Full-wave Field Simulation Research Articles

A multi-band elastic metamaterial for low-frequency multi-polarization vibration absorption

The vibration of engineering structures in actual practice occurs across numerous frequency ranges and includes diverse polarization modes such as bending, torsion, and expansion. Nevertheless, most reported elastic metamaterials are designed for a single frequency range or a single elastic wave mode, thereby making it challenging to simultaneously suppress the propagation of vibrational energy across multiple frequency ranges and polarization modes. To address this limitation, we propose a two-degree-of-freedom elastic metamaterial exhibiting a multi-frequency range elastic band gap and multi-polarization mode elastic wave band gap. By incorporating periodic vibration-absorbing units, gradient parameter vibration-absorbing units, and different polarization mode vibration-absorbing units to the actual equipment support structure, we achieve respective vibration attenuation enhancement, broadband vibration absorption, and multi-polarization mode vibration absorption. We systematically verify the effectiveness of our design through kinetic theoretical analysis, full-wave field simulations, and experimental tests. This metamaterial vibration absorption device can effectively meet the application requirements of complex vibration reduction involving multi-frequency ranges and modes in practical engineering, providing novel insights into equipment vibration and noise reduction design that holds significant reference value for engineering applications.

Elastic full-wave field simulation in 3D tunnel space with the variable staggered-grid finite-difference method in cylindrical coordinates

Tunnel advance detection technology is an important method for determining the structure of complex geological bodies in front of the tunnel face. Among the tunnel advance detection technologies, the seismic method is one of the most accurate methods with long detection distances. In seismic tunnel advance detection, the cylindrical configuration aggravates the complexity of the wave field in the 3D tunnel space and significantly influences the accuracy of the detection results. Thus, it is crucial to simulate an accurate seismic full-wave field of the tunnel space and to understand the propagation and wave-field characteristics of individual seismic waves for seismic tunnel advance detection. Usually, in 3D Cartesian coordinates, the tunnel wall is approximated with a staircase boundary, but it is not sufficiently accurate in shape and generates numerical dispersion in the simulation, especially in the presence of surface waves. Therefore, we developed a variable staggered-grid finite-difference method in cylindrical coordinates to simulate the elastic full-wave field in a 3D tunnel space. Properly setting free-surface boundary conditions solves the propagation of surface waves on the tunnel wall and face. The interference of the instability and discontinuity of the pole axis in the seismic wave field simulation was eliminated using our method. According to practical engineering situations, models containing three types of geological bodies in front of the tunnel face were designed. Their seismic wave propagation and wave field characteristics were analyzed. Compared with the simulation results in Cartesian coordinates, the results in cylindrical coordinates show that numerical dispersion is negligible and conclude that a higher signal-to-noise ratio and more accurate seismic wave field can be simulated with cylindrical coordinates in the 3D tunnel space. Our simulation method provides theoretical and practical guidance for analyzing and interpreting seismic wave fields in tunnel advance detection.

An efficient full-wavefield computational approach for seismic testing in a layered half-space

Inversion of subsurface shear-wave velocity profile based on effective dispersion curve or full wavefield is still rare due to the lack of efficient forward computation kernel for the full wavefield in a layered medium. To facilitate exploiting the complete signal content in seismic testing, an efficient new computational framework for modeling synthetic full wavefields in horizontally layered systems is proposed. Dynamic response of an isotropic elastic layered system subjected to vertical loading is implemented and thoroughly validated. The new procedure is based the Fourier-Bessel series expansion (not the traditional Fourier-Bessel transform), and it is at least two-orders faster than the current full wavefield computation method based on integral transformation. It considers survey parameters and models all wave phenomena, including near-field effect and leaky waves, which cannot be captured by the modal summation method. Examples of full wavefield simulation are presented to demonstrate different levels of information provided by the experimentally available fundamental mode, broadband effective dispersion curve, and the full velocity spectrum. Different earth models may have similar fundamental modes or even effective dispersion curves; however, their difference manifests in different higher-mode contributions and can only be exploited by utilizing the entire velocity spectra including the vertical and radial components. The coupling between the vertical and radial components in terms of their spectral ratio and phase difference can provide additional constraints (data) in seismic testing.

