Numerical Simulation Of Wave Propagation Research Articles

Simulating Seismic Wave Propagation in Viscoelastic Media with an Irregular Free Surface

In seismic numerical simulations of wave propagation, it is very important for us to consider surface topography and attenuation, which both have large effects (e.g., wave diffractions, conversion, amplitude/phase change) on seismic imaging and inversion. An irregular free surface provides significant information for interpreting the characteristics of seismic wave propagation in areas with rugged or rapidly varying topography, and viscoelastic media are a better representation of the earth’s properties than acoustic/elastic media. In this study, we develop an approach for seismic wavefield simulation in 2D viscoelastic isotropic media with an irregular free surface. Based on the boundary-conforming grid method, the 2D time-domain second-order viscoelastic isotropic equations and irregular free surface boundary conditions are transferred from a Cartesian coordinate system to a curvilinear coordinate system. Finite difference operators with second-order accuracy are applied to discretize the viscoelastic wave equations and the irregular free surface in the curvilinear coordinate system. In addition, we select the convolutional perfectly matched layer boundary condition in order to effectively suppress artificial reflections from the edges of the model. The snapshot and seismogram results from numerical tests show that our algorithm successfully simulates seismic wavefields (e.g., P-wave, Rayleigh wave and converted waves) in viscoelastic isotropic media with an irregular free surface.

Numerical Simulation of Wave Propagation over Structures on a Porous Seabed

ABSTRACT Min, E.-H. and Koo, W., 2018. Numerical simulation of wave propagation over structures on a porous seabed. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 966–970. Coconut Creek (Florida), ISSN 0749-0208. A wave-body interaction with semi-circular rigid structures placed on a porous seabed was simulated. Owing to the rigid structures installed at regular intervals, spatial modulation of the wave propagation due to a Bragg reflection was examined. The computational domain consisted of a potential-flow water domain and porous domain with Darcy's law interface boundary condition. Using the numerical wave tank technique, the two-domain boundary element method was developed to simulate wave propagation over seafloor structures on the porous boundary in the time domain. For various permeability constants and incident wave frequencies, wave amplitude was var...

Influence of the Source Square Size on the Accuracy of Numerical Simulation of Wave Propagation in Half Space

Influence of the Source Square Size on the Accuracy of Numerical Simulation of Wave Propagation in Half Space

High frequency generation in the corona: Resonant cavities

Aims. Null points are prominent magnetic field singularities in which the magnetic field strength strongly decreases in very small spatial scales. Around null points, predicted to be ubiquitous in the solar chromosphere and corona, the wave behavior changes considerably. Null points are also responsible for driving very energetic phenomena, and for contributing to chromospheric and coronal heating. In previous works we demonstrated that slow magneto-acoustic shock waves were generated in the chromosphere propagate through the null point, thereby producing a train of secondary shocks escaping along the field lines. A particular combination of the shock wave speeds generates waves at a frequency of 80 MHz. The present work aims to investigate this high frequency region around a coronal null point to give a plausible explanation to its generation at that particular frequency. Methods. We carried out a set of two-dimensional numerical simulations of wave propagation in the neighborhood of a null point located in the corona. We varied both the amplitude of the driver and the atmospheric properties to investigate the sensitivity of the high frequency waves to these parameters. Results. We demonstrate that the wave frequency is sensitive to the atmospheric parameters in the corona, but it is independent of the strength of the driver. Thus, the null point behaves as a resonant cavity generating waves at specific frequencies that depend on the background equilibrium model. Moreover, we conclude that the high frequency wave train generated at the null point is not necessarily a result of the interaction between the null point and a shock wave. This wave train can be also developed by the interaction between the null point and fast acoustic-like magneto-acoustic waves, that is, this interaction within the linear regime.

