Incoming Wave Field Research Articles

The i-FSC proxy for predicting inter-event and spatial variation of topographic site effects

Our study focuses on predicting topographic amplification of ground motion in the near-source region, where seismic rays reach the free-surface at varying incidence angles. We rely on data from previous 3D numerical simulations conducted on a topographic relief with a homogeneous medium. First, using neural networks, we identify which key parameters, describing the geometric characteristics of the relief relative to the seismic source position, control ground motion amplification. Then, we determine the functional form that relates these parameters to the simulated amplifications. Subsequently, we conduct a regression study to develop a model of topographic amplification, referred to as the i-FSC proxy (Illuminated Frequency-Scaled Curvature). Our estimator depends on the frequency-scaled (1) curvature, a parameter that accounts for the occurrence of amplifications over convex topographies and de-amplification over concave ones; (2) normalized illumination angle, a newly defined parameter that quantifies the slope exposure to the incoming wavefield, accounting for high amplification on slopes oriented opposite to the seismic source. The illumination parameter reduces the uncertainties of the proxy by a factor of 2 compared to estimators that rely solely on curvature. The proxy does not require high computational resources. It uses a digital elevation map and a seismic source position to predict amplification factors (without lithological effects) for an S-wave at any site on the surface topography. It allows exploration of variations in topographic amplification near seismic sources, representing a significant breakthrough as areas closest to the fault typically sustain the highest damages. A MATLAB script performing the i-FSC calculations is provided.

Exact boundary-value solution for an electromagnetic wave propagating in a linearly varying index of refraction

The propagation of electromagnetic waves in a linearly varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact solution is obtained for a given incoming wavefield specified on the boundary transverse to the direction of inhomogeneity by performing a spectral, rather than asymptotic, matching. Two case studies are then presented: a Gaussian beam at oblique incidence and a speckled wavefield at normal incidence. For the Gaussian beam, it is shown that when the waist $W$ is sufficiently large, oblique incidence manifests simply as rigid translation and focal shift of the corresponding diffraction pattern at normal incidence. The destruction of the hyperbolic umbilic caustic (corresponding to a critically focused beam) as $W$ is reduced is then demonstrated. The caustic disappears once $W \lesssim \delta _a \sqrt {L}$ ( $L$ being the medium length scale normalized by the Airy skin depth $\delta _a$ ), at which point the wave behaviour is increasingly described by Airy functions, but experiences less focusing as a result. To maximize the intensity of a launched Gaussian beam at a turning point, one should therefore minimize the imaginary part of the launched complex beam parameter while having the real part satisfy critical focusing. For the speckled wavefield, it is shown that the transverse speckle pattern only couples to the Airy longitudinal pattern when the coupling parameter $\eta = \sqrt {L}/f_{\#}$ is large, with $f_{\#}$ being the f-number of the launching aperture. When $\eta \ll 1$ , a reduced description of the total wavefield can be obtained by simply multiplying the incoming speckle pattern with the Airy swelling.

Wave-driven current and vortex patterns at an open beach: Insights from phase-resolving numerical computations and Lagrangian measurements

Wave-driven current and vortex patterns at an open beach: Insights from phase-resolving numerical computations and Lagrangian measurements

A 3D BEM-Coupled Mode Model for the Performance Analysis of Wave Energy Converter Parks in Nearshore-Coastal Regions

