On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography. The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

SAR imaging of buried objects from MoM modelled scattered field

Synthetic aperture radar (SAR) images of resonant buried objects are modelled in the presence of ground surface clutter. The method of moments (MoM) is used to model scattered fields from a resonant buried conductor and clutter is modelled as a bivariant Gaussian distribution. A diffraction stack SAR imaging technique is applied to the ultra-wideband waveforms to give a bipolar signal image. A number of examples have been computed to illustrate the combined effects of SAR processing with resonant targets and clutter. SAR images of different targets show differences which may facilitate target identification. To maximise the peak signal-to-clutter ratio, an image correlation technique is applied and the results are shown.

Ultraschallspektroskopie an fokussierenden Systemen unter Berücksichtigung vorgelagerter absorbierender Schichten

Ultrasound, ultrasonic, soundfield, layered Media, intramuscular fat content

Frequency-dependent attenuation as a potential indicator of oil saturation

At seismic frequencies, wave-induced fluid flow is a major cause of P-wave attenuation in partially saturated porous rocks. Attenuation is of great importance for the oil industry in the interpretation of seismic field data. Here, the effects on P-wave attenuation resulting from changes in oil saturation are studied for media with coexisting water, oil, and gas. For that, creep experiments are numerically simulated by solving Biot's equations for consolidation of poroelastic media with the finite-element method. The experiments yield time-dependent stress?strain relations that are used to calculate the complex P-wave modulus from which frequency-dependent P-wave attenuation is determined. The models are layered media with periodically alternating triplets of layers. Models consisting of triplets of layers having randomly varying layer thicknesses are also considered. The layers in each triplet are fully saturated with water, oil, and gas. The layer saturated with water has lower porosity and permeability than the layers saturated with oil and gas. These models represent hydrocarbon reservoirs in which water is the wetting fluid preferentially saturating regions of lower porosity. The results from the numerical experiments showed that increasing oil saturation, connected to a decrease in gas saturation, resulted in a significant increase of attenuation at low frequencies (lower than 2 Hz). Furthermore, replacing the oil with water resulted in a distinguishable behavior of the frequency-dependent attenuation. These results imply that, according to the physical mechanism of wave-induced fluid flow, frequency-dependent attenuation in media saturated with water, oil, and gas is a potential indicator of oil saturation.

Seismic characterization of heterogeneous sedimentary and fractured rocks based on Biot's theory of poroelasticity

