Browsing by Subject "Wave propagation"
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Item Analysis of soil-structure system response with adjustments to soil properties by perturbation method(2014-05) Patta, Sang Putra Pasca Rante; Tassoulas, John LambrosThe research described in this dissertation undertakes a computational study of wave motion due to ground excitation in layered soil media. Adjustments of soil properties consistent with the level of deformation is applied using an equivalent linear approach. The finite element method provides the basis of the numerical procedure for soil-structure system response calculation in conjunction with a first-order perturbation scheme. Available experimental data are employed for shear-modulus and damping adjustments. The findings of the research are expected to lead to efficient calculation of structural response to earthquake ground motion.Item Fast algorithms for frequency domain wave propagation(2012-12) Tsuji, Paul Hikaru; Ying, Lexing; Ghattas, Omar N.; Engquist, Bjorn; Fomel, Sergey; Ren, KuiHigh-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime. The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time.Item Fast methods to model the response of fluid-filled fractures and estimate the fracture properties(2018-11-21) Alulaiw, Badr Abdullah; Sen, Mrinal K.; Spikes, Kyle T; Fomel, Sergey; Grand, Stephen P; Foster, DouglasEstimation of fracture orientation and properties has become an important part of seismic reservoir characterization especially in unconventional reservoirs because of the crucial role of fractures in enhancing the permeability in tight reservoirs. The presence of fluid inside the fractures affects their seismic response. Using equivalent medium theories, seismic wave signatures such as Amplitude Variation with Offset and azimuth (AVOz), Normal Moveout (NMO) correction and shear waves splitting have been used to detect the presence of gas-filled and fluid-filled fractures. These methods, however, are unable to specify the type of fluid inside the fractures and cannot be used for thin beds and complex geology where the subsurface properties change laterally. Hence, modeling the seismic waveform using numerical methods is inevitable. The main limitation of those methods is their high computation costs. In this dissertation, I focus on developing two fast numerical methods to model the response of fluid-filled fractures as well as one fast global optimization method to estimate the fracture properties. Although local optimization methods are computationally cheap, the probability of being trapped in a local minimum becomes high when the initial model is not close to the global minimum especially when applied to highly nonlinear problems. Quantum Annealing (QA) is a recent global optimization method that was shown to be faster than Simulated Annealing (SA) in many situations. QA has been recently applied to geophysical problems. In this research, I modify QA by proposing using a new kinetic term that helps QA converge faster to the global minimum. With a synthetic dataset, I illustrate that QA is faster than Very Fast Simulated Annealing (VFSA) using a highly non-linear forward model that computes the response of seismic Amplitude Variation with Angle (AVA) for spherical waves. Most AVA inversion algorithms are based on plane wave solutions whereas seismic surveys use point sources to generate spherical waves. Although the plane wave solution is an excellent approximation for spherical waves, this approximation breaks down in the vicinity of the critical angle. Here, I implement an AVA inversion method for three parameters (P-wave velocity, S-wave velocity and density) based on analytical approximation for spherical waves. In addition, I apply this algorithm to a 2D seismic dataset from Cana field, Oklahoma with the primary objective of resolving the Woodford formation. I compare the results with those obtained by a local optimization method. The results clearly demonstrate superior performance of the proposed inversion method over that of local optimization. Specifically, the inverted images show clear delineation of the Woodford formation. For a reservoir containing vertical and rotationally invariant fractures, the linear slip model characterizes the reservoir using four properties: two elastic properties describing the isotropic host rock and two fracture properties – normal ΔN and tangential ΔT fracture weaknesses. This model, however, ignores the pore porosity effect on the anisotropy and hence the fracture properties might be inaccurate. In this work, I estimate the fracture properties as well as pore porosity using a new expression for the stiffness tensor for a porous fractured medium. I use the ray-Born approximation to calculate the seismic response of a laterally varying porous reservoir and QA to estimate the fracture properties. Using numerical experiments, I compare the inversion results from