Experimental validation of transient source term in porosity-based shallow water models

Porosity-based shallow water models for the simulation of urban floods incorporate additional energy dissipation terms compared to the usual two-dimensional shallow water equations. These terms account for head losses stemming from building drag. They are usually modelled using turbulence-based equations of state (drag proportional to the squared velocity). However, refined numerical simulations of wave propagation in periodic urban layouts indicate that such drag models do not suffice to reproduce energy dissipation properly. Correct wave propagation speeds, energy dissipation rates and flow fields are obtained by incorporating a new type of source term, active only under transient situations involving positive waves. This source term does not take the form of an equation of state. It can be modelled as an artificial increase in water inertia. In this communication, an experimental validation of this source term model is presented by means of new dam-break flow experiments in idealized, periodic urban layouts. The experimental results validate both the existence and the proposed formulation of this new source term.

A novel formulation of 3D spectral element for wave propagation in reinforced concrete

AbstractThe paper deals with numerical simulations of wave propagation in reinforced concrete for damage detection purposes. A novel formulation of a 3D spectral element was proposed. The reinforcement modelled as the truss spectral element was embedded in the 3D solid spectral finite element. Numerical simulations have been conducted on cuboid concrete specimens reinforced with two steel bars. Different degradation models were considered to study the real behaviour of bended beams.

Hydraulic fracture diagnostics from Krauklis-wave resonance and tube-wave reflections

Fluid-filled fractures support guided waves known as Krauklis waves. The resonance of Krauklis waves within fractures occurs at specific frequencies; these frequencies, and the associated attenuation of the resonant modes, can be used to constrain the fracture geometry. We use numerical simulations of wave propagation along fluid-filled fractures to quantify fracture resonance. The simulations involve solution of an approximation to the compressible Navier-Stokes equation for the viscous fluid in the fracture coupled to the elastic-wave equation in the surrounding solid. Variable fracture aperture, narrow viscous boundary layers near the fracture walls, and additional attenuation from seismic radiation are accounted for in the simulations. We then determine how tube waves within a wellbore can be used to excite Krauklis waves within fractures that are hydraulically connected to the wellbore. The simulations provide the frequency-dependent hydraulic impedance of the fracture, which can then be used in a frequency-domain tube-wave code to model tube-wave reflection/transmission from fractures from a source in the wellbore or at the wellhead (e.g., water hammer from an abrupt shut-in). Tube waves at the resonance frequencies of the fracture can be selectively amplified by proper tuning of the length of a sealed section of the wellbore containing the fracture. The overall methodology presented here provides a framework for determining hydraulic fracture properties via interpretation of tube-wave data.

A Hermite Spline Layerwise Time Domain Spectral Finite Element for Guided Wave Prediction in Laminated Composite and Sandwich Plates

A new time domain spectral plate finite element (FE) is developed to provide fast numerical calculations of guided waves and transient phenomena in laminated composite and sandwich plates. A new multifield layerwise laminate theory provides the basis for the FE, which incorporates cubic Hermite polynomial splines for the approximation of the in-plane and transverse displacement fields through the thickness of the plate, enabling the modeling of symmetric and antisymmetric wave modes. The time domain spectral FE with multi-degrees-of-freedom (DOF) per node is subsequently formulated, which uses integration points collocated with the nodes to yield consistent diagonal lumped mass matrix which expedites the explicit time integration process. Numerical simulations of wave propagation in aluminum, laminated carbon/epoxy and thick sandwich plates are presented and validated with an analytical solution and a three-dimensional (3D) solid element; moreover, the capability to accurately and rapidly predict antisymmetric and symmetric guided waves is demonstrated.

