Finite-difference Simulation Method Research Articles

Decoupling of Pacific subduction zone guided waves beneath central Japan: Evidence for thin slab

AbstractThe fine‐scale seismic structure of the northeast Japan subduction zone is studied based on waveform analyses of moderate‐sized (M4.5–6), deep‐focus earthquakes (h >350 km) and the finite difference method (FDM) simulation of high‐frequency (up to 8 Hz) wave propagation. Strong regional S wave attenuation anomalies for specific source‐receiver paths connecting the cluster of events occurring in central part of the Sea of Japan recorded at fore arc stations in northern and central Japanese Islands (Honshu) are used to model the deeper structure of the subducting Pacific Plate, where recent teleseismic tomography has shown evidence for a possible slab tear westward beneath the Sea of Japan. The character of the observed anomalous S wave attenuation and the following high‐frequency coda can be captured with the two‐dimensional (2‐D) FDM simulation of seismic waves in heterogeneous plate model, incorporating the thinning of the plate at depth, which is also compared with other possible causes of dramatic attenuation of high‐frequency S wave due to low‐Q or much weaker heterogeneities in the slab. The results of simulation clearly demonstrate that the dramatic loss of high‐frequency S wavefield from the plate into the surrounding mantle occurred due to the variation in the plate geometry (i.e., thinning of the plate) at depth near the source rather than due to variation in physical properties, such as due to the lowered‐Q and weaker heterogeneities in the plate. The presence of such a thin zone defocuses the high‐frequency slab‐guided S wave energy from the subducting plate into the surrounding mantle and acts as a geometric antiwaveguide. Based on the sequence of simulation results obtained, we propose thinning of Pacific Plate at depth subducting beneath northeastern Japan, localized to central part of Honshu, in agreement with the observations.

Surface wave excitation at the northern edge of the Kanto Basin, Japan

In this paper, we analyze the seismograms of a local earthquake (M W = 5.8) and find a clear surface wave excitation at the northern edge of the Kanto Basin, Japan. To conduct three-dimensional (3-D) finite difference method simulations for this observation, we investigate the characteristics of the S wave velocity in the Kanto Basin and construct a realistic sedimentary structure model. The S wave velocities derived from the vertical seismic profiling measurements in the Kanto Basin show smooth depth gradients rather than step-like increases and can be successfully modeled by an exponential asymptotically bounded velocity function. Our simulation using the modified Japan integrated velocity structure model by incorporating a sedimentary layer with S wave velocity-depth gradients well reproduces the excitation and dispersion of the observed surface waves. This result indicates that realistic modeling of the impedance contrast at the sediment-bedrock interface is indispensable for the precise evaluation of surface wave excitation at the basin edge.

Strong seismic wave scattering in the low-velocity anomaly associated with subduction of oceanic plate

Analyses of dense seismic records in Kanto, Japan, revealed distinct pulse broadening and peak delay of high-frequency S waves at central Chiba. These phenomena are observed at frequency range of 1–8 Hz and exist only for ray paths passing through the low-velocity (LV) zone at depth of 20–40 km beneath northwestern Chiba. To obtain a more detailed understanding of these phenomena, we conducted 2-D and 3-D finite difference method simulations of seismic wave propagation using a realistic heterogeneous structure model. Through numerous simulations we demonstrated that strong seismic scattering, due to localized strong small-scale heterogeneities in the LV zone and in the oceanic crust, is a major cause of strong pulse broadening and peak delay of high-frequency S waves. After comparing simulation results with observations, the most preferable small-scale velocity heterogeneity in the LV zone is characterized by a Gaussian power spectral density function (PSDF) with correlation distance a of 1–2 km and rms value ε = 0.07–0.09, superposed on a background exponential PSDF (a = 3 km, ε = 0.07). Assuming strong velocity heterogeneities, observed amplitude decay at Chiba is also well explained by strong scattering attenuation in the LV zone. Because the LV zone, which has been reported by seismic tomography studies, is interpreted as being constructed by the dehydration of the subducting oceanic crust of the Philippine Sea Plate, strong small-scale velocity heterogeneity in the LV zone may be related to the random distribution of fluid in this volume.