Estimation on the production capacity of wave energy converter arrays (WECs) of the type of simple floaters deployed in nearshore locations highly depends on the evaluation of their performance. The latter also depends on various factors, including the dimensions and inertial characteristics of the devices, their relevant positioning, and the power take-off (PTO) system characteristics. Studying the system operation, based on the prevailing sea conditions in the region considered for deployment, can ensure that such WEC farms are sized and designed in an effective way. Furthermore, the wavelength and propagation direction of incoming wave fields can be significantly impacted by wave-seabed interactions in coastal areas, which can alter the WECs’ response pattern and ultimately the array’s power output. In this work, a 3D BEM hydrodynamic model is proposed aiming to assess the energy-capturing capacity of WEC arrays, accounting for the hydrodynamic interactions between various identical floating devices, as well as the local seabed topography. The model is supplemented by a Coupled Mode System (CMS) to calculate the incident wave field propagating over variable bathymetry, in order to simulate realistic nearshore environments. Finally, a case study is performed for an indicative geographical area, north of the coast of the island of Ikaria, located in the Eastern Aegean Sea region, where the wave potential is high, using long-term data. The latter study highlights the applicability of the proposed method and suggests its usage as a tool to support optimal WEC park design.

A caustic terminating at an inflection point

A caustic terminating at an inflection point

Earthquake location based on Distributed Acoustic Sensing (DAS) as a seismic array

Earthquake location based on Distributed Acoustic Sensing (DAS) as a seismic array

CROSS-SHORE TRANSFORMATION OF BOUND AND FREE INFRAGRAVITY WAVES OFF THE DUTCH COAST

Infragravity (IG) waves are key drivers for coastal erosion and thus need to be properly included in process-based modelling of coastal hazards. Uncertainties remain regarding the offshore boundary conditions for these long waves. Typically, only bound IG waves are included at the boundary, which means that the possible contribution of free IG waves, such as those radiated from distant coastlines, is neglected. Recent studies however suggest that incoming free IG waves could be significant, particularly in semi-enclosed basins such as the North Sea where they could contribute to coastal hazards (e.g., Reniers et al., 2021, Rijnsdorp et al. 2021). The objective of this work is to improve the understanding of the incoming IG wave field along the Dutch coast. We will quantify how bound and free IG waves develop in intermediate water depths and assess in which conditions (onshore directed) free IG waves become significant.

Intensity of focused waves near turning points.

A wave near an isolated turning point is typically assumed to have an Airy function profile with respect to the separation distance. This description is incomplete, however, and is insufficient to describe the behavior of more realistic wave fields that are not simple plane waves. Asymptotic matching to a prescribed incoming wave field generically introduces a phase front curvature term that changes the characteristic wave behavior from the Airy function to that of the hyperbolic umbilic function. This function, which is one of the seven classic "elementary" functions from catastrophe theory along with the Airy function, can be understood intuitively as the solution for a linearly focused Gaussian beam propagating in a linearly varying density profile, as we show. The morphology of the caustic lines that govern the intensity maxima of the diffraction pattern as one alters the density length scale of the plasma, the focal length of the incident beam, and also the injection angle of the incident beam are presented in detail. This morphology includes a Goos-Hänchen shift and focal shift at oblique incidence that do not appear in a reduced ray-based description of the caustic. The enhancement of the intensity swelling factor for a focused wave compared to the typical Airy solution is highlighted, and the impact of a finite lens aperture is discussed. Collisional damping and finite beam waist are included in the model and appear as complex components to the arguments of the hyperbolic umbilic function. The observations presented here on the behavior of waves near turning points should aid the development of improved reduced wave models to be used, for example, in designing modern nuclear fusion experiments.

Control-oriented wave surface elevation forecasting strategies: Experimental validation and comparison*

Control-oriented wave surface elevation forecasting strategies: Experimental validation and comparison*

Space-variant polarization conversion with artificial birefringent metallic elements

We present an artificial birefringent space-variant polarization converter for the near infrared, λ = 1550 nm. Each hollow waveguide has a rectangular shape with lateral dimensions of 1550 nm in the x-direction and 1034 nm as the largest length in the y-direction. The whole device consists of approximately 2000 × 2500 hollow waveguides realized in a 2-µm-thick gold structure. They are separated by sidewalls with a width of less than 500 nm. By proper choice of the lateral widths of the individual holes, a pixel-wise polarization conversion of an incoming wave field is possible. By suitable choice of the fabrication parameters, a birefringent phase shift up to 2π can be achieved. Hence, the structure is able to fully convert the state of polarization, e.g., from linear to circular. For fabrication of the device, femtosecond 3D direct laser writing was combined with electroplating. Here, we describe the operation of our device as a space-variant polarization converter by measuring the angle-dependent transmitted power and by calculating the ellipticity and the phase delay dependent on position as well as the azimuth angle from the experimentally determined powers.