both unconstrained and constrained simultaneous (PP and PSV components) seismic inversion as well as constrained inversion using only the PP component. I explain the importance of including a constraint to mitigate the effect of the equivalence problem between ΔN and porosity. Unlike the unconstrained inversion, the estimated properties from the constrained inversion are acceptable. Also, I illustrate that the simultaneous constrained inversion is more robust than using the PP component alone. I apply this algorithm to a 3D multicomponent seismic dataset acquired in Saudi Arabia. The estimated fracture orientation agrees with those obtained in previous studies using borehole image logs, oriented cores, drilling observation and seismic in the same area. Also, the computed porosity using available well logs matches the inverted porosity very well. Computationally cheap analytical methods and equivalent medium theories available to model seismic wavefields diffracted by multiple fluid-filled fractures are not capable of handling complex fracture models or wave multi-scattering. Hence, using expensive numerical methods is inevitable. The advantages of boundary element method (BEM) over domain methods, such as finite difference and finite element methods, include the ease of handling irregular fracture geometry and reduction of the problem dimensions making the computation fast. Moreover, BEM models the complete wavefield including multiples, reverberations and refracted waves inside the fractures. The downside of BEM is that the computation cost increases rapidly whenever we increase the number of boundary elements making these methods computationally inefficient to model a large number of 2D cracks or 3D fractures. By combining the Indirect Boundary Element Method (IBEM) and a Generalized Born Series (GBS), I propose a new algorithm that can compute the response of 3D fluid-filled fracture sets effectively. In addition, when I consider equally spaced fractures that have the same geometry within a fracture set, computation can be performed even more rapidly. I compare the wavefield obtained using this approximation in five numerical experiments with those obtained from IBEM and show that the results are accurate in many situations.Item Fast numerical methods for high frequency wave scattering(2012-05) Tran, Khoa Dang; Engquist, Björn, 1945-; Ling, Hao; Ghattas, Omar; Tsai, Richard; Ying, LexingComputer simulation of wave propagation is an active research area as wave phenomena are prevalent in many applications. Examples include wireless communication, radar cross section, underwater acoustics, and seismology. For high frequency waves, this is a challenging multiscale problem, where the small scale is given by the wavelength while the large scale corresponds to the overall size of the computational domain. Research into wave equation modeling can be divided into two regimes: time domain and frequency domain. In each regime, there are two further popular research directions for the numerical simulation of the scattered wave. One relies on direct discretization of the wave equation as a hyperbolic partial differential equation in the full physical domain. The other direction aims at solving an equivalent integral equation on the surface of the scatterer. In this dissertation, we present three new techniques for the frequency domain, boundary integral equations.Item Generalized homogenization theory and inverse design of periodic electromagnetic metamaterials(2013-05) Liu, Xing-Xiang; Alù, AndreaArtificial metamaterials composed of specifically designed subwavelength unit cells can support an exotic material response and present a promising future for various microwave, terahertz and optical applications. Metamaterials essentially provide the concept to microscopically manipulate light through their subwavelength inclusions, and the overall structure can be macroscopically treated as homogeneous bulk material characterized by a simple set of constitutive parameters, such as permittivity and permeability. In this dissertation, we present a complete homogenization theory applicable to one-, two- and three-dimensional metamaterials composed of nonconnected subwavelength elements. The homogenization theory provides not only deep insights to electromagnetic wave propagation among metamaterials, but also allows developing a useful and efficient analysis method for engineering metamaterials. We begin the work by proposing a general retrieval procedure to characterize arbitrary subwavelength elements in terms of a polarizability tensor. Based on this system, we may start the macroscopic analysis of metamaterials by analyzing the scattering properties of their microscopic building blocks. For one-dimensional linear arrays, we present the dispersion relations for single and parallel linear chains and study their potential use as sub-diffractive waveguides and leaky-wave antennas. For two-dimensional