Simulation of Fick’s Second Law for Spatially Variant Diffusion Coefficients

Simulations of cyclic voltammograms for a system with a spatially variant diffusion profile are presented. An expanded version of Fick’s Second Law is used to account for a diffusion coefficient that varies with x, distance normal to the electrode surface. Parameters to define the slope and magnitude of a linearly graded diffusion profile are described. A one dimensional explicit finite difference simulation method is used and parameters are made to be dimensionless. The simulation is vetted by comparison with Nicholson and Shain simulations and determination of the resolution limits. Morphological changes in cyclic voltammograms are observed that indicate an approach to steady state diffusion.

Fabrication and characterization of Ge20Sb15Se65 chalcogenide glass rib waveguides for telecommunication wavelengths

We report on the fabrication and optical properties of Ge20Sb15Se65 chalcogenide glass rib waveguides on a single photonic chip. Radio-frequency magnetron sputtering method is employed to deposit 1.36-μm-thick films and reactive ion etching with CHF3 is used to pattern 0.76-μm-deep rib waveguides of 1–4 μm wide with low surface roughness and vertical sidewalls. Using lensed fibers, the insertion losses for rib waveguides of different widths are measured and propagation losses are estimated to be lower than 1 dB/cm. Finite difference method simulations and refractive index/curve fitting are used to observe a moderate normal dispersion of the waveguides at 1550 nm.

An Effective Finite Difference Method for Simulation of Bioheat Transfer in Irregular Tissues

A three-dimensional (3D) simulation of bioheat transfer is crucial to analyze the physiological processes and evaluate many therapeutic/diagnostic practices spanning from high to low temperature medicine. In this paper we develop an efficient numerical scheme for solving 3D transient bioheat transfer equations based on the alternating direction implicit finite-difference method (ADI-FDM). An algorithm is proposed to deal with the boundary condition for irregular domain which could capture accurately the complex boundary and reduce considerably the staircase effects. Furthermore, the local adaptive mesh technology is introduced to improve the computational accuracy for irregular boundary and the domains with large temperature gradient. The detailed modification to ADI-FDM is given to accommodate such special grid structure, in particular. Combination of adaptive-mesh technology and ADI-FDM could significantly improve the computational accuracy and decrease the computational cost. Extensive results of numerical experiments demonstrate that the algorithm developed in the current work is very effective to predict the temperature distribution during hyperthermia and cryosurgery. This work may play an important role in developing a computational planning tool for hyperthermia and cryosurgery in the near future.

Seismic- and Tsunami-Wave Propagation of the 2011 Off the Pacific Coast of Tohoku Earthquake as Inferred from the Tsunami-Coupled Finite-Difference Simulation

Abstract The 2011 Tohoku earthquake ( M 9.0) caused significant hazards including strong ground motion, coseismic ground deformation, and tsunamis. For a deeper understanding of these phenomena, we conducted a large‐scale, parallel computer simulation by means of the finite‐difference method (FDM) with newly developed tsunami‐coupled equations of motion. This method is based on the equations of motion for an elastic medium, treating seawater as elastic material having zero S ‐wave velocity. Tsunami waves are included by taking into account gravity and their equilibrium with the pressure gradient. An effective method of FDM simulation using the state‐of‐the‐art massively parallelized K computer is also studied. With the use of a 3D layered velocity structure that includes topography and bathymetry, basement structure, Moho depth, and plate boundaries, and use of the appropriate source‐rupture model based on joint inversion of seismic waves and geodetic observations, the simulated seismic waves demonstrate anomalous seismic‐wave propagation by the thick 3D basin structure inland. We also found that the sea column acts as a strong absorber of seismic waves for shallow up‐dip slip. On the ocean side, coseismic deformation and tsunamis are dynamically generated in this simulation. Tsunami attacks on the subsided Pacific coast are simulated without any additional assumptions. We also modeled the tsunami and seismic records of ocean‐bottom pressure gauges above the fault. Because sea‐bottom tsunami and seismic observation is powerful but very complex, recording both seismic and tsunami waves, the use of these coupled numerical simulations has great potential for resolving complex source fault rupture processes in a 3D heterogeneous structure. Online Material: Mpeg movies of fault slip, seismic‐wave propagation, seafloor and ground displacement, and tsunamic propagation.

A New Model for Light-induced Degradation by B-O Defects in p- and n-type Silicon

Light-induced degradation of the carrier lifetime in silicon due to the formation of boron-oxygen defects has been investigated using photoluminescence measurements. A finite difference simulation method has also been created to test theoretical models of the factors controlling defect generation. Experimental photoluminescence data is compared with simulated results. It is found that the maximum defect density in both p- and n-type material can be described as a function of the hole density during degradation.

