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Three-dimensional Fréchet sensitivity kernels for electromagnetic wave propagation
Electromagnetic imaging methods are useful tools for monitoring subsurface changes in pore-fluid content and the associated changes in electrical permittivity and conductivity. The most common method for georadar tomography uses a high frequency ray-theoretic approximation that is valid when material variations are sufficiently small relative to the wavelength of the propagating wave. Georadar methods, however, often utilize electromagnetic waves that propagate within heterogeneous media at frequencies where ray theory may not be applicable. In this paper we describe the 3-D Fréchet sensitivity kernels for EM wave propagation. Various data functional types are formulated that consider all three components of the electric wavefield and incorporate near-, intermediate-, and far-field contributions. We show that EM waves exhibit substantial variations for different relative source-receiver component orientations. The 3-D sensitivities also illustrate out-of-plane effects that are not captured in 2-D sensitivity kernels and can influence results obtained using 2-D inversion methods to image structures that are in reality 3-D.
Rapid calculation of paraxial wave propagation for cylindrically symmetric optics
Not Available
Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.
The detection of upwardly propagating waves channeling energy from the chromosphere to the low corona
There have been ubiquitous observations of wave-like motions in the solar atmosphere for decades. Recent improvements to space- and ground-based observatories have allowed the focus to shift to smaller magnetic structures on the solar surface. In this paper, high-resolution ground-based data taken using the Swedish 1 m Solar Telescope is combined with co-spatial and co-temporal data from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) satellite to analyze running penumbral waves (RPWs). RPWs have always been thought to be radial wave propagation that occurs within sunspots. Recent research has suggested that they are in fact upwardly propagating field-aligned waves (UPWs). Here, RPWs within a solar pore are observed for the first time and are interpreted as UPWs due to the lack of a penumbra that is required to support RPWs. These UPWs are also observed co-spatially and co-temporally within several SDO/AIA elemental lines that sample the transition region and low corona. The observed UPWs are traveling at a horizontal velocity of around 17 ± 0.5 km s{sup –1} and a minimum vertical velocity of 42 ± 21 km s{sup –1}. The estimated energy of the waves is around 150 W m{sup –2}, which is on the lower bound required to heat the quiet-Sun corona. This is a new, yet unconsidered source of wave energy within the solar chromosphere and low corona.
A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems
For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.
Numerical investigation of fast-wave propagation and radio-frequency sheath interaction with a shaped tokamak wall
Interactions between propagating fast waves and radio-frequency (RF) sheaths in the ion cyclotron range of frequencies are numerically investigated based on a cold fluid plasma model coupled with a sheath boundary condition. In this two-dimensional study, the capability of the finite element code rfSOL, which was developed in previous numerical work, is extended to analyze self-consistent RF sheath-plasma interaction problems in a tokamak with a non-circular cross-section. It is found that a large sheath voltage is generated near the edges of the limiter-shaped deformation as a result of the conversion from fast to slow waves on the sheaths. The sheath voltage associated with this conversion is particularly significant in the localized region where the contact angle between the magnetic field line and the conducting wall varies rapidly along the curved sheath surface, which is consistent with the results in previous one-dimensional theoretical work. The dependences of the RF sheaths on various parameters in plasma such as the toroidal wavenumber, edge plasma density, and the degree of the RF wave absorption in the core region are also examined in detail.
Compact representations of partially coherent undulator radiation suitable for wave propagation
Not Available
Experimental realization of an additively manufactured monatomic lattice for studying wave propagation
Increasing interest in wave propagation in phononic systems and metamaterials motivates the development of experimental designs, measurement techniques, and fabrication methods for use in basic research and classroom demonstrations. The simplest phononic system, the monatomic chain, exhibits rich physics such as dispersion and frequency-domain filtering. However, a limited number of experimental studies showcase monatomic chains for macroscale observation of phonons. Herein, we discuss the design, fabrication, and testing of monatomic lattices as enabled by three-dimensional (3D) printing. Using this widely available technology, we provide design guidelines for realization of a monatomic chain composed of 3D printed serpentine springs and press-fitted cylindrical masses. We also present measurement techniques that record propagating waves and algorithms for the experimental determination of dispersion behavior.