Understanding and quantifying seismic energy dissipation, which manifests itself in terms of velocity dispersion and attenuation, in fluid-saturated porous rocks is of considerable interest, since it offers the perspective of extracting information with regard to the elastic and hydraulic rock properties. There is increasing evidence to suggest that wave-induced fluid flow, or simply WIFF, is the dominant underlying physical mechanism governing these phenomena throughout the seismic, sonic, and ultrasonic frequency ranges. This mechanism, which can prevail at the microscopic, mesoscopic, and macroscopic scale ranges, operates through viscous energy dissipation in response to fluid pressure gradients and inertial effects induced by the passing wavefield. In the first part of this thesis, we present an analysis of broad-band multi-frequency sonic log data from a borehole penetrating water-saturated unconsolidated glacio-fluvial sediments. An inherent complication arising in the interpretation of the observed P-wave attenuation and velocity dispersion is, however, that the relative importance of WIFF at the various scales is unknown and difficult to unravel. An important generic result of our work is that the levels of attenuation and velocity dispersion due to the presence of mesoscopic heterogeneities in water-saturated unconsolidated clastic sediments are expected to be largely negligible. Conversely, WIFF at the macroscopic scale allows for explaining most of the considered data while refinements provided by including WIFF at the microscopic scale in the analysis are locally meaningful. Using a Monte-Carlo-type inversion approach, we compare the capability of the different models describing WIFF at the macroscopic and microscopic scales with regard to their ability to constrain the dry frame elastic moduli and the permeability as well as their local probability distribution. In the second part of this thesis, we explore the issue of determining the size of a representative elementary volume (REV) arising in the numerical upscaling procedures of effective seismic velocity dispersion and attenuation of heterogeneous media. To this end, we focus on a set of idealized synthetic rock samples characterized by the presence of layers, fractures or patchy saturation in the mesocopic scale range. These scenarios are highly pertinent because they tend to be associated with very high levels of velocity dispersion and attenuation caused by WIFF in the mesoscopic scale range. The problem of determining the REV size for generic heterogeneous rocks is extremely complex and entirely unexplored in the given context. In this pilot study, we have therefore focused on periodic media, which assures the inherent self- similarity of the considered samples regardless of their size and thus simplifies the problem to a systematic analysis of the dependence of the REV size on the applied boundary conditions in the numerical simulations. Our results demonstrate that boundary condition effects are absent for layered media and negligible in the presence of patchy saturation, thus resulting in minimum REV sizes. Conversely, strong boundary condition effects arise in the presence of a periodic distribution of finite-length fractures, thus leading to large REV sizes. In the third part of the thesis, we propose a novel effective poroelastic model for periodic media characterized by mesoscopic layering, which accounts for WIFF at both the macroscopic and mesoscopic scales as well as for the anisotropy associated with the layering. Correspondingly, this model correctly predicts the existence of the fast and slow P-waves as well as quasi and pure S-waves for any direction of wave propagation as long as the corresponding wavelengths are much larger than the layer thicknesses. The primary motivation for this work is that, for formations of intermediate to high permeability, such as, for example, unconsolidated sediments, clean sandstones, or fractured rocks, these two WIFF mechanisms may prevail at similar frequencies. This scenario, which can be expected rather common, cannot be accounted for by existing models for layered porous media. Comparisons of analytical solutions of the P- and S-wave phase velocities and inverse quality factors for wave propagation perpendicular to the layering with those obtained from numerical simulations based on a ID finite-element solution of the poroelastic equations of motion show very good agreement as long as the assumption of long wavelengths remains valid. A limitation of the proposed model is its inability to account for inertial effects in mesoscopic WIFF when both WIFF mechanisms prevail at similar frequencies. Our results do, however, also indicate that the associated error is likely to be relatively small, as, even at frequencies at which both inertial and scattering effects are expected to be at play, the proposed model provides a solution that is remarkably close to its numerical benchmark. -- Comprendre et pouvoir quantifier la dissipation d'énergie sismique qui se traduit par la dispersion et l'atténuation des vitesses dans les roches poreuses et saturées en fluide est un intérêt primordial pour obtenir des informations à propos des propriétés