Sensitivity kernels for receiver function misfits in a full waveform inversion workflow

SUMMARY Receiver functions have been used for decades to study the Earth’s major discontinuities by focusing on converted waves. Deconvolution, which is the mathematical backbone of the method, is assumed to remove the source time function and the far-field dependence on structure, making it a useful method to map the nearby Earth structure and its discontinuities. Ray theory, a plane incoming wavefield, and a sufficiently well-known near-receiver background velocity model are conventionally assumed to map the observations to locations in the subsurface. Many researchers are aware of the shortcoming of these assumptions and several remedies have been proposed for mitigating their consequences. Adjoint tomography with a quasi-exact forward operator is now within reach for most researchers, and we believe is the way forward in receiver function studies. A first step is to calculate adjoint sensitivity kernels for a given misfit function. Here, we derive the adjoint source for a receiver function waveform misfit. Using a spectral element forward code, we have calculated sensitivity kernels for P-to-S converted waves using several 2-D models representing an average crust with an underlying mantle. The kernels show profound differences between P- and S-wave speed sensitivity. The sensitivity to P-wave speed is wide-ranging and related to the scattered P-wavefield which interferes with that of the P-to-S converted wave. The S-wave speed sensitivity is more local and mostly associated to potential locations of P-to-S conversion, although more distant sensitivity is also observed. Notably, there is virtually no sensitivity to impedance. We further observe the well-known trade-off between depth of the discontinuity and wave speed, but find that considering a longer waveform that includes more surface reverberations reduces this trade-off significantly.

Real-Time Wave Excitation Forces Estimation: An Application on the ISWEC Device

Optimal control strategies represent a widespread solution to increase the extracted energy of a Wave Energy Converter (WEC). The aim is to bring the WEC into resonance enhancing the produced power without compromising its reliability and durability. Most of the control algorithms proposed in literature require for the knowledge of the Wave Excitation Force (WEF) generated from the incoming wave field. In practice, WEFs are unknown, and an estimate must be used. This paper investigates the WEF estimation of a non-linear WEC. A model-based and a model-free approach are proposed. First, a Kalman Filter (KF) is implemented considering the WEC linear model and the WEF modelled as an unknown state to be estimated. Second, a feedforward Neural Network (NN) is applied to map the WEC dynamics to the WEF by training the network through a supervised learning algorithm. Both methods are tested for a wide range of irregular sea-states showing promising results in terms of estimation accuracy. Sensitivity and robustness analyses are performed to investigate the estimation error in presence of un-modelled phenomena, model errors and measurement noise.

Generation of a polarized optical field from a given scalar field for wide-viewing-angle holographic displays