arrays, we interpret the metasurfaces as homogeneous surfaces and characterize their properties by a complete six-by-six tensorial effective surface susceptibility. This model also offers the possibility to derive analytical transmission and reflection coefficients for metasurfaces composed of arbitrary nonconnected inclusions with TE and TM mutual coupling. For three-dimensional metamaterials, we present a generalized theory to homogenize arrays by effective tensorial permittivity, permeability and magneto-electric coupling coefficients. This model captures comprehensive anisotropic and bianisotropic properties of metamaterials. Based on this theory, we also modify the conventional retrieval method to extract physically meaningful effective parameters of given metamaterials and fundamentally explain the common non-causality issues associated with parameter retrieval. Finally, we conceptually propose an inverse design procedure for three-dimensional metamaterials that can efficiently determine the geometry of the inclusions required to achieve the anomalous properties, such as double-negative response, in the desired frequency regime.Item Improving accuracy and efficiency of seismic data analysis using deep learning(2022-05-02) Kaur, Harpreet, Ph. D.; Fomel, Sergey B.; Sen, Mrinal K; Spikes, Kyle T; Abma, Raymond; Biros, GeorgeThe ultimate goal of seismic data analysis is to retrieve high-resolution information about the subsurface structures. It comprises different steps such as data processing, model building, wave propagation, and imaging, etc. Increasing the resolution and fidelity of the different seismic data analysis tasks eventually leads to an improved understanding of fine-scale structural features. Conventional implementation of these techniques is computationally intensive and expensive, especially with large data sets. Recent advances in neural networks have provided an ability to produce a reasonable result to computationally intensive and time-consuming problems. Deep neural networks are capable of extracting complex nonlinear relationships among variables and have shown efficacy as compared to conventional statistical methods in different areas. A major bottleneck for seismic data analysis is the tradeoff between resolution and efficiency. I address some of these challenges by implementing neural network based frameworks. First, I implement a neural network based workflow for stable and efficient wave extrapolation. Conventionally, it is implemented by finite differences (FD), which have a low computational cost but for larger time-steps may suffer from dispersion artifacts and instabilities. On the other hand, recursive integral time extrapolation (RITE) methods, especially the low-rank extrapolation, which are mixed-domain space-wavenumber operators are designed to make time extrapolation stable and dispersion free in heterogeneous media for large time steps, even beyond the Nyquist limit. They have high spectral accuracy; however, they are expensive as compared to finite-difference extrapolation. The proposed framework overcomes the numerical dispersion of finite-difference wave extrapolation for larger time steps and provides stable and efficient wave extrapolation results equivalent to low-rank wave extrapolation at a significantly reduced cost. Second, I address wave-mode separation and wave-vector decomposition problem to separate a full elastic wavefield into different wavefields corresponding to their respective wave mode. Conventionally, wave mode separation in heterogeneous anisotropic media is done by solving the Christoffel equation in all phase directions for a given set of stiffness-tensor coefficients at each spatial location of the medium, which is a computationally expensive process. I circumvent the need to solve the Christoffel equation at each spatial location by implementing a deep neural network based framework. The proposed approach has high accuracy and efficiency for decoupling the elastic waves, which has been demonstrated using different models of increasing complexity. Third, I propose a hyper-parameter optimization (HPO) workflow for a deep learning framework to simulate boundary conditions for acoustic and elastic wave propagation. The conventional low-order implementation of ABCs and PMLs is challenging for strong anisotropic media. In the tilted transverse isotropic (TTI) case, instabilities may appear in layers with PMLs owing to exponentially increasing modes, which eventually degrades the reverse time migration output. The proposed approach is stable and simulates the effect of higher-order absorbing boundary conditions in strongly anisotropic media, especially TTI media, thus having a great potential for application in reverse time migration. Fourth, I implement a coherent noise attenuation framework, especially for ground-roll noise attenuation using deep learning. Accounting for non-stationary properties of seismic data and associated