wavelet estimation and inversion tools. For the forward modeling and iterative data inversion I use two open-source software packages, gprMax and PEST. The source wavelet, which is the most challenging component that guarantees the success of the method, is estimated with a novel Sparse Blind Deconvolution (SBD) algorithm that I have developed. The present dissertation indicates that with FWI, GPR can yield better quantitative estimates, for example, of both the diameters of small pipes and rebar and their electromagnetic properties (permittivity, conductivity). Also better estimates of electrical properties of the surrounding media (i.e. soil or concrete) are achieved with FWI.

Multisource Least-Squares Migration (LSM) of phase-encoded supergathers has shown great promise in reducing the computational cost of conventional migration. But for the marine acquisition geometry this approach faces the challenge of erroneous misfit due to the mismatch between the limited number of live traces/shot recorded in the field and the pervasive number of traces generated by the finite-difference modeling method. To tackle this mismatch problem, I present a frequency selection strategy with LSM of supergathers. The key idea is, at each LSM iteration, to assign a unique frequency band to each shot gather, so that the spectral overlap among those shots—and therefore their crosstallk—is zero. Consequently, each receiver can unambiguously identify and then discount the superfluous sources—those that are not associated with the receiver in marine acquisition. To compare with standard migration, I apply the proposed method to 2D SEG/EAGE salt model and obtain better resolved images computed at about 1/8 the cost; results for 3D SEG/EAGE salt model, with Ocean Bottom Seismometer (OBS) survey, show a speedup of 40×. This strategy is next extended to multisource Full Waveform Inversion (FWI) of supergathers for marine streamer data, with the same advantages of computational efficiency and storage savings. In the Finite-Difference Time-Domain (FDTD) method, to mitigate spectral leakage due to delayed onsets of sine waves detected at receivers, I double the simulation time and retain only the second half of the simulated records. To compare with standard FWI, I apply the proposed method to 2D velocity model of SEG/EAGE salt and to Gulf Of Mexico (GOM) field data, and obtain a speedup of about 4× and 8×. Formulas are then derived for the resolution limits of various constituent wavepaths pertaining to FWI: diving waves, primary reflections, diffractions, and multiple reflections. They suggest that inverting multiples can provide some low and intermediate-wavenumber components of the velocity model not available in the primaries. In addition, diffractions can provide twice or better the resolution as specular reflections for comparable depths of the reflector and diffractor. The width of the diffraction-transmission wavepath is on the order of λ at the diffractor location for the diffraction-transmission wavepath.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20061号 / 工博第4249号 / 新制||工||1658(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 三ｹ田 均, 教授 小池 克明, 教授 木村 亮 高梨 将 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The main objective of this thesis is to develop novel misfit functions for full-waveform inversion such that (a) the estimation of the long-wavelength model will less likely stagnate in spurious local minima and (b) the inversion is immune to wavelet inaccuracy. First, I investigate the pros and cons of misfit functions based on optimal transport theory to indicate the traveltime discrepancy for seismic data. Even though the mathematically well-defined optimal transport theory is robust to highlight the traveltime difference between two probability distributions, it becomes restricted as applied to seismic data mainly because the seismic data are not probability distribution functions. We then develop a misfit function combining the local cross-correlation and dynamic time warping. This combination enables the proposed misfit automatically identify arrivals associated with a phase shift. Numerical and field data examples demonstrate its robustness for early arrivals and limitations for later arrivals.%, which means that a proper pre-processing step is still required. Next, we introduce differentiable dynamic time warping distance as the misfit function highlighting the traveltime discrepancy without non-trivial human intervention. Compared to the conventional warping distance, the differentiable version retains the property of representing the traveltime difference; moreover, it can eliminate abrupt changes in the adjoint source, which helps full-waveform inversion converge to geologically relevant estimates. Finally, we develop a misfit function entitled the deconvolutional double-difference measurement. The new misfit measures the first difference by deconvolution rather than cross-correlation. We also present the derivation of the adjoint source with the new misfit function. Numerical examples and mathematical proof demonstrate that this modification makes full-waveform inversion with the deconvolutional double-difference measurement immune to wavelet inaccuracy.