élastique et hydraulique des roches en question. De plus en plus d'études montrent que le déplacement relatif du fluide par rapport au solide induit par le passage de l'onde (wave induced fluid flow en anglais, dont on gardera ici l'abréviation largement utilisée, WIFF), représente le principal mécanisme physique qui régit ces phénomènes, pour la gamme des fréquences sismiques, sonique et jusqu'à l'ultrasonique. Ce mécanisme, qui prédomine aux échelles microscopique, mésoscopique et macroscopique, est lié à la dissipation d'énergie visqueuse résultant des gradients de pression de fluide et des effets inertiels induits par le passage du champ d'onde. Dans la première partie de cette thèse, nous présentons une analyse de données de diagraphie acoustique à large bande et multifréquences, issues d'un forage réalisé dans des sédiments glaciaux-fluviaux, non-consolidés et saturés en eau. La difficulté inhérente à l'interprétation de l'atténuation et de la dispersion des vitesses des ondes P observées, est que l'importance des WIFF aux différentes échelles est inconnue et difficile à quantifier. Notre étude montre que l'on peut négliger le taux d'atténuation et de dispersion des vitesses dû à la présence d'hétérogénéités à l'échelle mésoscopique dans des sédiments clastiques, non- consolidés et saturés en eau. A l'inverse, les WIFF à l'échelle macroscopique expliquent la plupart des données, tandis que les précisions apportées par les WIFF à l'échelle microscopique sont localement significatives. En utilisant une méthode d'inversion du type Monte-Carlo, nous avons comparé, pour les deux modèles WIFF aux échelles macroscopique et microscopique, leur capacité à contraindre les modules élastiques de la matrice sèche et la perméabilité ainsi que leur distribution de probabilité locale. Dans une seconde partie de cette thèse, nous cherchons une solution pour déterminer la dimension d'un volume élémentaire représentatif (noté VER). Cette problématique se pose dans les procédures numériques de changement d'échelle pour déterminer l'atténuation effective et la dispersion effective de la vitesse sismique dans un milieu hétérogène. Pour ce faire, nous nous concentrons sur un ensemble d'échantillons de roches synthétiques idéalisés incluant des strates, des fissures, ou une saturation partielle à l'échelle mésoscopique. Ces scénarios sont hautement pertinents, car ils sont associés à un taux très élevé d'atténuation et de dispersion des vitesses causé par les WIFF à l'échelle mésoscopique. L'enjeu de déterminer la dimension d'un VER pour une roche hétérogène est très complexe et encore inexploré dans le contexte actuel. Dans cette étude-pilote, nous nous focalisons sur des milieux périodiques, qui assurent l'autosimilarité des échantillons considérés indépendamment de leur taille. Ainsi, nous simplifions le problème à une analyse systématique de la dépendance de la dimension des VER aux conditions aux limites appliquées. Nos résultats indiquent que les effets des conditions aux limites sont absents pour un milieu stratifié, et négligeables pour un milieu à saturation partielle : cela résultant à des dimensions petites des VER. Au contraire, de forts effets des conditions aux limites apparaissent dans les milieux présentant une distribution périodique de fissures de taille finie : cela conduisant à de grandes dimensions des VER. Dans la troisième partie de cette thèse, nous proposons un nouveau modèle poro- élastique effectif, pour les milieux périodiques caractérisés par une stratification mésoscopique, qui prendra en compte les WIFF à la fois aux échelles mésoscopique et macroscopique, ainsi que l'anisotropie associée à ces strates. Ce modèle prédit alors avec exactitude l'existence des ondes P rapides et lentes ainsi que les quasis et pures ondes S, pour toutes les directions de propagation de l'onde, tant que la longueur d'onde correspondante est bien plus grande que l'épaisseur de la strate. L'intérêt principal de ce travail est que, pour les formations à perméabilité moyenne à élevée, comme, par exemple, les sédiments non- consolidés, les grès ou encore les roches fissurées, ces deux mécanismes d'WIFF peuvent avoir lieu à des fréquences similaires. Or, ce scénario, qui est assez commun, n'est pas décrit par les modèles existants pour les milieux poreux stratifiés. Les comparaisons des solutions analytiques des vitesses des ondes P et S et de l'atténuation de la propagation des ondes perpendiculaires à la stratification, avec les solutions obtenues à partir de simulations numériques en éléments finis, fondées sur une solution obtenue en 1D des équations poro- élastiques, montrent un très bon accord, tant que l'hypothèse des grandes longueurs d'onde reste valable. Il y a cependant une limitation de ce modèle qui est liée à son incapacité à prendre en compte les effets inertiels dans les WIFF mésoscopiques quand les deux mécanismes d'WIFF prédominent à des fréquences similaires. Néanmoins, nos résultats montrent aussi que l'erreur associée est relativement faible, même à des fréquences à laquelle sont attendus les deux effets d'inertie et de diffusion, indiquant que le modèle proposé fournit une solution qui est remarquablement proche de sa référence numérique.