Hybrid SAFE-GMM approach for predictive modeling of guided wave propagation in layered media
Not provided.
Identification of the dominant ULF wave mode and generation mechanism for obliquely propagating waves in the Earth's foreshock
Abstract We discuss mechanisms of the generation of ultralow frequency (ULF) upstream waves in the terrestrial foreshock that are essential for the acceleration of ions in space plasmas. The analysis is based on global hybrid kinetic simulations of the magnetosphere that provide realistic environment for the growth of the ULF waves in a quasi‐radial configuration of the interplanetary magnetic field. We focus on a long‐debated problem of the generation mechanism of oblique and parallel ULF waves and provide quantitative arguments in favor of the ion/ion cyclotron resonant instability. We also show that parallel propagating waves are predominantly generated in this configuration, but geometrical effects related to the phase space density in wave vector space lead to apparent predominance of obliquely propagating waves. Correspondence between the results outlined above and previously published experimental claims is thoroughly discussed and our results are shown to be consistent with spacecraft measurements.
Modeling Frequency–Independent Q Viscoacoustic Wave Propagation in Heterogeneous Media
Quantifying the attenuation of seismic waves propagating in the Earth interior is critical to study the subsurface structure. Previous studies have proposed fractional anelastic wave equations to model the frequency–independent Q seismic wave propagation. Such wave equations involve fractional derivatives that pose computational challenges for the numerical schemes in terms of accuracy and efficiency when dealing with heterogeneous Earth media. To tackle these challenges, here we derive a new viscoacoustic wave equation, where the power terms of the fractional Laplacian operators are spatially independent, thus accurate and efficient methods (e.g., the Fourier pseudospectral method) can be adopted. Our derivation enables the resultant equation to capture both amplitude and phase signatures of the anelastic wave propagation by matching the complex wave numbers for all the frequencies of interest. We verify the derivation by comparing the dispersion curves of both the attenuation factor and the phase velocity produced by the new wave equation with their theoretical values as well as the Pierre Shale in situ measurements. Following that, we use a synthetic attenuating gas chimney model to demonstrate the attenuation effects on seismic waveforms and then construct the Q–compensated reverse time migration to undo these effects for seismic image enhancement. Finally, we find that our forward modeling results can characterize the spatiotemporal attenuation effects revealed in the Frio–II CO2 injection time–lapse seismic monitoring data. Here, we expect this proposed equation to be useful to quantify the attenuation in seismic data to push the resolution limits of seismic imaging and inversion.
Effects of density turbulence on helicon wave propagation in the core plasmas
Radio frequency wave propagation can be significantly affected by density irregularities, such as filaments in the scrape-off layer or instabilities in the core plasma. In this study, we examine the impact of edge turbulence on helicon wave propagation using the Petra-M simulation tool. To analyze the effect of edge turbulence, we utilize a realistic background plasma derived from XGC simulations, which includes spatial density fluctuations at the edge. This focus is particularly relevant for the DIII-D configuration, characterized by edge density turbulence of the core plasmas in a wide pedestal QH-mode. We focus on helicon wave propagation in the core plasma since the slow mode cannot propagate into the core plasma when the density is higher than the lower hybrid resonance, where a wide pedestal QH-mode occurs. The simulation results indicate that edge density fluctuations have a substantial impact on helicon wave coupling due to scattering in the core. We specifically demonstrate that the toroidal mode number and the level of density fluctuations are significant factors influencing scattering. While we have minimized the excitation of slow modes from the antenna, we still observe mode-converted slow modes resulting from the incoming helicon waves. The insights derived from these simulations will inform upcoming tokamak experiments regarding helicon antenna coupling in long pulse scenarios.