Imaging the Kanto Basin seismic basement with earthquake and noise autocorrelation functions

SUMMARYSedimentary basins can strongly amplify seismic waves from earthquakes. To better predict future ground motions, detailed knowledge of the sediment thickness and internal structure of basins is required. We image the sediment-to-bedrock interface of the Kanto Basin in Japan using the P-wave reflectivity response from earthquake and ambient seismic noise autocorrelation functions (ACFs) at 286 shallow borehole stations. Earthquake ACFs are computed using P-wave records from 50 Mw 6+ teleseismic events. Noise ACFs are obtained using 1 month of continuous data. Both methods are used to retrieve P-wave traveltimes between the surface and the bedrock interface and map the basin basement geometry. Our prediction of the basement depth agrees generally well with that from a reference velocity model, except for smoother variations in the central part of the basin. Using full-wavefield simulations, we show that the nature of the autocorrelated wavefield has a significant impact on the shape of the ACF waveforms and that earthquake ACFs yield more accurate results in the Kanto Basin.

Fast and Memory-Efficient Frequency-Domain Least-Squares Reverse-Time Migration Using Singular Value Decomposition (SVD)

Least-squares reverse time migration (LSRTM) is linearized inversion based on Born approximation, which commonly seeks to high-quality migration result by least-squares sense. Contrary to time domain LSRTM which performs the wavefield simulation as much as several times of the number of shots, frequency-domain LSRTM (F-LSRTM) has advantage to efficiently deal with multiple shot records. Furthermore, if Green’s function can be saved on memory storage, the full wavefield simulation is implemented only once at the first iteration during entire LSRTM iterations. However, huge memory storage may be required to save the Green’s function for large dataset and model size. To alleviate this computational issue, we propose an efficient F-LSRTM scheme using singular value decomposition (SVD). In our scheme, Green’s function can be saved efficiently as two unitary matrices and one singular value vector with a few number of dominant singular values. Because the number of dominant singular values, called as the optimal rank, is much smaller than the minimum value in each dimension size of Green’s function, the proposed method can make it possible to save the Green’s function into the computing memory with keeping the accuracy. After demonstrating the feasibility of reducing the rank of Green’s function, we examine our proposed F-LSRTM scheme and comparative F-LSRTM schemes (F-LSRTM using adjoint-state method and saved full Green’s function, respectively) using the simple layered and modified marmousi-2 model. Numerical tests indicate that our proposed F-LSRTM scheme can generate migration results as accurate as comparative F-LSRTM schemes with less memory usages and computational cost.

Tectonic tremors in the Northern Mexican subduction zone remotely triggered by the 2017 Mw8.2 Tehuantepec earthquake

Surface waves from the 2017 Mw8.2 Tehuantepec earthquake remotely triggered tectonic tremors in the Jalisco region, approximately 1000 km WNW in the northern Mexican subduction zone. This is the first observation of tremor triggering in this region and one of the largest known examples of a triggered tremor in the world. Although prior studies have found tectonic tremors triggered by teleseismic waves in subduction zones and plate boundaries, further investigation of tremor triggering is crucially important for understanding the causative mechanism. We calculate the stress and strain changes across the three-dimensional plate interface attributable to seismic waves from the earthquake by full wavefield simulation. The maximum magnitude of the dynamic strain tensor eigenvalues on the plate interface, where tremors likely occur, is approximately 10–6. The subducting slab geometry effectively amplifies triggering waves. The triggering Coulomb failure stress changes resolved for a thrust fault plane consistent with the geometry are estimated to be approximately 10–40 kPa. The relationship between the triggering stress and triggered tremor amplitude may indicate that the aσ of the rate–state-dependent friction law is 10–100 kPa.

