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Wave Propagation (wave + propagation)
Terms modified by Wave Propagation Selected AbstractsWave propagation in an inhomogeneous cross-anisotropic mediumINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010Cheng-Der Wang Abstract Analytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E,) and shear modulus (G,) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, , and ,, remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain,displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, VP, VSV, and VSH, and the wave vectors, , and , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E,, G,/E,, and ,/,,); and (3) the phase angle, ,. Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium. Copyright © 2009 John Wiley & Sons, Ltd. [source] Wave propagation in nonlinear one-dimensional soil modelINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2009J. Ahn Abstract The objective of the research conducted by the authors is to explore the feasibility of determining reliable in situ values of shear modulus as a function of strain. In this paper the meaning of the material stiffness obtained from impact and harmonic excitation tests on a surface slab is discussed. A one-dimensional discrete model with the nonlinear material stiffness is used for this purpose. When a static load is applied followed by an impact excitation, if the amplitude of the impact is very small, the measured wave velocity using the cross-correlation indicates the wave velocity calculated from the tangent modulus corresponding to the state of stress caused by the applied static load. The duration of the impact affects the magnitude of the displacement and the particle velocity but has very little effect on the estimation of the wave velocity for the magnitudes considered herein. When a harmonic excitation is applied, the cross-correlation of the time histories at different depths estimates a wave velocity close to the one calculated from the secant modulus in the stress,strain loop under steady-state condition. Copyright © 2008 John Wiley & Sons, Ltd. [source] Analysis and design of band-pass frequency-selective surfaces using the FEM CAD toolINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 5 2004P. T. Teo Abstract Three-dimensional (3D) full-wave analysis and design of bandpass frequency-selective surfaces (FSSs) is presented. By using the unique features of a unit cell and the periodic boundary conditions, infinite FSSs can be simulated. Wave propagation through FSSs, which is otherwise difficult to quantify, can be visualised by using a commercial CAD tool. The creation of the simulation model, interpretation and analysis of the outcome, and comparison with experimental results are presented for the square-slot and the square-loop-slot band-pass FSS. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 391,397, 2004. [source] Damage Detection by Wave Propagation Observation with Laser SpeckleInterferometryPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Alexander Schmidt For quality insurance and fault detection, one and three dimensional ESPI (Electronic Speckle Pattern Interferometry) technique is applied to various structures. These experiments are an extension of previous experiments with Holographic Interferometry [4], a related measurement technique. ESPI is a non contact, high resolution Laser measurement technique. It facilitates transient full field vibration measurements that deliver absolute deflections, either one dimensional out-of-plane or three dimensional in and out-of-plane. Experiments have been performed with a full scale concrete embedded track segment. Different known artificial defects represent various flaws and voids due to the fabrication process and operation. Wave propagation due to impact is observed and allows for damage detection. ESPI measurements are in good accordance with expectations. An in-situ measurement setup for quality management of concrete embedded railway tracks has been built. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Structural seismic response analysis based on multiscale approach of computing fault,structure systemEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2009T. Ichimura Abstract Structural safety for earthquake waves emitted from a nearby fault is a major concern. For a large complex structure, it might be desired to estimate its seismic response by analyzing a fault,structure system: a full three-dimensional model in which a source fault and a target structure are modeled so that fault processes, wave propagation and amplification processes, and resulting dynamic responses of the structure can be computed numerically. To analyze this fault,structure system, this paper proposes an efficient approach based on multiscale analysis, i.e. waves emitted from the source fault are computed in the entire system in the geological length-scale; then they are refined in a small part of the system that includes the structure, and the seismic response of the structure is accurately computed in the engineering length-scale. Using a long highway tunnel as an example, this paper examines the validity of the proposed approach. The usefulness and applicability of the proposed approach to estimate the structural seismic responses are discussed. Copyright © 2008 John Wiley & Sons, Ltd. [source] Macro,micro analysis method for wave propagation in stochastic mediaEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2006T. Ichimura Abstract This paper presents a new analysis