ground-roll noise, I create training labels using local-time frequency transform (LTF) and regularized non-stationary regression (RNR). The proposed approach automates the ground-roll attenuation process without requiring any manual input in picking the parameters for each shot gather other than in the training data. Lastly, I address the limitation of the iterative methods with conventional implementation for true amplitude imaging. I implement a workflow to correct migration amplitudes by estimating the inverse Hessian operator weights using a neural network based framework. To incorporate non-stationarity in the framework, I condition the input migrated image with different conditioners like the velocity model and source illumination. To correct for the remnant artifacts in the deep neural network (DNN) output, I perform iterative least-squares migration using neural network output as an initial model. The network output is close to the true model and therefore, with fewer iterations, a true-amplitude image with the improved resolution is obtained. The proposed method is robust in areas with poor illumination and can easily be generalized to more-complex cases such as viscoacoustic, elastic, and others. The proposed frameworks are numerically stable with high accuracy and efficiency and are, therefore, desirable for different seismic data analysis tasks. I use synthetic and field data examples of varying complexities in both 2D and 3D to test the practical application and accuracy of the proposed approachesItem The inverse medium problem in PML-truncated elastic media(2010-12) Kucukcoban, Sezgin; Kallivokas, Loukas F.; Demkowicz, Leszek F.; Ghattas, Omar; Kinnas, Sypros A.; Rodin, Gregory J.; Torres-Verdin, CarlosWe introduce a mathematical framework for the inverse medium problem arising commonly in geotechnical site characterization and geophysical probing applications, when stress waves are used to probe the material composition of the interrogated medium. Specifically, we attempt to recover the spatial distribution of Lame's parameters ( and μ) of an elastic semi-infinite arbitrarily heterogeneous medium, using surface measurements of the medium's response to prescribed dynamic excitations. The focus is on characterizing near-surface deposits, and to this end, we develop a method that is implemented directly in the time-domain, is driven by the full waveform response collected at receivers on the surface, while the domain of interest is truncated using Perfectly-Matched-Layers (PMLs) to limit the originally semi-infinite extent of the physical domain. There are two key issues associated with the problem at hand: (a) the forward problem, namely the numerical simulation of the wave motion in the domain of interest; and (b) the framework and strategies for tackling the inverse problem. To address the forward problem, it is necessary that the domain of interest be truncated, and the resulting finite domain be forced to mimic the physics of the original problem: to this end, we introduce unsplit-field PMLs, and develop and implement two new formulations, one fully-mixed and one hybrid (mixed coupled with a non-mixed approach) that model wave motion within the, now PML-truncated, domain. To address the inverse problem, we adopt a partial-differential-equation-constrained optimization framework that results in the usual triplet of an initial-and-boundary-value forward problem, a final-and-boundary-value adjoint problem, and a time-independent boundary-value control problem. This triplet of boundary-value-problems is used to guide the optimizer to the target profile of the spatially distributed Lame parameters. Given the multiplicity of solutions, we assist the optimizer, by deploying regularization schemes, continuation schemes (regularization factor and source-frequency content), as well as a physics-driven simple procedure to bias the search directions. We report numerical examples attesting to the quality, stability, and efficiency of the forward wave modeling. We also report moderate success with numerical experiments targeting inversion of both smooth and sharp profiles in two dimensions.Item Investigation of wave propagation and antenna radiation in forested environments(2011-05) Li, Yang, 1982-; Ling, Hao; Pearce, John; Yilmaz, Ali; Alu, Andrea; Torres-Verdin, Carlos; Shvets, GennadyRecently, there is emerging interests in deploying wireless sensor networks in forests for applications such as forest fire detection, environmental monitoring and remote surveillance. One challenge in the design of such networks is to ensure reliable communication between sensors located near the ground and over short distances. However, the propagation mechanisms in this type of scenario are complex and not well understood. Furthermore, the design of antennas that can exploit the resulting propagation mechanisms for optimal power transfer remains an open question. The objective of this dissertation is