Full Waveform Inversion (FWI) is a powerful seismic imaging technique used to reconstruct high-resolution velocity models of the subsurface. It relies on the inversion of seismic data acquired from multiple sources and receivers to estimate the mechanical properties of geologic materials and can be used to detect anomalous subsurface conditions. The accuracy of FWI results is influenced by various factors related to the workflow used for its implementation. This includes the survey parameters, the mathematical framework of the inversion, and the complexity of the subsurface conditions modeled during the inversion process. Therefore, it is crucial to have a fundamental understanding of the interplay between these factors and their impact on the accuracy of the reconstructed model, particularly given the effects of these factors on computational costs. This is an area that has been understudied within the context of near-surface geotechnical applications for anomaly detection, which is an application that presents unique challenges relative to seismic exploration for hydrocarbons where FWI has been more fully developed. One key aspect that has not received sufficient attention is the impact of survey parameters on the accuracy of FWI results. The lack of formal research in this topic may lead to near-surface FWI studies that use more seismic sources than required for subsurface feature reconstruction, which results in data collection and computational inefficiencies. The selection of misfit function and starting model are also essential factors influencing the reliability of the reconstructed model. The physics employed for forward modeling can also affect the ability to simulate wave propagation in the domain of interest. These factors have significant implications for near-surface applications of FWI, and further research is required to explore their interplay and improve FWI workflow.Given the gaps in the current implementation of FWI for geotechnical applications, this research will explore the role of parameterization and workflow on FWI results when applied to anomaly detection in karst conditions. This will include selection of an FWI workflow that can improve the feasibility of fieldwork and reduce the processing time. The research will investigate four key factors of the FWI workflow (i.e., survey design, initial model, misfit function, and forward modeling physics) for detection of sinkholes using numerical and field testing in different subsurface conditions. Overall, the outcomes of this research will help practitioners with more appropriate choices in the FWI process and consequently promote its high potential in near-surface applications. / Civil Engineering

Full Waveform Inversion (FWI) is a widely used optimization technique for subsurface imaging where the goal is to estimate the seismic wave velocity beneath the Earth's surface from the observed seismic data at the surface. The problem is primarily governed by the wave equation, which is a non-linear second-order partial differential equation. A number of approaches have been developed for FWI including physics-based iterative numerical solvers as well as data-driven machine learning (ML) methods. Existing numerical solutions to FWI suffer from three major challenges: (1) sensitivity to initial velocity guess (2) non-convex loss landscape, and (3) sensitivity to noise. Additionally, they suffer from high computational cost, making them infeasible to apply in complex real-world applications. Existing ML solutions for FWI only solve for the inverse and are prone to yield non-unique solutions. In this work, we propose to solve both forward and inverse problems jointly to alleviate the issue of non-unique solutions for an inverse problem. We study the FWI problem from a new perspective and propose a novel approach based on Invertible Neural Networks. This type of neural network is designed to learn bijective mappings between the input and target distributions and hence they present a potential solution to solve forward and inverse problems jointly. In this thesis, we developed a data-driven framework that can be used to learn forward and inverse mappings between any arbitrary input and output space. Our model, Invertible X-net, can be used to solve FWI to obtain high-quality velocity images and also predict the seismic waveforms data. We compare our model with the existing baseline mod- els and show that our model outperforms them in velocity reconstruction on the OpenFWI dataset. Additionally, we also compare the predicted waveforms with a baseline and ground truth and show that our model is capable of predicting highly accurate seismic waveforms simultaneously. / Master of Science / Recent advancements in deep learning have led to the development of sophisticated methods that can be used to solve scientific problems in many disciplines including medical imaging, geophysics, and signal processing. For example, in geophysics, we study the internal structure of the Earth from indirect physical measurements. Often, these kind of problems are challenging due to existence of non-unique and unstable solutions. In this thesis, we look at one such problem called Full Waveform Inversion which aims to estimate velocity of mechanical wave inside the Earth from wave amplitude observations on the surface. For this problem, we explore a special class of neural networks that allows to uniquely map the input and output space and thus alleviate the non-uniqueness and instability in performing Full Waveform Inversion for seismic imaging.

L’amélioration des images sismiques peut aider à mieux contraindre l’exploration deshydrocarbures. Les ondes élastiques qui se propagent dans la Terre peuvent être classifiéescomme ondes de volume et ondes de surface. Si ces dernières sont les plus énergétiques,seules les ondes de volume sont couramment considérées comme des signaux utiles.Cependant, les ondes de surface sont utiles pour caractériser la proche sub-surface.Classiquement, les ondes de surface sont analysées dans des contextes de propriétésélastiques localement 1D.Nous proposons une modification de l’inversion des formes d’onde classique pourreconstruire des profils de propriétés 2D (la windowed-Amplitude Waveform Inversion, w-AWI). La w-AWI est spécialement robuste en ce qui concerne le choix du modèle initial.Nous appliquons la w-AWI aux données synthétiques ainsi qu’aux données réelles, montrantque cette approche permet de récupérer des propriétés 2D. / High-resolution seismic imaging is essential to improve results of hydrocarbon exploration.Elastic waves propagate in the Earth as body and surface waves, the latter being the mostenergetic ones. Body waves are preferred for exploration seismic imaging while surfacewaves are usually considered to be noise. However, it has been recognised that the nearsurface can be characterised by analysing surface waves and that such result may improvethe outcome of body-wave processing. Currently, surface waves analysis leads to retrievelocal 1D property profiles.We propose a waveform-based inversion procedure to derive 2D velocity models fromsurface waves. This method consists of a misfit functional modification of classical FullWaveform Inversion and we call it windowed-Amplitude Waveform Inversion (w-AWI). Weshow that w-AWI is robust regarding the choice of initial velocity model. We apply w-AWI tosynthetic and real data obtaining encouraging near-surface imaging results