Numerical Wave Propagation Research Articles

Scattering and Frequency Effects on Ultrasonic Velocities of Carbonates

AbstractScattering of elastic waves causes velocity dispersion, which increases uncertainty in seismic analysis. Understanding the sources of scattering and the degree of velocity dispersion are critical to improve subsurface imaging in efforts to locate resources and study subsurface processes. In addition to scattering, other mechanisms, such as the wave‐induced fluid flow in saturated rocks cause velocity dispersion. To study the effect of scattering on velocity dispersion, we conducted laboratory measurements of ultrasonic velocities on dry rock samples and performed wave‐propagation simulations on CT‐scanned 3D volumes of those samples. The set of samples consists of homogeneous and heterogeneous carbonate rocks with porosities between 3% and 26%. Ultrasonic velocities were measured at frequencies between 0.3 and 1 MHz, and numerical wave propagation simulations on the digital volumes were performed using an elastic approximation and a finite‐difference method. The homogeneous sample and the corresponding numerical simulations exhibit negligible velocity dispersion. On the other hand, heterogeneous samples exhibit significant dispersion, and the corresponding numerical simulations accurately reproduce the observed dispersion in terms of magnitude and frequency shift. We conclude that scattering has a first‐order effect on the velocities of the elastic waves in heterogeneous samples. This effect should be considered in conjunction with laboratory measurements in heterogeneous carbonates similar to those studied here. Furthermore, we illustrate a method to characterize frequency‐dependent ultrasonic velocities (i.e., dispersion) and show that finite‐difference modeling can reproduce the laboratory‐observed dispersion.

Numerical Analysis of the Submerged Horizontal Plate Device Subjected to Representative Regular and Realistic Irregular Waves of a Sea State

This study numerically analyzes a submerged horizontal plate (SHP) device subjected to both regular and irregular waves. This device can be used either as a breakwater or a wave energy converter (WEC). The WaveMIMO methodology was applied for the numerical generation and wave propagation of the sea state of the Rio Grande coast in southern Brazil. The finite volume method was employed to solve conservation equations for mass, momentum, and volume fraction transport. The volume of fluid model was employed to handle the water-air mixture. The SHP length (Lp) effects were carried out in five cases. Results indicate that relying solely on regular waves in numerical studies is insufficient for accurately determining the real hydrodynamic behavior. The efficiency of the SHP as a breakwater and WEC varied depending on the wave approach. Specifically, the SHP demonstrates its highest breakwater efficiency in reducing wave height at 2.5Lp for regular waves and 3Lp for irregular waves. As a WEC, it achieves its highest axial velocity at 3Lp for regular waves and 2Lp for irregular waves. Since the literature lacks studies on SHP devices under the incidence of realistic irregular waves, this study significantly contributes to the state of the art.

A non-invasive short range acoustic technique for liquid level measurement in containers

Techniques to measure liquid level in containers and vessels non-invasively are of great interest for the manufacturing, chemical industries, and energy sectors. Most commercial solutions use invasive techniques, which are not always practical and can lead to unsafe conditions when measuring devices encounter high pressures or hazardous chemical contents. In this study, a portable, non-invasive acoustic liquid level identification technique is developed. The technique relies on comprehensive analysis of acoustic guided wave modes in the container walls and their coupling to liquid contents to determine the optimal sensor separation distance and excitation signal characteristics, resulting in liquid level determination with high accuracy and precision. First, dispersion characteristics of guided wave propagation in container walls in contact with a liquid boundary are studied in detail. Based on the dispersion analysis a general-purpose short-range liquid level detection methodology is developed. The developed methodology is then validated using numerical wave propagation simulations and experiments on various metal containers with different physical characteristics, illustrating the versatility of the method. Compared to existing techniques, which are optimized for specific applications, the proposed method, due to its short range and non-invasive nature, has the potential for universal applicability on virtually any container, irrespective of its shape, size, wall-thickness, and whether it has any internal components.

Nonlinear modeling of wave–structure interaction for a flexible floating structure

We present a coupled high-fidelity numerical approach for accurately modeling the fully nonlinear wave–structure interaction of a floating highly-flexible structure in waves. The methodology combines numerical methods that solve the Navier–Stokes equations for viscous-flow dynamics with a free surface, and formulates the nonlinear dynamics of the flexible floating structure as a set of differential–algebraic equations. A verification study was conducted for numerical wave generation and propagation, and the discretization error was quantified. The validation was performed against experimental measurements of a flexible structure subjected to regular waves, where its upstream edge was constrained to the vertical equilibrium location. Our comparisons with the experimental data showed a favorable agreement. This study specifically focused on comparing the wave-driven hydroelasticity of a constrained and a freely floating flexible structures. It provided insights into the effects of rigid body motions on its structural deformations in waves. Developed as an open-source tool, our study demonstrates the potential of the coupled methodology for accurately modeling the wave–structure interactions of flexible floating structures in various nonlinear sea states.