• A model for wide-viewing-angle holographic display of scalar fields is developed. • A novel transformation from scalar wave fields to polarized optical fields is introduced. • The scalar wave theory is made useful beyond the paraxial regime. Although the scalar wave theory does not fully describe the nature of the light, which is a vector wave field, it is common to characterize the optical field propagated from an object as a scalar wave in 3DTV research. A given scalar wave field is usually directly mapped to the transverse field components of a simply polarized optical field during the generation of the optical field by a holographic 3D display; this procedure gives accurate results in terms of the optical intensity if the field is paraxial. However, due to the nonnegligibly large longitudinal component of the vector field, this method fails in wide-angle fields. In order to generate a polarized optical field which has the same resultant effect as prescribed by a wide-angle scalar field, we extend this simple polarization approach to tilted and rotated planes. That is, we first put a constraint on the generated vector wave field such that each plane wave component has a simple polarization relation at its locally transverse plane. Then, we map the complex plane wave amplitudes of a given scalar field to the plane wave amplitudes of locally transverse field components of the polarization-constrained optical field. As a consequence of the developed mapping, for an observer which is located at a tilted and rotated plane and captures a locally paraxial segment of the incoming wave field, the intended scalar intensity results can also be obtained in wide-viewing-angle 3D holographic displays. The developed model is valid if the chosen local coordinate frames of the locally transverse planes of the propagating plane waves vary slowly as the propagation direction changes. For a 3DTV setup where the display is located at a z -plane and the observers are located away from the z -axis, an analytical representation for appropriate coordinate frames is developed. For the same setup, computer simulation results showed that the excessive amplification of the longitudinal component due to the conventional mapping does not arise in the proposed method and the desired scalar results are observed. Moreover, since the determined polarization state is preserved at each tilted and rotated plane, the new model can also be used in an optical setup where the polarization information is important. As a result, the proposed mapping enables the scalar wave theory to be used in wide-viewing angle holographic display applications under the given constraints.

Standing wave field observations at a vertical wall

Abstract To withstand the local wave climate, coastal structure design relies on our understanding of the wave characteristics at the structure wall and the forces they impose onto the wall. However, despite the vast number of protective structures along our coasts, detailed field observations of waves measured directly at the structure wall are virtually absent. In this study, rare observations of wave characteristics at a vertical wall are presented. Contrary to linear wave theory, results suggest that the standing waves are highly nonlinear. Waves at the wall have considerably larger kurtosis and skewness compared to the incoming wave field and the wave steepness at the wall is observed to exceed the theoretical wave steepness limit of standing waves.

Extreme Inundation Statistics on a Composite Beach

The runup of initial Gaussian narrow-banded and wide-banded wave fields and its statistical characteristics are investigated using direct numerical simulations, based on the nonlinear shallow water equations. The bathymetry consists of the section of a constant depth, which is matched with the beach of constant slope. To address different levels of nonlinearity, time series with five different significant wave heights are considered. The selected wave parameters allow for also seeing the effects of wave breaking on wave statistics. The total physical time of each simulated time-series is 1000 h (~360,000 wave periods). The statistics of calculated wave runup heights are discussed with respect to the wave nonlinearity, wave breaking and the bandwidth of the incoming wave field. The conditional Weibull distribution is suggested as a model for the description of extreme runup heights and the assessment of extreme inundations.

Phase‐Coherent Amplification of Ocean Swells Over Submarine Canyons

AbstractOcean swells can be a significant coastal hazard, potentially causing coastal disasters with costly damage to infrastructure and tragic loss of lives. We have observed this in the coastal region of Toyama Bay in the Sea of Japan, which has been devastated by severe winter swell events (the so‐called YoriMawari‐nami; YM wave). An extreme swell event was recorded in February 2008 in which the wave height at a site in the bay reached 9+ m, which corresponds to 16 times the local climatological average. Substantial efforts by the Japanese coastal engineering community have been expended to reproduce YM wave events with phase‐averaged wave models but, to our knowledge, with no success. During an archetype YM event, we found that the Noto peninsula filtered the incoming wavefield such that in the bay incident waves were quasi‐monochromatic. The swell then refracted over a submarine canyon resulting in a bimodal directional distribution of wave energy. This initiated conditions favorable for coherent interference, violating the assumptions of the phase‐averaged approach. Coherent interference is the key mechanism for understanding the formation of the large amplitudes and for matching observed high space‐time variability. Our results demonstrate the significance of the coherent interference for wave statistics over coastal bathymetry; only by accounting for phase‐resolving phenomena were we able to adequately reproduce the observations.