method, called macro,micro analysis method (MMAM) for numerical simulation of wave propagation in stochastic media, which could be used to predict distribution of earthquake strong motion with high accuracy and spatial resolution. This MMAM takes advantage of the bounding medium theory (BMT) and the singular perturbation expansion (SPE). BMT can resolve uncertainty of soil and crust structures by obtaining optimistic and pessimistic estimates of expected strong motion distribution. SPE leads to efficient multi-scale analysis for reducing a huge amount of computation. The MMAM solution is given as the sum of waves of low resolution covering a whole city and waves of high resolution for each city portion. This paper presents BMT and SPE along with the formulation of MMAM for wave propagation in three-dimensional elastic media. Application examples are presented to verify the validity of the MMAM and demonstrate potential usefulness of this approach. In a companion paper (Earthquake Engng. Struct. Dyn., this issue) application examples of earthquake strong motion prediction are also presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] Porous TiNi Biomaterial by Self-Propagating High-Temperature Synthesis,ADVANCED ENGINEERING MATERIALS, Issue 6 2004J.S. Kim Abstract Porous TiNi shape-memory alloy (TiNi SMA) bodies with controlled pore structure were produced from the (Ti+Ni) powder mixture by self-propagating high-temperature synthesis (SHS) method. The effect of processing variables such as the kind of starting powders, ignition temperature and preheating schedule on the behavior of combustion wave propagation, the formation of phases and pore structure was investigated. The relationship between pore structure and mechanical properties was also investigated. An in vivo test was performed to evaluate bone tissue response and histocompatibility of porous TiNi SMA using 15 New Zealand white rabbits. No apparent adverse reactions such as inflammation and foreign body reaction were noted on or around all implanted porous TiNi SMA blocks. Bone ingrowth was found in the pore space of all implanted blocks. [source] Theoretical and Applied Case Studies of Seismic Imaging in TunnellingGEOMECHANICS AND TUNNELLING, Issue 5 2008Thomas Dickmann Dr. Seismic measurements during tunnel operations aim at images of maximum spatial resolution. However, there are still principal limitations of the method applied in the tunnel with regard to spatial resolution by the signal frequency and attenuation and by the small angular illumination coverage. A finite-difference simulation of elastic wave propagation had been performed to compute a synthetic tunnel seismic reflection survey. Synthetic data are used optimizing the best practice tunnel data processing sequence for both P- and S-waves because every step between the acquisition of the seismic data and the derivation of the final image influences the final seismic resolution. Here, especially the use of attenuation models compensate amplitude loss as well as dispersion by an inverse Q-filtering and the use of a spatially variable velocity model yielding the right image position of a reflecting geological element in space. The transfer and capability of this practice to real tunnel application is finally demonstrated by the case study of the tunnel seismic prediction method in the Koralm tunnel project in Austria. Theoretische und praktische Fallbeispiele der seismischen Abbildung im Tunnelbau Seismische Messungen während der Tunnelbauausführungen sollen eine Abbildung von maximaler räumlicher Auflösung erzielen. Allerdings gibt es immer noch grundsätzliche Einschränkungen hinsichtlich räumlicher Auflösung aufgrund von Signalfrequenz und -dämpfung und aufgrund des eingeschränkten Winkelbereichs des Beleuchtungsraums, wenn die Methode aus dem Tunnel heraus nach vorne angewendet wird. Es wurde eine Finite-Differenzen Simulation der elastischen Wellenausbreitung durchgeführt, um synthetische tunnelseismische Reflexionsdaten zu erhalten. Diese synthetischen Daten dienten dazu, die optimale Bearbeitungsfolge von P- und S-Wellendaten aus dem Tunnel abzuleiten, da jeder einzelne Bearbeitungsschritt zwischen der seismischen Datenaufnahme und der Endabbildung die endgültige seismische Auflösung beeinflusst. Hierbei kompensiert besonders die Anwendung eines Dämpfungsmodels mittels eines inversen Q-Filters und eines räumlich variablen Geschwindigkeitsmodels den Verlust von Amplitudenstärke und die Dispersion, was zu einer richtigen räumlichen Abbildungsposition des Reflektors eines geologischen Elementes führt. Die Leistungsfähigkeit dieser Vorgehensweise und deren Übertragung auf die wirkliche Tunnelanwendung werden schließlich durch das Beispiel der tunnelseismischen Vorauserkundung am Koralmtunnel in Österreich demonstriert. [source] Required source distribution for interferometry of waves and diffusive fieldsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2009Yuanzhong Fan SUMMARY The Green's function that describes wave propagation between two receivers can be reconstructed by cross-correlation provided that the receivers are surrounded by sources on a closed surface. This technique is referred to as ,interferometry' in exploration seismology. The same technique for Green's function extraction can be applied to the solution of the diffusion equation if there are sources throughout in the volume. In practice, we have only a finite number of active sources. The issues of the required source distribution is investigated, as is the feasibility