to understand wave propagation and antenna radiation in forested environments in the HF/VHF frequency range. To achieve this objective, several forest scaled models are introduced. The first scaled forest model is a periodic metal cut-wire array. The transmission data inside the cut-wire array are simulated and measured. The propagation mechanisms inside the array are extracted. Several interesting propagation phenomena associated with surface waves and leaky waves are observed and explained. Next, a dielectric rod array consisting of water-filled straws is investigated as a more realistic forest model. Water is chosen since its dielectric constant in the microwave range is close to that of tree trunks in the HF/VHF frequencies. The propagation mechanisms in the water rod array are investigated through scaled model measurements in the laboratory, numerical simulations and an effective medium theory. Randomization effects due to rod spacing and rod height on the propagation mechanisms are also studied. Finally, the transmission data in a real forest are collected in the HF/VHF frequency range to corroborate the findings from the models. The measurement site is located at Bastrop, Texas. For comparison, the transmission data are also measured in an open field. The transmission data are processed and the resulting propagation mechanisms are extracted and compared with the model predictions. As an extension of the propagation study, the potential to achieve directive antenna radiations in a forest is explored. A simple metal cut-wire array environment is considered for ease in modeling. For the case when both the transmit antenna and the receive antenna are embedded inside the array, two design ideas are presented. The first design tries to couple the antenna radiation into the dominant propagation mechanism through phase matching and the second design uses a closely spaced Yagi array to decouple the antenna from its surrounding medium. For the case when the transmit antenna is embedded inside the array and the receive antenna is located outside the array, the leaky wave mechanism is explored to achieve directive radiation. These designs are verified through theoretical predictions, numerical simulations and prototype measurements.Item Multiple-grid adaptive integral method for general multi-region problems(2011-08) Wu, Mingfeng; Yilmaz, Ali E.; Ling, Hao; Pearce, John; Alu, Andrea; Ying, LexingEfficient electromagnetic solvers based on surface integral equations (SIEs) are developed for the analysis of scattering from large-scale and complex composite structures that consist of piecewise homogeneous magnetodielectric and perfect electrically/magnetically conducting (PEC/PMC) regions. First, a multiple-grid extension of the adaptive integral method (AIM) is presented for multi-region problems. The proposed method accelerates the iterative method-of-moments solution of the pertinent SIEs by employing multiple auxiliary Cartesian grids: If the structure of interest is composed of K homogeneous regions, it introduces K different auxiliary grids. It uses the k^{th} auxiliary grid first to determine near-zones for the basis functions and then to execute AIM projection/anterpolation, propagation, interpolation, and near-zone pre-correction stages in the k^{th} region. Thus, the AIM stages are executed a total of K times using different grids and different groups of basis functions. The proposed multiple-grid AIM scheme requires a total of O(N^{nz,near}+sum({N_k}^Clog{N_k}^C)) operations per iteration, where N^{nz,near} denotes the total number of near-zone interactions in all regions and {N_k}^C denotes the number of nodes of the k^{th} Cartesian grid. Numerical results validate the method’s accuracy and reduced complexity for large-scale canonical structures with large numbers of regions (up to 10^6 degrees of freedom and 10^3 regions). Then, a Green function modification approach and a scheme of Hankel- to Teoplitz-matrix conversions are efficiently incorporated to the multiple-grid AIM method to account for a PEC/PMC plane. Theoretical analysis and numerical examples show that, compared to a brute-force imaging scheme, the Green function modification approach reduces the simulation time and memory requirement by a factor of (almost) two or larger if the structure of interest is terminated on or resides above the plane, respectively. In addition, the SIEs are extended to cover structures composed of metamaterial regions, PEC regions, and PEC-material junctions. Moreover, recently introduced well-conditioned SIEs are adopted to achieve faster iterative solver convergence. Comprehensive numerical tests are performed to evaluate the accuracy, computational complexity, and convergence of the novel formulation which is shown to significantly reduce the number of iterations and the overall computational work. Lastly, the efficiency and capabilities of the proposed solvers are demonstrated by solving