Full wavefield simulation versus measurement of microwave scattering by a complex 3D-printed asteroid analogue

Context. The small bodies of the Solar System, and especially their internal structures, are still not well-known. Studies of the interior of comets and asteroids could provide important information about their formation and also about the early Solar System. Aims. In this paper, we investigate the possibility of obtaining information about their inner structure from their response to an incident electromagnetic field in preparation for future space radar missions. Our focus is on experimental measurements concerning two analog models with the shape of 25143 Itokawa, a small rubble pile asteroid monitored by the Japanese space agency’s (JAXA) Hayabusa mission in 2005. Methods. The analog models prepared for this study are based on the a priori knowledge of asteroid interiors of the time. The experimental data were obtained by performing microwave-range laboratory measurements. Two advanced in-house, full-wave modelling packages – one performing the calculations in the frequency domain and the other one in the time domain – were applied to calculate the wave interaction within the analog models. Results. The electric fields calculated via both the frequency and time domain approach are found to match the measurements appropriately. Conclusions. The present comparisons between the calculated results and laboratory measurements suggest that a high-enough correspondence between the measurement and numerical simulation can be achieved for the most significant part of the scattered signal, such that the inner structure of the analog can be observed based on these fields. Full-wave modeling that predicts direct and higher order scattering effects has been proven essential for this application.

Full wave sensitivity of SK(K)S phases to arbitrary anisotropy in the upper and lower mantle

SUMMARY Core-refracted phases such as SKS and SKKS are commonly used to probe seismic anisotropy in the upper and lowermost portions of the Earth’s mantle. Measurements of SK(K)S splitting are often interpreted in the context of ray theory, and their frequency dependent sensitivity to anisotropy remains imperfectly understood, particularly for anisotropy in the lowermost mantle. The goal of this work is to obtain constraints on the frequency dependent sensitivity of SK(K)S phases to mantle anisotropy, particularly at the base of the mantle, through global wavefield simulations. We present results from a new numerical approach to modelling the effects of seismic anisotropy of arbitrary geometry on seismic wave propagation in global 3-D earth models using the spectral element solver AxiSEM3D. While previous versions of AxiSEM3D were capable of handling radially anisotropic input models, here we take advantage of the ability of the solver to handle the full fourth-order elasticity tensor, with 21 independent coefficients. We take advantage of the computational efficiency of the method to compute wavefields at the relatively short periods (5 s) that are needed to simulate SK(K)S phases. We benchmark the code for simple, single-layer anisotropic models by measuring the splitting (via both the splitting intensity and the traditional splitting parameters ϕ and δt) of synthetic waveforms and comparing them to well-understood analytical solutions. We then carry out a series of numerical experiments for laterally homogeneous upper mantle anisotropic models with different symmetry classes, and compare the splitting of synthetic waveforms to predictions from ray theory. We next investigate the full wave sensitivity of SK(K)S phases to lowermost mantle anisotropy, using elasticity models based on crystallographic preferred orientation of bridgmanite and post-perovskite. We find that SK(K)S phases have significant sensitivity to anisotropy at the base of the mantle, and while ray theoretical approximations capture the first-order aspects of the splitting behaviour, full wavefield simulations will allow for more accurate modelling of SK(K)S splitting data, particularly in the presence of lateral heterogeneity. Lastly, we present a cross-verification test of AxiSEM3D against the SPECFEM3D_GLOBE spectral element solver for global seismic waves in an anisotropic earth model that includes both radial and azimuthal anisotropy. A nearly perfect agreement is achieved, with a significantly lower computational cost for AxiSEM3D. Our results highlight the capability of AxiSEM3D to handle arbitrary anisotropy geometries and its potential for future studies aimed at unraveling the details of anisotropy at the base of the mantle.

3D variable-grid full-waveform inversion on GPU

Full-waveform inversion (FWI) is a powerful tool to reconstruct subsurface geophysical parameters with high resolution. As 3D surveys become widely implemented, corresponding 3D processing techniques are required to solve complex geological cases, while a large amount of computation is the most challenging problem. We propose an adaptive variable-grid 3D FWI on graphics processing unit devices to improve computational efficiency without losing accuracy. The irregular-grid discretization strategy is based on a dispersion relation, and the grid size adapts to depth, velocity, and frequency automatically. According to the transformed grid coordinates, we derive a modified acoustic wave equation and apply it to full wavefield simulation. The 3D variable-grid modeling is conducted on several 3D models to validate its feasibility, accuracy and efficiency. Then we apply the proposed modeling method to full-waveform inversion for source and residual wavefield propagation. It is demonstrated that the adaptive variable-grid FWI is capable of decreasing computing time and memory requirements. From the inversion results of the 3D SEG/EAGE overthrust model, our method retains inversion accuracy when recovering both thrust and channels.