of reconstructing the Green's function of the diffusion equation using a limited number of sources within a finite volume. We study these questions for homogeneous and heterogeneous media for wave propagation and homogeneous media for diffusion using numerical simulations. These simulations show that for the used model, the angular distribution of sources is critical in wave problems in homogeneous media. In heterogeneous media, the position and size of the heterogeneous area with respect to the sources determine the required source distribution. For diffusion, the sensitivity to the sources decays from the midpoint between the two receivers. The required width of the source distribution decreases with frequency, with the result that the required source distribution for early- and late-time reconstruction is different. The derived source distribution criterion for diffusion suggests that the cross-correlation-based interferometry is difficult to apply in field condition. [source] Spectral-element simulations of wave propagation in porous mediaGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2008Christina Morency SUMMARY We present a derivation of the equations describing wave propagation in porous media based upon an averaging technique which accommodates the transition from the microscopic to the macroscopic scale. We demonstrate that the governing macroscopic equations determined by Biot remain valid for media with gradients in porosity. In such media, the well-known expression for the change in porosity, or the change in the fluid content of the pores, acquires two extra terms involving the porosity gradient. One fundamental result of Biot's theory is the prediction of a second compressional wave, often referred to as ,type II' or ,Biot's slow compressional wave', in addition to the classical fast compressional and shear waves. We present a numerical implementation of the Biot equations for 2-D problems based upon the spectral-element method (SEM) that clearly illustrates the existence of these three types of waves as well as their interactions at discontinuities. As in the elastic and acoustic cases, poroelastic wave propagation based upon the SEM involves a diagonal mass matrix, which leads to explicit time integration schemes that are well suited to simulations on parallel computers. Effects associated with physical dispersion and attenuation and frequency-dependent viscous resistance are accommodated based upon a memory variable approach. We perform various benchmarks involving poroelastic wave propagation and acoustic,poroelastic and poroelastic,poroelastic discontinuities, and we discuss the boundary conditions used to deal with these discontinuities based upon domain decomposition. We show potential applications of the method related to wave propagation in compacted sediments, as one encounters in the petroleum industry, and to detect the seismic signature of buried landmines and unexploded ordnance. [source] Body-wave traveltime and amplitude shifts from asymptotic travelling wave couplingGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2006F. Pollitz SUMMARY We explore the sensitivity of finite-frequency body-wave traveltimes and amplitudes to perturbations in 3-D seismic velocity structure relative to a spherically symmetric model. Using the approach of coupled travelling wave theory, we consider the effect of a structural perturbation on an isolated portion of the seismogram. By convolving the spectrum of the differential seismogram with the spectrum of a narrow window taper, and using a Taylor's series expansion for wavenumber as a function of frequency on a mode dispersion branch, we derive semi-analytic expressions for the sensitivity kernels. Far-field effects of wave interactions with the free surface or internal discontinuities are implicitly included, as are wave conversions upon scattering. The kernels may be computed rapidly for the purpose of structural inversions. We give examples of traveltime sensitivity kernels for regional wave propagation at 1 Hz. For the direct SV wave in a simple crustal velocity model, they are generally complicated because of interfering waves generated by interactions with the free surface and the Mohorovi,i, discontinuity. A large part of the interference effects may be eliminated by restricting the travelling wave basis set to those waves within a certain range of horizontal phase velocity. [source] Regional tomographic inversion of the amplitude and phase of Rayleigh waves with 2-D sensitivity kernelsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2006Yingjie Yang SUMMARY In this study, we test the adequacy of 2-D sensitivity kernels for fundamental-mode Rayleigh waves based on the single-scattering (Born) approximation to account for the effects of heterogeneous structure on the wavefield in a regional surface wave study. The calculated phase and amplitude data using the 2-D sensitivity kernels are compared to phase and amplitude data obtained from seismic waveforms synthesized by the pseudo-spectral method for plane Rayleigh waves propagating through heterogeneous structure. We find that the kernels can accurately predict the perturbation of the wavefield even when the size of anomaly is larger than one wavelength. The only exception is a systematic bias in the amplitude within the anomaly itself due to a site response. An inversion method of surface wave tomography based on the sensitivity kernels is developed and applied to synthesized data obtained from a numerical simulation modelling