FDM Simulation of Seismic-Wave Propagation for an Aftershock of the 2009 Suruga Bay Earthquake: Effects of Ocean-Bottom Topography and Seawater Layer

Abstract Feasibility studies on simulating seismic‐wave propagation in media for a suboceanic earthquake, including both land and ocean‐bottom topographies and a seawater layer, are scarce. Some of the conventional staggered‐grid finite‐difference method (FDM) simulations use a simplified structure model without a seawater layer and with a flat ocean‐bottom topography. In this study, we apply our heterogeneity, oceanic layer, and topography scheme (HOT)‐FDM and a 3D structure model including land and ocean‐bottom topographies, a seawater layer, and a fluid–solid boundary condition to an aftershock ( M w 5.8) of the 2009 Suruga Bay earthquake. We attempt to reproduce observations at seismic stations near the coast and then simulate waveforms in the ocean‐bottom stations. Our results show that a large difference between the cases with and without topographies can be seen in the coda part after the S wave in the simulated waveforms in terms of amplitudes and elongations. The synthetic waveforms in the model with topographies are in agreement with the observed waveforms. Our results also show that a significant difference in the amplification of the coda part between the cases with and without the seawater layer can be found at the ocean‐bottom stations. This coda part is the S ‐ and Rayleigh‐wave propagation associated with the ocean and the underlying sediment layers. Our results show that a realistic model with topographies and a seawater layer is needed in FDM simulations in order to precisely reproduce observed waveforms or predict seismic motion for a suboceanic earthquake.

Finite difference simulation methods as an educational tool

Finite difference methods can be a valuable and unexpected tool in acoustics education. As a wave acoustic simulation method, it provides instructive time-domain visualizations particularly useful for illustrating broadband wave effects like diffraction and interference. Furthermore, the knowledge required to implement these simulations can be taught in just a few hours of instruction with or without calculus in contrast to several other wave acoustic methods. The exposition provides opportunities for discussion of basic numerical methods as well as the physics of wave and diffusion processes. We present example projects from students of mixed science, engineering, and music backgrounds. After only four hours of instruction, they were able to independently simulate various room geometries with impedance boundary conditions along with a variety of other acoustical systems. Beyond strictly educational value, this is a flexible and free tool that the modern acoustician can use for research, physics-based sim...

FDM Simulation of Seismic Waves, Ocean Acoustic Waves, and Tsunamis Based on Tsunami-Coupled Equations of Motion

We have developed a new, unified modeling technique for the total simulation of seismic waves, ocean acoustic waves, and tsunamis resulting from earthquakes, based on a finite difference method simulation of the 3D equations of motion. Using the equilibrium between the pressure gradient and gravity in these equations, tsunami propagation is naturally incorporated in the simulation based on the equations of motion. The performance of the parallel computation for the newly developed tsunami-coupled equations using a domain partitioning procedure shows a high efficiency coefficient with a large number of CPU cores. The simulation results show how the near-field term associated with seismic waves produced by shallow earthquakes leads to a permanent coseismic deformation of the ground surface, which gives rise to the initial tsunami on the sea surface. Propagation of the tsunami along the sea surface as a gravity wave, and ocean acoustic waves in seawater with high-frequency multiple P-wave reflections between the free surface and sea bottom, are also clearly demonstrated by the present simulations. We find a good agreement in the tsunami waveform between our results and those obtained by other simulations based on an analytical model and the Navier–Stokes equations, demonstrating the effectiveness of the tsunami-coupling simulation model. Based on this simulation, we show that the ratio of the amplitude of ocean acoustic waves to the height of the tsunami, both of which are produced by the earthquake, strongly depends on the rise time of the earthquake rupture. This ratio can be used to obtain a more detailed understanding of the source rupture processes of subduction zone earthquakes, and for implementing an improved tsunami alert system for slow tsunami earthquakes.

Bias polarity and frequency effects of Cu-induced dielectric breakdown in damascene Cu interconnects

Cu-ion-migration-induced dielectric breakdown in damascene Cu interconnect was studied in alternating polarity-bias conditions using a metal–insulator–semiconductor (MIS) structured sample and a damascene Cu interconnect sample. Compared to a direct-current (DC) stress condition, the time to failure (TTF) obtained in the alternating-polarity test was twice as high in the damascene structure and more than five times greater in the MIS structure. This increased lifetime under alternating polarity over that in DC stress resulted from recovery due to the backward migration of Cu ions during the reverse-bias stress. However, the TTF increase was saturated due to the hindrance of backward Cu migration by diffusional flux during reverse-bias stress. The longest TTFs were obtained with the largest-polarity alternating frequency and this effect was analyzed through a one-dimensional finite-difference method simulation.