Numerical observation of the equipartition regime in a 3D random elastic medium, and discussion of the limiting parameters

At long lapse times in the weakly scattering regime, the energy of the coda in a randomly fluctuating isotropic medium is equipartitioned between P and S modes. This behavior is well understood mathematically and physically for full spaces. For realistic domains, analytical results are more scarce and numerical simulations become a valuable tool. This paper discusses, based on numerical simulations of wave propagation in a 3D randomly heterogeneous elastic medium, the transition to an equipartitioned regime of the wave field. Both the time to transition and the value of the ratio of energies after transition are evaluated. Several influencing parameters are discussed, either physical (ratio of background P- and S- velocities, propagation length, variance of the heterogeneities) or numerical (influence of Perfectly Matched Layers). Setting up of a localization regime, inefficient mixture of body waves and small propagation length compared to the transport mean free paths are identified as constraining for the transition toward an equipartition regime.

IMPLEMENTATION OF A NON-SPLITTING FORMULATION OF PERFECTLY MATCHED LAYER IN A 3D – 4TH ORDER STAGGERED-GRID VELOCITY-STRESS FINITE-DIFFERENCE SCHEME

One of the major problems in numerical simulations of wave propagation in elastodynamics using grid-point methods is the truncation of the computational space by artificial boundaries. These boundaries produce spurious reflections, polluting the results with artificial noise, therefore several efforts have been realized in order to achieve transparent or non-reflecting boundaries for truncating the computational space. Perfectly Matched Layer (PML) has been one of the most efficient methods for implementing artificial boundaries at the edges of the computational models. However the application of PML requires the “tuning” of several variables, for which very limited work has been presented. In the present study we employ the Non-Splitting formulation of PML (NPML) technique presented by Wang & Tang (2003), based on the introduction of small perturbations in the wavefield. The NPML formulation shows the same accuracy with the originally introduced PML but is easier to be implemented because it does not require the field splitting. The main scope of this paper is to perform a full analysis of the efficiency of NMPL based on numerical tests using a 3D–4th order staggered-grid velocity-stress finite-difference scheme. The analysis consists of direct, quantified comparisons with reference solution waveforms from a semi-analytical method (Discrete Wavenumber Method) with synthetic waveforms produced using the most popular Absorbing Boundary Conditions (ABCs) and PML, in various canonical models (homogeneous and layer over half-space).

Modelling RF-plasma interaction in ECR ion sources

This paper describes three-dimensional self-consistent numerical simulations of wave propagation in magnetoplasmas of Electron cyclotron resonance ion sources (ECRIS). Numerical results can give useful information on the distribution of the absorbed RF power and/or efficiency of RF heating, especially in the case of alternative schemes such as mode-conversion based heating scenarios. Ray-tracing approximation is allowed only for small wavelength compared to the system scale lengths: as a consequence, full-wave solutions of Maxwell-Vlasov equation must be taken into account in compact and strongly inhomogeneous ECRIS plasmas. This contribution presents a multi-scale temporal domains approach for simultaneously including RF dynamics and plasma kinetics in a “cold-plasma”, and some perspectives for “hot-plasma” implementation. The presented results rely with the attempt to establish a modal-conversion scenario of OXB-type in double frequency heating inside an ECRIS testbench.

Site response in a representative region of Manzanillo, Colima, Mexico, and a comparison between spectra from real records and spectra from normative

The October 1995 Mw=8.0 Colima-Jalisco earthquake triggered damage in buildings located in Manzanillo city (Tena, A, 1997) [1]. Great damages were reported in different regions of that city. It was also observed liquefaction in the Manzanillo port. In order to improve the knowledge of the subsoil of Manzanillo, Rayleigh waves were inverted applying spatial autocorrelation (SPAC) to array measurements of microtremors at five representative sites of the city. This procedure allowed us to obtain a shallow S-wave velocity profile at each site. We compute the transfer function for each profile and correlate the results with geology. We calculate theoretical surface records. For this purpose, we used a numerical simulation of wave propagation of an input signal (Green function) through the structure. In this case, records of two great subduction earthquakes were used as Green functions. We use these surface signals to estimate response spectra for each site. On the other hand, design spectra according to the manual of seismic design of the Federal Commission of Electricity 2008 edition (MOC-CFE) [2] were obtained and compared with previous results.We observed important differences between the seismic responses in different regions of Manzanillo. For instance, the response at site 5 (alluvial deposits) for a period of 0.25s is twice the response of site 4 (sand deposits) for the same period. Therefore, the site effects are relevant in Manzanillo.For the majority of the cases we observe a reasonable agreement between the values of the dominant periods computed according to the MOC-CFE [2] normative and those obtained directly from Transfer Function (TF). On the other hand, we found significant differences between design spectra and response spectra obtained from seismic records for the 0.1–0.6s interval. Amplitudes are underestimated for the first ones.