complex scattering problems, specifically those pertinent to analysis of wave propagation in natural forested environments, the design of metamaterials, and the application of metamaterials to radar cross section reduction.Item On the response of rubbers at high strain rates(2009-12) Niemczura, Johnathan Greenberg; Ravi-Chandar, K.The purpose of this study is to examine the propagation of waves of finite deformation in rubbers through experiments and analysis. First, attention is focused on the propagation of one-dimensional dispersive waves in strips of latex and nitrile rubber. Tensile wave propagation experiments were conducted at high strain-rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in rubber strips. Analysis of the response through the theory of finite wave propagation indicated a need for an appropriate constitutive model for rubber; by quantitative matching between the experimental observations and analytical predictions, an appropriate instantaneous elastic response for the rubbers was obtained. This matching process suggested that a simple power-law constitutive model was capable of representing the high strain-rate response for both rubbers used. Next, the propagation of one-dimensional shock waves in strips of latex and nitrile rubber is examined. Shock waves have been generated under tensile impact in pre-stretched rubber strips; analysis of the response yields the tensile shock adiabat for rubbers. The propagation of shocks is analyzed by developing an analogy with the theory of detonation. Attention is then focused on the propagation of unloading waves of finite deformation in a rubber specimen analytically and experimentally. A rubber strip stretched to many times its initial length is released at one end and the resulting unloading is examined. Dispersive waves as well as shock waves are observed in these experiments. Quantitative discrepancies between the analytical model and experimental observations are again used to motivate a power-law model. Hysteresis in the response is attributed to strain-induced crystallization and melting phase transitions in natural latex rubber, and to nonequilibrium microstructural deformation in nitrile rubber. Finally, a Kolsky experiment is conducted and analyzed under the framework of dispersive loading and unloading waves utilized in the previous experiments. In this experiment, a phase boundary is introduced separating low and high strain phases of the rubber and is demonstrated to persist as a stationary boundary in latex rubber.Item Parallel-in-time methods for wave propagation in heterogeneous media(2020-05-13) Nguyen, Hieu Huu; Tsai, Yen-Hsi R.; Bui-Thanh, Tan; Engquist, Bjorn; Ghattas, Omar; Ren, KuiWave propagation is ubiquitous in science and engineering applications, but solving the second-order wave equation in a parallel way is still computationally challenging. Specifically, as efficiency gained from spatial domain decomposition is saturated, time-domain becomes the next candidate for parallelization. However, most parallel-in-time methods are not effective in solving hyperbolic problems, including the wave equation. Motivated by the simple parareal algorithm developed by Lion, Maday, and Turinici, we propose a new parallel scheme called [theta]-parareal that generalizes the original parareal. The convergence and stability analysis of the [theta]-parareal scheme reveal the deficiency of the parareal method when applying to highly oscillatory problems. We then develop a new parallel-in-time iterative method for solving the homogeneous second-order wave equation. The new approach is a data-driven strategy in which we use pre-computed data to stabilize the iteration by minimizing the wave energy residual. We propose two techniques, a linear algebra-based method, and a deep neural network method. Numerical examples, including a wave speed with discontinuities, are provided to demonstrate the effectiveness of the proposed methods on the wave equation.Item Relaxation in harmonic oscillator systems and wave propagation in negative index materials(2009-05) Chimonidou, Antonia; Sudarshan, E. C. G.This dissertation is divided up into two parts, each examining a distinct theme. The rst part of our work concerns itself with open quantum systems and the relaxation phenomena arising from the repeated application of an interaction Hamiltonian on systems composed of quantum harmonic oscillators. For the second part of our work, we shift gears and investigate the wave propagation in left-handed media, or materials with simultaneously negative electric permeability and magnetic permeability . Each of these two parts is complete within its own context. In the rst part of this dissertation, we introduce a relaxation-generating model which we use to study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to bipartite harmonic oscillator systems for some characteristic time interval . The two important time scales which enter our