Modelagem de dados MT 2D em multicamadas com anisotropia arbitrária

Neste trabalho apresentamos a modelagem direta bidimensional do método Magnetotelúrico (MT) com anisotropia arbitrária na condutividade elétrica para modelos de multicamadas estratificadas horizontalmente, separando a resposta do campo resultante em duas partes, primária e secundária. A parte primária refere-se ao campo 1D do modelo na ausência de heterogeneidades; a secundária, à contribuição no campo resultante gerada pela anomalia. Esta modelagem foi feita via técnica numérica dos Elementos Finitos (EF). Apresentamos também a modelagem direta do caso MT 1D para o mesmo modelo e anisotropia arbitrária, porém, com solução analítica pelo método da matriz de propagação; tal resultado é usado como fonte na formulação 2D. No estudo a respeito do comportamento dos campos 1D em profundidade na presença da anisotropia, verificamos nas componentes horizontais que suas curvas dentro de cada camada se assemelham a de um campo na presença de fontes, pois experimentam um aumento na amplitude; além de verificar o surgimento da componente normal E_z do campo, sem que haja uma densidade de corrente nesta direção. Com arbitrariedade na anisotropia queremos dizer que seus eixos principais podem assumir qualquer orientação em relação ao eixo de referência adotado para o problema; tal orientação é descrita sob três rotações consecutivas, chamadas de strike, dip e slant, que simulam inclinações bastante presentes na geologia dos ambientes terrestres. Verificamos que a anisotropia provoca alterações no comportamento das pseudo-seções de resistividades aparentes, interferindo na interpretação correta dos dados.

Dynamic impedances of bridge abutments

The soil-structure interaction at bridge abutments may introduce important changes in the dynamic properties of short to medium span bridges. The paper presents the results obtained, through the use of the Boundary Element Method (B.E.M.) technique in several typical situations, including semiinfinite and layered media. Both stiffness and damping properties are included.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Finite element analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (C) 2000 Elsevier Science S.A. All rights reserved.

Capacity-approaching rate function for layered multiantenna architectures

The simultaneous use of multiple transmit and receive antennas can unleash very large capacity increases in rich multipath environments. Although such capacities can be approached by layered multi-antenna architectures with per-antenna rate control, the need for short-term feedback arises as a potential impediment, in particular as the number of antennas—and thus the number of rates to be controlled—increases. What we show, however, is that the need for short-term feedback in fact vanishes as the number of antennas and/or the diversity order increases. Specifically, the rate supported by each transmit antenna becomes deterministic and a sole function of the signal-to-noise, the ratio of transmit and receive antennas, and the decoding order, all of which are either fixed or slowly varying. More generally, we illustrate -through this specific derivation— the relevance of some established random CDMA results to the single-user multi-antenna problem.

Per-antenna rate and power control for MIMO layered architectures in the low- and high-power regimes

In a MIMO layered architecture, several codewordsare transmitted from a multiplicity of antennas. Although thespectral efficiency is maximized if the rates of these codewordsare separately controlled, the feedback rate within the linkadaptation loop is reduced if they are constrained to be identical.This poses a direct tradeoff between performance andfeedback overhead. This paper provides analytical expressionsthat quantify the difference in spectral efficiency between bothapproaches for arbitrary numbers of antennas. Specifically, thecharacterization takes place in the realm of the low- and highpowerregimes via expansions that are shown to have a widerange of validity.In addition, the possibility of adjusting the transmit powerof each codeword individually is considered as an alternative tothe separate control of their rates. Power allocation, however,turns out to be inferior to rate control within the context of thisproblem.

Handling of TDM Connections with Cello Media Gateway

UMTS is a 3rd generation telecommunication system, which introduces new network architecture. The change in the network architecture introduces new logical network nodes and changes the role of existing nodes in the network. This architecture changes the current vertically specialized network into a horizontally layered structure. In practice, the layering means that different levels in network hierarchy are separated, and they communicate over well-specified interfaces. The Connectivity Layer, at the bottom of the UMTS network architecture, contains Media Gateways (MGW). The GSM radio access network and UMTS access network are connected to the connectivity network via a MGW. External networks, e.g. ISDN networks, are accessed via other MGWs. The user plane is transported across the connectivity network between/via MGWs. ATM network is used as the backbone in Ericsson’s UMTS core network release 2.0. The main goal of this thesis is to study how the MGW is used to bridge ATM and TDM networks. The Circuit Emulation Service (CES) for ATM is studied, as the conversion from TDM to ATM is made according it. The transportation is made using AAL2 and the issues that it has with voice traffic are studied. The implementation and usage of TDM switching service in MGW are described in detail.