MPI-OpenMP hybrid simulations using boundary integral equation and finite difference methods for earthquake dynamics and wave propagation: Application to the 2007 Niigata Chuetsu-Oki earthquake (Mw6.6)

Abstract For the past two decades, the combination between the boundary integral equation method (BIEM) and the finite difference method (FDM) has provided a powerful approach for simulating the dynamic rupture process along a complex fault system and the resultant seismic wave radiation and propagation for the purpose of understanding the physics of seismology and the generation of strong ground motion by large earthquakes. In the many-core architecture currently in use, it can be useful to take advantage of hybrid MPI-OpenMP programming. In this study, we are investigating the Mw6.6, 2007 Niigata Chuetsu-Oki, Japan, earthquake. In the BIEM simulation of the dynamic rupture process, MPI-OpenMP hybrid programming is 24 to 38% faster than MPI programming on the same resource using 8 to 16 nodes (with 8 cores). In the FDM simulation on the wave propagation, hybrid programming is 25 to 37% faster. This performance allows us to investigate this earthquake using various parameter settings. First we obtain the frictional parameters based on the proposed kinematic finite source model using BIEM, then model both the spontaneous dynamic rupture propagation and wave radiation by combining BIEM and FDM. It is found that on the given asperities, the peak stress can reach 20 MPa and reduced stress, -20 MPa. Dynamic rupture simulations require a barrier around the southernmost asperity so that this asperity is ruptured in a reverse manner. This effect can be observed very locally in the wave radiation. Furthermore, we observe that the dynamic rupture propagation between two cross-cutting segments generates a more complex wavefield. The change in fault geometry may be dominant over the asperities on a single plane for this earthquake.

Fundamental Efficiency of Nanothermophones: Modeling and Experiments

Scaling down the dimensions of thermoacoustic sound sources (thermophones) improves efficiency by means of reducing speaker heat capacity. Recent experiments with nanoscale thermophones have revealed properties which are not fully understood theoretically. We develop a Green's function formalism which quantitatively explains some observed discrepancies, e.g., the effect of a heat-absorbing substrate in the proximity of the sound source. We also find a generic ultimate limit for thermophone efficiency. We verify the theory with experiments and finite difference method simulations which deal with thermoacoustically operated suspended arrays of nanowires. The efficiency of our devices is measured to be 1 order of magnitude below the ultimate bound. At low frequencies this mainly results from the presence of a substrate. At high frequencies, on the other hand, the efficiency is limited by the heat capacity of the nanowires. Measured sound pressure level and efficiency are in good agreement with simulations. We discuss the feasibility of reaching the ultimate limit in practice.

Optimized‐geometry ARROW waveguides using TiO2 as anti‐resonant layer

AbstractThe simulation, fabrication and characterization of ARROW waveguides using dielectric films deposited by Plasma Enhanced Chemical Vapor Deposition (PECVD) and Sputtering techniques, are presented in this work. Amorphous titanium oxide (TiO2) films were used as first cladding layer and silicon oxynitride (SiOxNy) films, as core layer. Furthermore, homemade routines based in two computational methods were used, for numerical simulations: Transfer Matrix Method (TMM) for the determination of the optimum thickness values of the Fabry‐Perot layers, and the Finite Difference Method (FDM) for 2D design and determination of the maximum width that allows single‐mode operation. The utilization of thermally grown silicon oxide as second anti‐resonant layer, along with improvements in the Reactive Ion Etching conditions for the definition of sidewalls of the optical waveguides were responsible for diminishing optical attenuations. Optimization of the waveguide rib height was done both through FDM simulations and experimentally. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Distortion of the apparentS-wave radiation pattern in the high-frequency wavefield: Tottori-Ken Seibu, Japan, earthquake of 2000