results are discussed in detail. We show that the relaxation time obtained by the application of this repeated interaction scheme is proportional to both the strength of interaction and to the characteristic time interval . Through discussing the implications of our model, we show that, for the case where the oscillator frequencies are equal, the initial Maxwell-Boltzmann distributions of the uncoupled parts evolve to a new Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann distributions, or quasi-stationary, non-equilibrium states. We further analyze the case in which the two oscillator frequencies are unequal and show how the application of the same model leads to a non-thermal steady state. The calculations are exact and the results are obtained through an iterative process, without using perturbation theory. In the second part of this dissertation, we examine the response of a plane wave incident on a at surface of a left-handed material, a medium characterized by simultaneously negative electric permittivity and magnetic permeability . We do this by solving Maxwell's equations explicitly. In the literature up to date, it has been assumed that negative refractive materials are necessarily frequency dispersive. We propose an alternative to this assumption by suggesting that the requirement of positive energy density can be relaxed, and discuss the implications of such a proposal. More speci cally, we show that once negative energy solutions are accepted, the requirement for frequency dispersion is no longer needed. We further argue that, for the purposes of discussing left-handed materials, the use of group velocity as the physically signi cant quantity is misleading, and suggest that any discussion involving it should be carefully reconsidered.Item Subsurface elastic wave energy focusing based on a time reversal concept(2017-06-12) Koo, Seungbum; Kallivokas, Loukas F; Fomel, Sergey B; Stokoe, Kenneth H; Demkowicz, Leszek F; Ghattas, Omar; Tassoulas, John LIn the context of wave propagation, time-reversal refers to the invariance of the wave equation when the direction of traversing the time line is reversed. To date, there have been several applications rooted in the time-reversal concept, primarily in acoustics and in electromagnetics, and in settings that typically involve closed, finite, domains. In recent times, the concept has been predominantly used for steering and focusing wave energy in medical therapeutics. The extension of the time-reversal concept to elastodynamics, particularly in unbounded domains, entails challenges: the presence of two velocities and two body wave types, the presence of surface waves, the unboundness of the host domain, and aperture constraints, all conspire to limit or weaken wave focusing. This dissertation concentrates on a computational study for assessing the feasibility of focusing elastic waves to one or multiple subsurface targets, based on the time-reversal concept. Of particular interest is the focusing of wave energy to subterranean geologic formations, embedded within heterogeneous hosts. The motivation stems from potential applications to wave-based enhanced oil recovery, though other applications also stand to benefit. We report on a study that systematically assesses each and every limitation that is present when a small number of surface motion records are time-reversed and broadcast back into a heterogenous halfspace, aimed at the illumination of subsurface targets. We report the results of numerical experiments in two and three dimensions, and the impact of the limitations on the focusing resolution. All in all, despite the difficulties imposed by the physical setting, we conclude that focusing of elastic wave energy is feasible and competitive when compared against inverse source methods with similar targeting or focusing goals.Item Topographic amplification of seismic motion(2017-05) Poursartip, Babak; Kallivokas, Loukas F.; Assimaki, Dominic; Demkowicz, Leszek F.; Manuel, Lance; Stokoe II, Kenneth H.; Tassoulas, John L.Seismic hazard assessment relies increasingly on the numerical simulation of ground motion, since recent advances in numerical methods and computer architectures have made it ever more practical to obtain the surface response to idealized or realistic seismic events. The key motivation stems from the need to assess the performance of sensitive components of the civil infrastructure (nuclear power plants, bridges, lifelines, etc.), when subjected to realistic scenarios of seismic events. To date, most simulation tools rely on a flat-earth assumption, which ignores topography and its effects on seismic motion amplification. In an attempt to narrow the gap between modeling and physical reality, in this dissertation we study systematically the effects topographic features have on the surface motion when compared against motion obtained using a at-surface assumption. To this end, we discuss first an integrated approach