Impedance Model of Cylindrical Nanowires for Metamaterial Applications.

In metamaterials, metallic nanowires are used for creating artificial materials to functionalize them for various nanophotonics applications. Strong polarization-dependent response coupled with complex dielectric function at optical frequencies gives additional degrees of freedom to achieve scattering, absorption, and other benefits that go much beyond what is possible with conventional materials. In this paper, we propose an extended cylindrical wave impedance approach at optical frequencies to model the internal and external impedance of the metallic nanowire. Equivalent analytical expression for the scattering, extinction, and absorption cross-sectional area efficiencies are derived in terms of impedances. The motivation is to develop an all-mode solution ( and modes), by bringing the complex problem of plasmonic nanowire to linear system theory, where established methods can be applied to enable new applications. The equivalence of the impedance solution is compared with electromagnetic field solution and numerical full-wave field simulations. The proposed solution is accurate and may contribute to the rapid and efficient future designs for the metallic nanowire-based nanophotonic metamaterials.

Tremor-rich shallow dyke formation followed by silent magma flow at Bárðarbunga in Iceland

The Barðarbunga eruption in Iceland in 2014 and 2015 produced about 1.6 km3 of lava. Magma propagated away from Barðarbunga to a distance of 48 km in the subsurface beneath Vatnajokull glacier, emerging a few kilometres beyond the glacier’s northern rim. A puzzling observation is the lack of shallow (<3 km deep), high-frequency earthquakes associated with shallow dyke formation near the subaerial and subglacial eruptive sites, suggesting that near-surface dyke formation is seismically quiet. However, seismic array observations and seismic full wavefield simulations reveal the presence and nature of shallow, pre-eruptive, long-duration seismic tremor activity. Here we use analyses of seismic data to constrain the relationships between seismicity, tremor, dyke propagation and magma flow during the Barðarbunga eruption. We show that although tremor is usually associated with magma flow in volcanic settings, pre-eruptive tremor at Barðarbunga was probably caused by swarms of microseismic events during dyke formation, and hence is directly associated with fracturing of the upper 2–3 km of the crust. Subsequent magma flow in the newly formed shallow dyke was seismically silent, with almost a complete absence of seismicity or tremor. Hence, we suggest that the transition from temporarily isolated, large, deep earthquakes to many smaller, shallower, temporally overlapping earthquakes (<magnitude 2) that appear as continuous tremor announces the arrival of a dyke opening in the shallow crust, forming a pathway for silent magma flow to the Earth’s surface. Magma movement is thought to trigger volcanic tremor. However, analysis of seismic data suggests that tremor prior to the Barðarbunga eruption in Iceland instead marked the crust cracking open, whereas subsequent magma flow was seismically silent.

An investigation into the remote triggering of the Oita earthquake by the 2016 Mw 7.0 Kumamoto earthquake using full wavefield simulation

High-amplitude seismic waves from the Mw 7.0 Kumamoto earthquake of April 16, 2016, triggered another large earthquake 80 km to the NE roughly 30 s later. The source was located at shallow depths beneath the Yufuin geothermal field, Oita Prefecture, Japan, and the event magnitude was approximately 5.9. To date, this is one of the clearest known examples of a remotely triggered large earthquake. The triggered Oita event was followed by significant seismicity, which was distinct from the aftershocks of the Kumamoto earthquake. The Coulomb failure stress change around the hypocenter, calculated for the passing waves of the Kumamoto earthquake by full wavefield simulation, was about 0.7 MPa when the Oita earthquake was triggered, with the static stress change being an order of magnitude smaller. The dynamic stress changes likely played an important role in triggering. A return to low seismicity levels 1 month after the triggered earthquake may have important implications for seismic hazard due to dynamic triggering.

AN EFFICIENT TECHNIQUE FOR DESIGN OF ELECTRICALLY THICK DIFFERENTIALLY-DRIVEN PROBE-FED MICROSTRIP ANTENNAS

This paper presents a computationally efficient technique for designing electrically thick differentially-driven rectangular microstrip antennas with coaxial probe feed. It concerns the use of a transmission line model for probe positioning, along with a full-wave field simulator that yields accurate results with reduced number of required full-wave simulations. An electrically thick antenna was designed with the proposed technique to operate at 2442 MHz, having its radiation patterns and input impedance measured and compared against a single-feed rectangular microstrip antenna to demonstrate the advantages of using differential feed to reduce cross-polarization in H-plane.