The Roles of Westward-Propagating Waves and the QBO in Limiting MJO Propagation
Abstract A recent study categorized the Madden–Julian oscillation (MJO) during boreal winter season into four types called stand, jump, slow, and fast MJO. This study focuses on the stand and jump MJO. Based on whether their convection penetrates the Maritime Continent (MC), stand and jump MJOs are seen as non-penetrating (NP) MJOs, while the other two are seen as eastward-penetrating (EP) MJOs. Results reveal the relative roles of the westward-propagating wave (WPW), as well as the QBO and ENSO, in limiting MJO propagation. Lack of the premoistening over the southern sea surface of the MC stops NP MJO from penetrating the MC. The active convection of the WPWs hinders the descending branch of the NP MJO circulation and therefore leads to the insufficient meridional advective moistening over the southern sea surface of the MC. The independent convection over the Pacific for jump MJOs is influenced by a combined effect of the QBO and ENSO. The tropopause instability induced by the MJO is found to significantly decouple from its convection over the Pacific in westerly QBO (QBOW) winters more than in easterly QBO (QBOE) winters. For jump MJOs, the independent convection over the central Pacific comes from local WPWs whose amplification and further development into deep convection are correlated to jump the MJOs’ decoupled tropopause instability. For stand MJOs, however, the seasonal-mean La Niña–like cool SST anomalies weaken the WPW activity over the central Pacific and confine WPWs within the western Pacific. Therefore, the decoupled tropopause instability of stand MJOs is out phase of WPWs and fails to induce an independent convection over the central Pacific.
Effect of dielectric target properties on plasma surface ionization wave propagation
Surface ionization waves (SIWs) propagating along dielectric covered, grounded surfaces have been studied for various dielectric bulk and surface conditions; a dependence on the propagation velocity with respect to dielectric electrical thickness and near surface permittivity profiles are observed. SIWs generated by an atmospheric pressure plasma source are imaged interacting with planar dielectric surface. Surface wave velocity is obtained by tracking emission intensity as a function of time. Target dielectric thickness is varied from $d = 0.15-10$ mm and dielectric constant is varied from $\epsilon_r = 6.21 - 9.4$. The propagation of SIWs can be generally predicted by relating their velocity to the RC time constant of the circuit generated between the plasma and the dielectric surface, but it is found that this approximation breaks down for dielectric substrates of sufficient thickness and wave velocity becomes constant. The results show that wave velocity is stable and predictable for target thicknesses beyond a certain point determined by the permittivity of the target material. It is also shown that SIW propagation is strongly driven by the dielectric material near to the surface of the target in addition to the bulk material. The possible mechanisms driving these thickness dependent behaviors is discussed.
Exploring wave propagation in heterogeneous metastructures using the relaxed micromorphic model
Metamaterials are artificial structures that can manipulate and control sound waves in ways not possible with conventional materials. While much effort has been undertaken to widen the bandgaps produced by these materials through design of heterogeneities within unit cells, comparatively little work has considered the effect of engineering heterogeneities at the structural scale by combining different types of unit cells. In this paper, we use the relaxed micromorphic model to study wave propagation in heterogeneous metastructures composed of different unit cells. We first establish the efficacy of the relaxed micromorphic model for capturing the salient characteristics of dispersive wave propagation through comparisons with direct numerical simulations for two classes of metamaterial unit cells: namely phononic crystals and locally resonant metamaterials. We then use this model to demonstrate how spatially arranging multiple unit cells into metastructures can lead to tailored and unique properties such as spatially-dependent broadband wave attenuation, rainbow trapping, and pulse shaping. In the case of the broadband wave attenuation application, we show that by building layered metastructures from different metamaterial unit cells, we can slow down or stop wave packets in an enlarged frequency range, while letting other frequencies through. In the case of the rainbow-trapping application, we show that spatial arrangements of different unit cells can be designed to progressively slow down and eventually stop waves with different frequencies at different spatial locations. Finally, in the case of the pulse-shaping application, our results show that heterogeneous metastructures can be designed to tailor the spatial profile of a propagating wave packet. Collectively, these results show the versatility of the relaxed micromorphic model for effectively and accurately simulating wave propagation in heterogeneous metastructures, and how this model can be used to design heterogeneous metastructures with tailored wave propagation functionalities.
A modular methodology for time-domain stochastic seismic wave propagation
Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.
Transient processes in the parametric interaction of counter-propagating waves
We present a comparative analysis of transient processes in media with a negative refractive index for the parametric interaction of co- and counter-propagating waves. The transient time for the interaction of counter-propagating waves is shown to considerably exceed that for the interaction of co-propagating waves. In the case of counter-propagating waves, we present fitting results for the generated wave amplitude as a function of time and for the transient time vs. the amplitude of the pump wave and the length of the medium. (optical metamaterials)