Rayleigh wave propagation over checkerboard structure. By comparing recovered images to input structure, we illustrate that the method can almost completely recover anomalies within an array of stations when the size of the anomalies is larger than or close to one wavelength of the surface waves. Surface wave amplitude contains important information about Earth structure and should be inverted together with phase data in surface wave tomography. [source] A one-way wave equation for modelling seismic waveform variations due to elastic heterogeneityGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2005D. A. Angus SUMMARY The application of a new one-way narrow-angle elastic wave equation to isotropic heterogeneous media is described. This narrow-angle finite-difference propagator should provide an efficient and accurate method of simulating primary body wave(s) passing through smoothly varying heterogeneous media. Although computationally slower than ray theory, the narrow-angle propagator can model frequency-dependent forward diffraction and scattering as well as the averaging effects due to smooth variations in medium parameters that vary on the sub-Fresnel zone level. Example waveforms are presented for the propagation of body waves in deterministic as well as stochastic heterogeneous 3-D Earth models. Extrapolation within deterministic media will highlight various familiar wave-diffraction and pulse-distortion effects associated with large-scale inhomogeneities, such as geometrical spreading, wavefront folding and creeping-wave diffraction by a compact object. Simulation within stochastic media will examine the effects of varying the correlation lengths of random heterogeneities on wave propagation. In particular, wave phenomena such as frequency-dependent forward scattering, the appearance of random caustics and the generation of seismic coda will be shown. [source] Numerical modelling method for wave propagation in a linear viscoelastic medium with singular memoryGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2004Jian-Fei Lu SUMMARY A numerical modelling method for wave propagation in a linear viscoelastic medium with singular memory is developed in this paper. For a demonstration of the method, the Cole,Cole model of viscoelastic relaxation is adopted here. A formulation of the Cole,Cole model based on internal variables satisfying fractional relaxation equations is applied. In order to avoid integrating and storing of the entire history of the variables, a new method for solving fractional differential equations of arbitrary order based on a set of secondary internal variables is developed. Using the new method, the velocity,stress equations and the fractional relaxation equations are reduced to a system of first-order ordinary differential equations for the velocities, stresses, primary internal variables as well as the secondary internal variables. The horizontal spatial derivatives involved in the governing equations are calculated by the Fourier pseudo-spectral (PS) method, while the vertical ones are calculated by the Chebychev PS method. The physical boundary conditions and the non-reflecting conditions for the Chebychev PS method are also discussed. The global solution of the first-order system of ordinary differential equations is advanced in time by the Euler predictor,corrector methods. For the demonstration of our method, some numerical results are presented. [source] A deterministic seismic hazard map of India and adjacent areasGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2003Imtiyaz A. Parvez SUMMARY A seismic hazard map of the territory of India and adjacent areas has been prepared using a deterministic approach based on the computation of synthetic seismograms complete with all main phases. The input data set consists of structural models, seismogenic zones, focal mechanisms and earthquake catalogues. There are few probabilistic hazard maps available for the Indian subcontinent, however, this is the first study aimed at producing a deterministic seismic hazard map for the Indian region using realistic strong ground motion modelling with the knowledge of the physical process of earthquake generation, the level of seismicity and wave propagation in anelastic media. Synthetic seismograms at a frequency of 1 Hz have been generated at a regular grid of 0.2°× 0.2° by the modal summation technique. The seismic hazard, expressed in terms of maximum displacement (Dmax), maximum velocity (Vmax), and design ground acceleration (DGA), has been extracted from the synthetic signals and mapped on a regular grid over the studied territory. The estimated values of the peak ground acceleration are compared with the observed data available for the Himalayan region and are found to be in agreement. Many parts of the Himalayan region have DGA values exceeding 0.6 g. The epicentral areas of the great Assam earthquakes of 1897 and 1950 in northeast India represent the maximum hazard with DGA values reaching 1.2,1.3 g. The peak velocity and displacement in the same region is estimated as 120,177 cm s,1 and 60,90 cm, respectively. [source] Traveltime approximation for a reflected wave in a homogeneous anisotropic elastic layerGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002M. Zillmer Summary An approximation to the traveltime field is calculated for an elastic wave that propagates in a homogeneous anisotropic layer and is reflected at a plane boundary. The traveltime is approximated by a Taylor series expansion with the third derivative of the