CLEAN beamforming for the enhanced detection of multiple infrasonic sources

SUMMARY The detection and characterization of signals of interest in the presence of (in)coherent ambient noise is central to the analysis of infrasound array data. Microbaroms have an extended source region and a dynamical character. From the perspective of an infrasound array, these coherent noise sources appear as interfering signals that conventional beamform methods may not correctly resolve. This limits the ability of an infrasound array to dissect the incoming wavefield into individual components. In this paper, this problem will be addressed by proposing a high-resolution beamform technique in combination with the CLEAN algorithm. CLEAN iteratively selects the maximum of the f/k spectrum (i.e. following the Bartlett or the Capon method) and removes a percentage of the corresponding signal from the cross-spectral density matrix. In this procedure, the array response is deconvolved from the f/k spectral density function. The spectral peaks are retained in a ‘clean’ spectrum. A data-driven stopping criterion for CLEAN is proposed, which relies on the framework of Fisher statistics. This allows the construction of an automated algorithm that continuously extracts coherent energy until the point is reached that only incoherent noise is left in the data. CLEAN is tested on a synthetic data set and is applied to data from multiple International Monitoring System infrasound arrays. The results show that the proposed method allows for the identification of multiple microbarom source regions in the Northern Atlantic that would have remained unidentified if conventional methods had been applied.

STATIONARY DYNAMIC RESPONSE OF A CIRCULAR RIGID FOUNDATION PARTIALLY SUPPORTED BY A FLEXIBLE PILE AND INTERACTING WITH A HALF-SPACE

This article describes an analysis of the dynamic response of coupled soil-pile-foundation systems. The soil and the pile models were developed in previous research works. This article describes the influence of three issues on the vertical dynamic foundation response. First, the influence of the foundation bearing mechanism is investigated. The foundation may be supported by the soil, by the pile or by a combination of both supporting mechanisms. A parameter is introduced to allow for a continuous change in the foundation supporting mechanism. Second, the influence of the excitation mechanism is investigated. The considered excitation mechanism are external forces applied directly at the foundation and an incoming wave field impinging the soil-pile-foundation system. Third, the article investigates if, for both excitation mechanism, the response at the pile head only is able to describe properly the soil-pile response. The analysis presented in the article contributes to an in-depth understanding of the dynamic response of coupled soil-pile-foundation systems.

Reflection and transmission of high-frequency acoustic, electromagnetic and elastic waves at a distinguished class of irregular, curved boundaries

AbstractReflection and transmission phenomena associated with high-frequency linear wave incidence on irregular boundaries between adjacent acoustic or electromagnetic media, or upon the irregular free surface of a semi-infinite elastic solid, are studied in two dimensions. Here, an ‘irregular’ boundary is one for which small-scale undulations of an arbitrary profile are superimposed upon an underlying, smooth curve (which also has an arbitrary profile), with the length scale of the perturbation being prescribed in terms of a certain inverse power of the large wave-number of the incoming wave field. Whether or not the incident field has planar or cylindrical wave-fronts, the associated phase in both cases is linear in the wave-number, but the presence of the boundary irregularity implies the necessity of extra terms, involving fractional powers of the wave-number in the phase of the reflected and transmitted fields. It turns out that there is a unique perturbation scaling for which precisely one extra term in the phase is needed and hence for which a description in terms of a Friedlander–Keller ray expansion in the form as originally presented is appropriate, and these define a ‘distinguished’ class of perturbed boundaries and are the subject of the current paper.

A Critical Comparison of Excitation Force Estimators for Wave-Energy Devices

The implementation of energy-maximizing control systems (EMCSs) can significantly increase the efficiency and economic viability of resonant wave-energy converters (WECs). To achieve optimal control and drive the WEC into resonance with the incoming wave field, knowledge of the wave excitation force is required. In operational conditions, this quantity is immeasurable and, thus, has to be estimated. This article presents a critical comparison of the available excitation force estimators found in the literature. A reference measurement of the excitation force is determined using computational fluid dynamics (CFD) simulation, allowing an absolute comparison of the different estimation strategies. The estimators are compared based on the required input data, achieved accuracy, computational delay, and estimation time. In total, 11 estimation strategies are compared, with three, in particular, emerging with relatively superior performance.