The distortion properties of the apparent S-wave radiation pattern in the high-frequency seismic wavefield of over f > 2 Hz is investigated using a large number of waveform records of the main shock and 29 aftershocks of the Tottori-Ken Seibu, Japan, magnitude (Mw) 6.6 earthquake in 2000. The dense seismic records from the KiK-net strong motion network show a clear four-lobe pattern in the apparent S-wave radiation pattern in the low-frequency wavefield of f < 2 Hz, and shows an almost isotropic distribution in all directions as the frequency increases above 5 Hz. The distortion of the apparent S-wave radiation pattern in the high-frequency wavefield increases as travel distance increases. Therefore, the path effect caused by the scattering of seismic waves due to small-scale heterogeneities in the crust is a major cause of distortion of the radiation pattern. This hypothesis is examined by a 2-D finite-difference method simulation of seismic waves in heterogeneous structure models. The results of simulations clearly demonstrate the collapse of the S-wave front due to seismic wave scattering in the heterogeneous structure. By comparing the observed wavefield and the results of simulations using different sorts of stochastic heterogeneous models, the most preferable model that can explain the observation is described by a von Karman autocorrelation function with correlation distance of a = 3–5 km, order of κ = 0.5 and rms value of ɛ = 0.07. However, our simple stochastic random heterogeneity model proposed, herein, somewhat overestimates the scattering of low-frequency signals below 2 Hz.

Small Copper Clusters in Ar Shells: A Study of Local Structure

Small copper clusters embedded in argon shells were obtained using the pick-up technique. The clusters were analyzed using X-ray absorption near-edge spectroscopy (XANES) measured at the Cu L23-edge. Theoretical interpretation of the experimental spectra has been performed using full-potential finite difference method simulations and density functional theory (DFT) to optimize the geometry of the clusters. As a result, it was found that the icosahedral Cu13 nanocluster with the geometry optimized by DFT produces theoretical Cu L23-XANES similar to the experimental one, whereas the theoretical XANES of the cuboctahedral cluster differs from that of the experimental. The bonding energy for the icosahedral cluster obtained by the present DFT study has a higher absolute value than that for the cuboctahedral cluster, thus also supporting the higher stability of the icosahedral Cu13 nanocluster.

差分法による 3次元不均質場での地震波伝播の大規模計算

The development of high-performance parallel computers such as the cluster of PCs and the Earth Simulator supercomputers made it possible for realistic 3-D simulation of seismic wave propagation and strong ground motions in heterogeneous structure. The seismic wavefield in heterogeneous structure is often evaluated numerically by solving equation of motions based on the finite-difference method (FDM). In the present paper, the FDM simulation of seismic wave propagation in heterogeneous structure is reviewed briefly with recently developed techniques such as for accurate representation of seismic phenomena in heterogeneous structure. Efficient techniques to reduce computational cost of the FDM simulation are also presented. The effectiveness of the vector-computing hardware for the FDM simulation and a parallel simulation technique are demonstrated with linearly increasing computational performance using large number of processors of the Earth Simulator.

SIMULATION OF INCIDENT NONLINEAR SOUND BEAM AND 3D SCATTERING FROM COMPLEX TARGETS

This paper presents an integrated simulation method for investigating nonlinear sound beams and three-dimensional (3D) acoustic scattering from any combination of complicated objects. A standard finite-difference simulation method is used to model pulsed nonlinear sound propagation from a source to a scattering target via the Khokhlov–Zabolotskaya–Kuznetsov equation. Then, a parallel 3D acoustic simulation method based on the finite integration technique is used to model the acoustic wave interaction with the target. Any combination of objects and material layers can be placed into the 3D simulation space to study the resulting interaction. Several example simulations are presented to demonstrate the simulation method and 3D visualization techniques. The combined simulation method is validated by comparing experimental and simulation data and a demonstration of how this combined simulation method assisted in the development of a nonlinear acoustic concealed weapons detector is also presented.

Numerical simulation study of ground vibrations using forces from wheels of a running high-speed train

A 3-D viscoelastic finite difference method (FDM) was adopted to study the mechanism of ground vibrations induced by a high-speed train. Time-series data of the forces acting on the railroad were observed from the wheels of a running Shinkansen train in Japan and were used to develop a realistic source function as an input to numerical simulations for a single wheel. This is because the measured forces include suitable frequency components. A 3-D numerical model of the embankment of the railroad was designed to mimic a test field site for which borehole logging data were available. Simple analytical discussions concluded that a rail length of 120 m and a grid spacing of 0.25 m were acceptable for stable FDM simulations without numerical dispersion, and a model with about 32 million grid points was adopted for this study. A staggered-grid FDM with fourth-order accuracy in space was used for the numerical simulations. Finally, the simulated ground vibration was compared with the observed vibrations at the test site. The simulated ground vibrations closely resembled the observed ones. At the test site, the quality factor ( Q) was not observed experimentally; however, the best match with field data was realized by assuming Q=5–50.