traveltime being taken into account. The coefficients of the series refer to the seismic ray, which is locally the fastest ray. Simple formulae are obtained for orthorhombic media in the crystal coordinate system, which relate the traveltimes of the reflected waves to the elastic constants of the medium. A numerical example is presented for wave propagation in orthorhombic olivine, which is a constituent of the Earth's mantle. A second example is given by an isotropic host rock with a set of parallel cracks, which is an important model for wave propagation in the Earth's crust. The elastic parameters can be determined by measuring the reflection times as a function of source,receiver offset. The approximate traveltime,distance curves are compared with traveltimes obtained from seismic ray tracing. [source] Spectral-element simulations of global seismic wave propagation,II.GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2002Three-dimensional models, oceans, rotation, self-gravitation Summary We simulate global seismic wave propagation based upon a spectral-element method. We include the full complexity of 3-D Earth models, i.e. lateral variations in compressional-wave velocity, shear-wave velocity and density, a 3-D crustal model, ellipticity, as well as topography and bathymetry. We also include the effects of the oceans, rotation and self-gravitation in the context of the Cowling approximation. For the oceans we introduce a formulation based upon an equivalent load in which the oceans do not need to be meshed explicitly. Some of these effects, which are often considered negligible in global seismology, can in fact play a significant role for certain source,receiver configurations. Anisotropy and attenuation, which were introduced and validated in a previous paper, are also incorporated in this study. The complex phenomena that are taken into account are introduced in such a way that we preserve the main advantages of the spectral-element method, which are an exactly diagonal mass matrix and very high computational efficiency on parallel computers. For self-gravitation and the oceans we benchmark spectral-element synthetic seismograms against normal-mode synthetics for the spherically symmetric reference model PREM. The two methods are in excellent agreement for all body- and surface-wave arrivals with periods greater than about 20 s in the case of self-gravitation and 25 s in the case of the oceans. At long periods the effect of gravity on multiorbit surface waves up to R4 is correctly reproduced. We subsequently present results of simulations for two real earthquakes in fully 3-D Earth models for which the fit to the data is significantly improved compared with classical normal-mode calculations based upon PREM. For example, we show that for trans-Pacific paths the Rayleigh wave can arrive more than a minute earlier than in PREM, and that the Love wave is much shorter in duration. [source] Migration velocity analysis and waveform inversionGEOPHYSICAL PROSPECTING, Issue 6 2008William W. Symes ABSTRACT Least-squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long-scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single-scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey-sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey-sinking (depth-oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning-based (surface-oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth-oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model-based data fitting. [source] Diffraction imaging in depthGEOPHYSICAL PROSPECTING, Issue 5 2008T.J. Moser ABSTRACT High resolution imaging is of great value to an interpreter, for instance to enable identification of small scale faults, and to locate formation pinch-out positions. Standard approaches to obtain high-resolution information, such as coherency analysis and structure-oriented filters, derive attributes from stacked, migrated images. Since they are image-driven, these techniques are sensitive to artifacts due to an inadequate migration velocity; in fact the attribute derivation is not based on the physics of wave propagation. Diffracted waves on the other hand have been recognized as physically reliable carriers of high- or even super-resolution structural information. However, high-resolution information, encoded in diffractions, is generally lost during the conventional processing sequence, indeed migration kernels in current migration algorithms are biased against diffractions. We propose here methods for a diffraction-based, data-oriented approach to image resolution. We also demonstrate the different behaviour of diffractions compared to specular reflections and how this can be leveraged to assess characteristics of subsurface features. In this way a rough surface such as a fault plane or unconformity may be distinguishable on a diffraction image and not on a traditional reflection image. We outline some characteristic properties of diffractions and diffraction imaging, and present two novel approaches to diffraction imaging in the depth domain. The first technique is based on reflection focusing in the depth domain and subsequent filtering of reflections from prestack data. The second technique modifies the migration kernel and consists of a reverse application of stationary-phase migration to suppress contributions from specular reflections to the diffraction image. Both techniques are proposed as a complement to conventional full-wave pre-stack depth migration, and both assume the existence of an accurate migration velocity. [source] Modelling of GPR waves for lossy media obeying a complex power law of frequency for dielectric permittivityGEOPHYSICAL PROSPECTING, Issue 1 2004Maksim Bano ABSTRACT The attenuation of ground-penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity. We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency-independent- Q or simply a constant- Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency-bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response. Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial-and-error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling. [source] Seismic modelling study of a subglacial lakeGEOPHYSICAL PROSPECTING, Issue 6 2003José M. Carcione ABSTRACT We characterize the seismic response of Lake Vostok, an Antarctic subglacial lake located at nearly 4 km depth below the ice sheet. This study is relevant for the determination of the location and morphology of subglacial lakes. The characterization requires the design of a methodology based on rock physics and numerical modelling of wave propagation. The methodology involves rock-physics models of the shallow layer (firn), the ice sheet and the lake sediments, numerical simulation of synthetic seismograms, ray tracing, ,,p transforms, and AVA analysis, based on the theoretical reflection coefficients. The modelled reflection seismograms show a set of straight events (refractions through the firn and top-ice layer) and the two reflection events associated with the top and bottom of the lake. Theoretical AVA analysis of these reflections indicates that, at near offsets, the PP-wave anomaly is negative for the ice/water interface and constant for the water/sediment interface. This behaviour is shown by AVA analysis of the synthetic data set. This study shows that subglacial lakes can be identified by using seismic methods. Moreover, the methodology provides a tool for designing suitable seismic surveys. [source] Wave propagation in an inhomogeneous cross-anisotropic mediumINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010Cheng-Der Wang Abstract Analytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E,) and shear modulus (G,) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, , and ,, remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain,displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, VP, VSV, and VSH, and the wave vectors, , and , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E,, G,/E,, and ,/,,); and (3) the phase angle, ,. Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium. Copyright © 2009 John Wiley & Sons, Ltd. [source] Transient solution for multilayered poroviscoelastic media obtained by an exact stiffness matrix formulationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 18 2009A. Mesgouez Abstract The authors propose a semi-analytical approach to studying wave propagation in multilayered poroviscoelastic grounds due to transient loads. The theoretical development is based on the exact stiffness matrix method for the Biot theory coupled with a matrix conditioning technique. It is developed in the wavenumber frequency domain after a Fourier transform on the surface space variables and the time variable. The usual methods yield a poorly conditioned numerical system. This is due in particular to the presence of mismatched exponential terms. In this article, increasing exponential terms are eliminated and only decreasing exponential terms remain. Consequently, the method can be applied to a large field of configurations without restriction concerning high frequencies, large Fourier transform parameters or large layer thicknesses. Validation and efficiency of the method are discussed. Effects of layering show that the layer impedance influence on solid and fluid displacements. Moreover, this approach can be of interest for the validation of numerical tools. Copyright © 2009 John Wiley & Sons, Ltd. [source] Considerations of the discontinuous deformation analysis on wave propagation problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2009Jiong Gu Abstract In rock engineering, the damage criteria of the rock mass under dynamic loads are generally governed by the threshold values of wave amplitudes, such as the peak particle velocity and the peak particle acceleration. Therefore, the prediction of wave attenuation across fractured rock mass is important on assessing the stability and damage of rock mass under dynamic loads. This paper aims to investigate the applications of the discontinuous deformation analysis (DDA) for modeling wave propagation problems in rock mass. Parametric studies are carried out to obtain an insight into the influencing factors on the accuracy of wave propagations, in terms of the block size, the boundary condition and the incident wave frequency. The reflected and transmitted waves from the interface between two materials are also numerically simulated. To study the tensile failure induced by the reflected wave, the spalling phenomena are modeled under various loading frequencies. The numerical results show that the DDA is capable of modeling the wave propagation in jointed rock mass with a good accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [source] Coupled simulation of wave propagation and water flow in soil induced by high-speed trainsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2008P. Kettil Abstract The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water-saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright © 2007 John Wiley & Sons, Ltd. [source] P-wave transmission across fractures with nonlinear deformational behaviourINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2006X. B. Zhao Abstract Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P-wave across parallel fractures with nonlinear deformational behaviour (static Barton,Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd. [source] A three-phase soil model for simulating stress wave propagation due to blast loadingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 1 2004Zhongqi Wang Abstract A three-phase soil model is proposed to simulate stress wave propagation in soil mass to blast loading. The soil is modelled as a three-phase mass that includes the solid particles, water and air. It is considered as a structure that the solid particles form a skeleton and their voids are filled with water and air. The equation of state (EOS) of the soil is derived. The elastic,plastic theory is adopted to model the constitutive relation of the soil skeleton. The damage of the soil skeleton is also modelled. The Drucker,Prager strength model including the strain rate effect is used to describe the strength of the soil skeleton. The model is implemented into a hydrocode Autodyn. The recorded results obtained by explosion tests in soil are used to validate the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source] Fabric evolution of granular assembly under K0 loading/unloadingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2003Jyh-Chau Liou Abstract This study attempted to investigate the fabric evolution in K0 loading/unloading. The work made use of a field simulator to control K0 loading/unloading in large specimens prepared by air-pluviation. In each loading stage, wave velocities along various propagation directions were measured. On the basis of the theories of micro-mechanics and wave propagation, the microscopic parameters of the granular assembly were back calculated to investigate the fabric evolution of granular soil during K0 loading/unloading. In this study, the Geometric fabric was modelled by fabric tensors of ranks 2 and 4. The comparison of calibrated results using ranks 2 and 4 revealed the advantage of the usage of rank-4 fabric tensor in modelling fabric evolution in spite of its complexity. By comparing relative magnitudes of vertical and horizontal components of geometric fabric, it was demonstrated that relative constraint in lateral directions increased during K0 -unloading in order to maintain a K0 condition. It revealed that fabric evolution was responsible for a higher K0 in unloading than K0 in loading. Copyright © 2003 John Wiley & Sons, Ltd. [source] Instability of wave propagation in saturated poroelastoplastic mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2002Xikui Li Abstract In the present work, stationary discontinuities and fluttery instabilities of wave propagation in saturated poro-elastoplastic media are analysed in the frame of Biot theory. The generalized Biot formulations are particularly employed for simulating non-linear coupled hydro-mechanical behaviour of the media. Inertial coupling effect between the solid and the fluid phases of the media is also taken into account. The non-associated Drucker,Prager criterion to describe non-linear constitutive behaviour of pressure dependent elasto-plasticity for the solid skeleton of the media is particularly considered. With omission of compressibility of solid grains and the pore fluid, the critical conditions of stationary discontinuities and flutter instabilities occurring in wave propagation are given in explicit forms. It is shown that when the stationary discontinuity is triggered at the surface of discontinuity there still may exist real wave speeds. The wave speeds across the stationary discontinuity surface entirely cease to be real only in non-associated plasticity, certain ranges of value of Poisson's ratio and when compression stress normal to the surface of discontinuity dominates the stress state at the surface. It is also indicated that the fluttery instabilities, under which some wave speeds cease to be real even in strain hardening stage, may occur prior to stationary discontinuities only for non-associated plasticity under certain conditions. These conditions are: (1) both the porosity and the Poisson's ratio possess relatively low values and (2) the deviatoric part of the effective stress normal to the surface of discontinuity is compressive. A region in the porosity,Poisson's ratio plot, in which fluttery instabilities are possible to occur, is given. Copyright © 2002 John Wiley & Sons, Ltd. [source] Suppressing local particle oscillations in the Hamiltonian particle method for elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010Masahiro Kondo Abstract The governing equation of elasticity is discretized into motion equations of the particles in a Hamiltonian system. A weighted least-square method is adopted to evaluate the Green,Lagrange strain. Using a symplectic scheme for the Hamiltonian system, we obtain the property of energy conservation in the discretized calculations. However, local particle oscillations occur, and they excessively decrease low frequency motion. In this study, we propose the use of an artificial potential force to suppress the local oscillations. The accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation. With the inclusion of the artificial force, the local oscillations are reduced while energy conservation is maintained. 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