that deploys best-practice tools for simulating seismic events in arbitrarily heterogeneous formations, while also accounting for topography. Specifically, we describe an explicit forward wave solver based on a hybrid formulation that couples a single-field formulation for the computational domain with an unsplit mixed-field formulation for Perfectly-Matched-Layers (PMLs or M-PMLs) used to limit the computational domain. We use spectral elements for spatial discretization, and an efficient Runge-Kutta explicit solver for time integration. Due to the material heterogeneity and the contrasting discretization needs it imposes, we also use an adaptive Runge-Kutta-Fehlberg time-marching scheme to optimally adjust the time step so that the local truncation error rests below a predefined tolerance. To account for the seismic load, we use the Domain- Reduction-Method to introduce the incoming seismic motion in the computational domain whenever the introduction of the actual seismic source would make the computational domain unnecessarily large. Lastly, we couple the DRM with the PMLs to complete the seismic motion simulation engine. Using the developed toolchain, we then report results of parametric studies involving idealized topographic features, which show motion amplification that depends, as expected, on the relation between the topographic features' characteristics and the dominant wavelength. More interestingly, we also report motion de-amplification patterns. Given the prevalence of lower dimensionality models for seismic risk assessment, we also report on the effects model dimensionality has in the presence of heterogeneity and topography. The results reported herein, support the thesis that, for purposes of seismic risk assessment, topography and heterogeneity are best treated when fully accounted for in three-dimensional models. Even this is only a first and necessary step towards higher fidelity modeling of seismic motion effects.Item Viscoelastic wave propagation along a borehole using squirt flow and Biot poroelastic theory(2018-01-23) Dahl, Elliot Jeremy Hans; Spikes, Kyle; Torres-Verdin, Carlos; Sen, Mrinal; Mohrig, David; Daigle, HughObservations of seismic waves provide valuable understanding of Earth subsurface properties. These measurements are used to study large-scale subsurface features, kilometers in width, borehole-scale situations, meters of interest, and with core samples, a few centimeters in length. A common practice is to assume that the elastic rock-properties (P- and S-wave velocities) are the same for all frequencies. This is why sonic logs without corrections, for example, are used to constrain velocity models that transform seismic data from time to depth and to calibrate rock physics models used in seismic inversion to link elastic properties to reservoir properties. However, when seismic waves propagate in Earth materials, they are subject to different dispersion mechanisms, which makes the velocities frequency dependent. Understanding these effects on acoustic wave propagation can improve our models that constrain the subsurface and ultimately give us better hydrocarbon predictability. The main objective of this dissertation is to contribute to the understanding of how fluid in the pore space affects acoustic wave propagation. To achieve this goal, I first developed a frequency-dependent wave equation that accounts for local (squirt) and global (Biot) flow. The new model is tested against other squirt-Biot flow theories for both synthetic cases and utrasonic velocity data. I find the developed model to be consistent with the compared models in the synthetic cases. For the utrasonic velocity data, I find predictions from the new model to be closest to the measured data. In the second part of the dissertation, I use the developed squirt-Biot flow wave equation to simulate wave propagation in fluid-filled boreholes containing formations with different quantities of compliant pores. These are compared with formations where no compliant pores are present. I use the discrete wavenumber summation method with both a monopole and a dipole source to generate the wave fields. I find that fluid-saturated compliant pores can significantly affect the effective formation P- and S-wave velocities. This in turn affects the various acoustic wave modes causing increasing dispersion and attenuation. Thus, knowledge of the micro-scale structure of the fluid-saturated rock is of importance for understanding the acoustic waveforms and the dispersive behavior of the various modes. Depending on the locations where the critical frequencies for the different dispersion mechanisms occurs, acoustic velocity estimates can differ from the seismic-frequency velocities. Having a frequency dependent model accounting for the various dispersion mechanisms can help better connect the various velocity measurements and ultimately serve to give us an even more realistic picture of the subsurface.