Estimation of seismic velocity changes at different depths associated with the 2014 Northern Nagano Prefecture earthquake, Japan (M W 6.2) by joint interferometric analysis of NIED Hi-net and KiK-net records

To estimate the seismic velocity changes at different depths associated with a large earthquake, we apply passive image interferometry to two types of seismograms: KiK-net vertical pairs of earthquake records and Hi-net continuous borehole data. We compute the surface/borehole deconvolution waveform (DCW) of seismograms recorded by a KiK-net station and the autocorrelation function (ACF) of ambient noise recorded by a collocated Hi-net station, 26 km from the epicenter of the 2014 Northern Nagano Prefecture earthquake, Japan (M W 6.2). Because the deeper KiK-net sensor and the Hi-net sensor are collocated at 150 m depth, and another KiK-net sensor is located at the surface directly above the borehole sensors, we can measure shallow ( 150 m depth) velocity changes separately. The sensitivity of the ACF to the velocity changes in the deeper zone is evaluated by a numerical wave propagation simulation. We detect relative velocity changes of −3.1 and −1.4% in the shallow and deep zones, respectively, within 1 week of the mainshock. The relative velocity changes recover to −1.9 and −1.1%, respectively, during the period between 1 week and 4 months after the mainshock. The observed relative velocity reductions can be attributed to dynamic strain changes due to the strong ground motion, rather than static strain changes due to coseismic deformation by the mainshock. The speed of velocity recovery may be faster in the shallow zone than in the deep zone because the recovery speed is controlled by initial damage in the medium. This recovery feature is analogous to the behavior of slow dynamics observed in rock experiments.

Numerical simulation of wave propagation in inhomogeneous media using Generalized Plane Waves

The Trefftz Discontinuous Galerkin (TDG) method is a technique for approximating the Helmholtz equation (or other linear wave equations) using piecewise defined local solutions of the equation to approximate the global solution. When coefficients in the equation (for example, the refractive index) are piecewise constant it is common to use plane waves on each element. However when the coefficients are smooth functions of position, plane waves are no longer directly applicable. In this paper we show how Generalized Plane Waves (GPWs) can be used in a modified TDG scheme to approximate the solution for piecewise smooth coefficients. GPWs are approximate solutions to the equation that reduce to plane waves when the medium through which the wave propagates is constant. We shall show how to modify the TDG sesquilinear form to allow us to prove convergence of the GPW based version. The new scheme retains the high order convergence of the original TDG scheme (when the solution is smooth) and also retains the same number of degrees of freedom per element (corresponding to the directions of the GPWs). Unfortunately it looses the advantage that only skeleton integrals need to be performed. Besides proving convergence, we provide numerical examples to test our theory.

A second-order, perfectly matched layer formulation to model 3D transient wave propagation in anisotropic elastic media

Numerical simulation of wave propagation in an infinite medium is made possible by surrounding a finite region by a perfectly matched layer (PML). Using this approach a generalized three-dimensional (3D) formulation is proposed for time-domain modeling of elastic wave propagation in an unbounded lossless anisotropic medium. The formulation is based on a second-order approach that has the advantages of, physical relationship to the underlying equations, and amenability to be implemented in common numerical schemes. Specifically, our formulation uses three second-order equations of the displacement field and nine auxiliary equations, along with the three time histories of the displacement field. The properties of the PML, which are controlled by a complex two-parameter stretch function, are such that it acts as near perfect absorber. Using finite element method (FEM) 3D numerical results are presented for a highly anisotropic medium. An extension of the formulation to the particular case of a Kelvin-Vogit viscoelastic medium is also presented.