Efficient Broadband Circuit-Modeling Approach for Parallel-Plane Structures of Arbitrary Shape

A methodology for creating highly efficient and inherently stable equivalent-circuit models for arbitrarily shaped parallel-plane pairs is presented. Based on Green's function with accelerated convergence, a general impedance expression is derived for circular ports, comprising the static capacitance and inductances and a small number of resonant terms. It can be directly cast into an equivalent multiport circuit for arbitrary number of ports, enabling the application in a SPICE circuit-simulation environment for broadband system analysis with active, passive, and nonlinear components. The equivalent-circuit elements are determined by a simple finite-difference scheme in combination with an analytical port model, which allows us to perform the required modal and the quasi-static analysis with a uniform mesh. Validation by numerical full-wave field simulations demonstrates the versatility of the suggested approach and the high computational savings of several orders of magnitude in frequency and time domain.

Efficient Foster-Type Macromodels for Rectangular Planar Interconnections

A novel macromodeling technique for passive linear multiport interconnecting structures is presented. It is based on an inherently stable Foster-type equivalent-circuit realization of the Greens function, given in the form of an infinite eigenfunction expansion. In order to obtain a finite number of equivalent-circuit elements, a rapidly convergent double sum representation of the corresponding port transfer-impedance function is cast into a newly modified Foster-type equivalent circuit with additional inductive elements. For a time-domain analysis, a system-theory based model-order estimation is presented and evaluated for trapezoidal excitation functions. Numerical computations are shown for a rectangular parallel-plate example structure, and validated by the results of full-wave field simulations, based on the finite-integration theory and method of moments. The suggested macromodeling technique provides a computationally very efficient and versatile approach for system analysis in the frequency- and time-domain with linear/nonlinear passive and active components.

Influence of near‐surface volcanic structure on long‐period seismic signals and on moment tensor inversions: Simulated examples from Mount Etna

Long‐period (LP) seismicity on volcanoes is thought to be associated with moving fluids or resonating fluid‐filled conduits, hence LP moment tensor (MT) source inversions might have a direct bearing on our understanding of the plumbing system. Using 3‐D full wavefield simulations and 2‐D sensitivity kernels in a digital elevation model of Mount Etna, we investigate the influence of near‐surface volcanic structure on LP signals and on moment tensor inversions. Contrary to common wisdom in crustal seismology we find that, despite their relatively long wavelengths, LPs are severely distorted by near‐surface structures including layering and topographic features. In particular near‐surface low‐velocity structures which are commonly observed on volcanoes play a critical role in controlling the nature of LP signals. If not accounted for, these path effects leak into the source solution, leading to the emergence of erroneous source geometries, spurious forces and incorrect source time functions. This is particularly problematic if one adopts an “unconstrained” solution space for the source, with many free parameters. Hence there is a fine balance in the trade‐off between the velocity model and the source. In the absence of high‐resolution near‐surface velocity control we demonstrate the importance of employing a priori source information from other fields (e.g., structural geology), for shallow LPs, constraining the number of free parameters in the inversion. A probabilistic approach should then be taken, as the model with the “best fit” is not necessarily the “true” solution.

Simulations of Strong Ground Motion and 3D Amplification Effect in the Taipei Basin by Using a Composite Grid Finite-Difference Method

We perform full elastic wave-field simulations within the Taipei basin by using a three-dimensional (3D) discontinuous finite-difference method. The 3D Taipei basin model is determined from a seismic reflection study. Two major subsurfaces, the Songshan formation (surface soil layer) and the basin basement, are constituted in the model. A parallel-based composite grid technique, a containing scalene grid and a discontinuous grid, is developed in this study to deal with the possible numerical prob- lem of thin depth and low velocity of the Songshan formation. Taking advantage of the composite grid, the resolution of the subsurface structure can be reached to 20 m, and a higher frequency (up to 3 Hz) of the synthetic waveform can be achieved. In our strong ground motion simulations, we assume a constant velocity in each subsurface. Three different types of models are considered in the study: the Songshan formation with a basement structure model, a basin basement model, and a layered half-space model. Results indicate that only the model with both the Songshan formation and the basement structure can produce the apparent basin amplification effects. First, the surface wave generated after the primary S wave is trapped at the shallow part of the basin. Then, when the wave propagates through the deepest part of the basin, most of the energy is reflected from the boundary and focused back into the basin. In addi- tion, part of the seismic wavefront turns and follows the shallow basin edge resulting in further amplification. Our study indicates that the complex Taipei basin geometry and fairly low velocity of the Songshan formation dominate the amplification and wave propagation behavior that result in extraordinary strong shaking patterns in the Taipei metropolitan region.

Shear wave birefringence in wedge-shaped anisotropic regions

SUMMARY A popular method for studies of seismic wave speed anisotropy within the Earth is based on observations of birefringence in subvertically propagating shear waves. A well-recognized shortcoming of the method is that individual birefringence measurements, commonly interpreted as a path-average of anisotropy, do not reveal the potential complexity of anisotropic structure. Consequently, there is a necessary ambiguity in the interpretation of observed birefringence parameters (fast polarization directions and delays between components). In this paper, we explore the influence of observational geometry and the configuration of an anisotropic region on the birefringence parameters. We use full wavefield simulations in 3-D models to access these influences in a subduction zone setting. Our primary findings are that (a) modest wavefield complications associated with the non-planar geometry of a subduction zone can significantly bias the determination of the fast polarization and time delay associated with shear wave birefringence; (b) shear wave splitting associated with flow in the mantle wedge near the trench (e.g. the forearc) is likely to be weak, owing to short path lengths through an anisotropic region and (c) popular splitting estimators are vulnerable to waveform distortions caused by S-wave interaction with the dipping slab interface. We show that simultaneous interpretation of numerous birefringence observations from a variety of propagation directions is a more reliable way to constrain parameters of anisotropy at depth.

Planar negative refractive index media using periodically L-C loaded transmission lines

Recent demonstrations of negative refraction utilize three-dimensional collections of discrete periodic scatterers to synthesize artificial dielectrics with simultaneously negative permittivity and permeability. In this paper, we propose an alternate perspective on the design and function of such materials that exploits the well-known L-C distributed network representation of homogeneous dielectrics. In the conventional low-pass topology, the quantities L and C represent a positive equivalent permeability and permittivity, respectively. However, in the dual configuration, in which the positions of L and C are simply interchanged, these equivalent material parameters assume simultaneously negative values. Two-dimensional periodic versions of these dual networks are used to demonstrate negative refraction and focusing; phenomena that are manifestations of the fact that such media support a propagating fundamental backward harmonic. We hereby present the characteristics of these artificial transmission-line media and propose a suitable means of implementing them in planar form. We then present circuit and full-wave field simulations illustrating negative refraction and focusing, and the first experimental verification of focusing using such an implementation.

Synthesis of amplitude‐versus‐offset variations in ground‐penetrating radar data

To evaluate the importance of amplitude‐versus‐offset information in the interpretation of ground‐penetrating radar (GPR) data, GPR reflections are synthesized as a function of antenna separation using a 2.5-D finite‐difference solution of Maxwell’s equations. The conductivity, the complex dielectric permittivity, and the complex magnetic permeability are varied systematically in nine suites of horizontally layered models. The source used is a horizontal transverse‐electric dipole situated at the air‐earth interface. Cole‐Cole relaxation mechanisms define the frequency dependence of the media. Reflection magnitudes and their variations with antenna separation differ substantially, depending on the contrast in electromagnetic properties that caused the reflection. The spectral character of the dielectric and magnetic relaxations produces only second‐order variations in reflection coefficients compared with those associated with contrasts in permittivity, conductivity, and permeability, so they may not be separable even when they are detected. In typical earth materials, attenuation of propagating GPR waves is influenced most strongly by conductivity, followed by dielectric relaxation, followed by magnetic relaxation. A pervasive feature of the simulated responses is a locally high amplitude associated with the critical incident angle at the air‐earth interface in the antenna radiation pattern. Full wavefield simulations of two field data sets from a fluvial/eolian environment are able to reproduce the main amplitude behaviors observed in the data.