HELIOSEISMIC HOLOGRAPHY OF SIMULATED SUNSPOTS: MAGNETIC AND THERMAL CONTRIBUTIONS TO TRAVEL TIMES.

Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level in the simulations) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it would suggest a path toward inversions for sunspot structure.

Numerical modeling of wave processes in layered media in the Arctic region

The aim of this work is the numerical simulation of wave propagation in media with linear-elastic and acoustic layers as exemplified by the seismic prospecting problems in the Arctic region and the explosive impact on an iceberg. The complete system of equations describing the state of a linearly elastic body and the system of equations describing the acoustic field are solved. The grid-characteristic method is used to provide the contact and boundary conditions, including the contact condition between acoustic and linear-elastic layers, to be correctly described.

Numerical Simulation of Transit-Time Ultrasonic Flowmeters by a Direct Approach.

This paper deals with the development of a computational code for the numerical simulation of wave propagation through domains with a complex geometry consisting in both solids and moving fluids. The emphasis is on the numerical simulation of ultrasonic flowmeters (UFMs) by modeling the wave propagation in solids with the equations of linear elasticity (ELE) and in fluids with the linearized Euler equations (LEEs). This approach requires high performance computing because of the high number of degrees of freedom and the long propagation distances. Therefore, the numerical method should be chosen with care. In order to minimize the numerical dissipation which may occur in this kind of configuration, the numerical method employed here is the nodal discontinuous Galerkin (DG) method. Also, this method is well suited for parallel computing. To speed up the code, almost all the computational stages have been implemented to run on graphical processing unit (GPU) by using the compute unified device architecture (CUDA) programming model from NVIDIA. This approach has been validated and then used for the two-dimensional simulation of gas UFMs. The large contrast of acoustic impedance characteristic to gas UFMs makes their simulation a real challenge.

Wave propagation modeling with non-Markov phase screens.

A recently introduced [J. Opt. Soc. Am. A30, 479 (2013)10.1364/JOSAA.30.000479JOAOD61084-7529] sparse spectrum (SS) model of statistically homogeneous random fields makes it possible to generate 3D samples of refractive-index fluctuations with prescribed spectral density at a very reasonable computational cost. The SS technique can be used in the framework of the split-step Fourier method for numerical simulation of wave propagation in turbulence. It allows generation of the phase screen samples that are free from the limitations of the Markov approximation, which is commonly used for theoretical description and numerical modeling of optical waves propagation through turbulence. We investigate statistics of these phase screens and present a numerical algorithm for their generation.

Numerical simulations of wave propagation over a vegetated platform

Vegetated platforms have been constructed in recent years for the purpose of shore protection. This paper addresses some fundamental questions concerning the vegetated platform: (1) What is the difference in wave attenuation between a vegetated platform and a simple platform, and how much can vegetation increase the efficiency of reducing wave transmission? (2) Are there any differences between the effects of stems and roots on wave attenuation? (3) Does vegetation always reduce wave transmission? (4) Is it possible to develop an empirical formula for estimating the wave transmission of a vegetated platform? To answer the above questions, a numerical model solving the Navier–Stokes equations for wave propagation over a vegetated platform is established and validated by several existing laboratory experiments. A total of 244 numerical experiments based on this model have been carried out. The simulated results suggest that the platform plays a major role and the vegetation plays a supporting role in reducing wave transmission except for some special cases. Stems tend to have a larger influence than roots in reducing wave transmission with the same height. The roots always help reduce wave transmission, while the stems may increase wave transmission when the platform width is in the range of 37.5–62.5% of the incident wavelength. Based on our numerical experiments and existing laboratory data, the paper proposes a simple formula for predicting the wave transmission coefficient of a vegetated platform for engineering applications.