Projecting compound wave and sea-level events at a coastal structure site under climate change

In this paper, an innovative framework is introduced for assessing the impact of climate change on coastal structures, with a primary emphasis on modeling future climate conditions. The framework encompasses several key components: the development of a new climate emulator to facilitate multivariate extreme value analysis; a hybrid statistical–numerical wave propagation strategy; and the integration of a novel compound modeling approach specific to coastal structure sites. These advancements are designed to effectively manage multiple climate scenarios and models within the context of high uncertainty. The methodology is applied and validated for a coastal structure located on the Mediterranean coast in Spain. Focusing on compound wave and sea-level events, the projections indicate an increase in the frequency and severity of extreme conditions, exacerbating coastal impacts such as wave overtopping. For instance, the present-day 500-year coastal flooding level would be associated with a return period of 50 years by mid-century under a stabilization scenario and would be further reduced to 25 years under a high-emission global warming scenario, resulting in important consequences for structure performance if no adaptation is implemented.

Image Recovery for Low Earth Orbit by Leveraging Turbulence and Light Curves

This paper shows a novel method to characterize human-made objects in low Earth orbit (LEO) using compressed sensing on light curve measurements. The proposed approach minimizes total variation to recover a resolved object image from a fully unresolved light curve and a so-called point spread function (PSF) map. The light curves are generated through numerical wave propagation, which considers atmospheric turbulence under anisoplanatic conditions. Subsequently, the light curve model is transformed into a linear measurement model to apply compressed sensing techniques. Notably, the sensing matrix is found to be a superposition of spatially variable PSFs, which significantly downsamples the ideal object image. The proposed approach robustly recovers clear images of objects in LEO, even with imperfect PSF map estimates and Poisson noise in the light curve measurement.

A Digital Twin for Detecting Liquid-Liquid Interface in Containers

This study introduces a digital twin (DT) architecture for detecting liquid-liquid interfaces in containers, aimed at improving real-time monitoring and optimising the separation process in the petroleum industry. The research employs the DT concurrent to the physical twin to enhance the system performance by integrating response error measures with knowledge of industrial processes. The DT uses ultrasonic sensors to collect data and a high-fidelity numerical wave propagation model for an adaptive fitting algorithm to update the interface responses. Both experimental studies and numerical simulations confirm the ability of the DT to accurately determine liquid levels by analysing interfacial responses from ultrasonic signal features in transmission mode. Cross-validation and error metrics validate the DT’s adaptability and accuracy in interface detection, even with undersampled data.

Laser seeker design with multi-focal diffractive lens

Diffractive optical elements are increasingly favoured due to their ability to provide numerous design freedoms by adjusting the Fresnel regions. The design freedoms make it possible to meet multiple system functions in electro-optical systems simultaneously by using a single optical element. This research introduces a novel laser seeker design with a multi-focal diffractive lens that enhances a laser seeker’s measurement sensitivity and linear measurement range. The development of the multi-focal combined lens, featuring two distinct regions with unique focal lengths, aims to simultaneously fulfill two system functions within the laser seeker. The central region of the lens is intended for adjusting the linear measurement range, while the outer region is utilized to regulate the measurement sensitivity of the seeker. The numerical optical wave propagation method was employed to simulate the behaviour of the laser seeker with a multi-focal diffractive lens, and the combined diffractive lens was compared to an ideal lens in the scope of laser seeker application. The simulation results indicate that the measurement sensitivity of the seeker has been increased between 0° to ±3° angular incidence, and the linear measurement range has been increased from ±18° to ±26°. The findings of this study contribute to the advancement of multi-focal diffractive lenses, which fulfil multiple functions within an electro-optical system concurrently.

Temporal dispersion correction for wave‐propagation modelling with a series approach

AbstractTemporal dispersion correction of second‐order finite‐difference time stepping for numerical wave propagation modelling exploits the fact that the discrete operator is exact but for the wrong frequencies. Mapping recorded traces to the correct frequencies removes the numerical error. Most of the implementations employ forward and inverse Fourier transforms. Here, it is noted that these can be replaced by a series expansion involving higher time derivatives of the data. Its implementation by higher‐order finite differencing can be sensitive to numerical noise, but this can be suppressed by enlarging the stencil. Tests with the finite‐element method on a homogeneous acoustic problem with an exact solution show that the method can achieve the same accuracy as higher‐order time stepping, similar to that obtained with Fourier transforms. The same holds for an inhomogeneous problem with topography where the solution on a very fine mesh is used as reference. The series approach costs less than dispersion correction with the Fourier method and can be used on the fly during the time stepping. It does, however, require a wavelet that is sufficiently many times differentiable in time.

Prediction of the internal structure of a lithium-ion battery using a single ultrasound wave response

This paper describes a means to predict the internal structure of a lithium-ion battery from the response of an ultrasonic pulse, using a genetic algorithm. Lithium-ion batteries are sealed components and the internal states of the cell such as charge, health, and presence of structural defects are difficult to measure. Ultrasonic inspection of lithium-ion batteries is a recent and growing area of research. Reflected and transmitted ultrasound pulses are proposed as a non-invasive means of gaining insights into the internal structure and changes within the closed body of a cell. However, the multiple layers present in a lithium-ion cell are problematic when attempting to interpret waveforms as many internal reflections superimpose. Attributing specific features of a cell to wave characteristics is challenging.In this work a genetic algorithm has been developed as a means to reverse engineer a single ultrasound wave response to predict the internal layered structure of a lithium-ion battery cell. A first randomised guess at the layered structure is made. A numerical wave propagation model is used to predict the ultrasound waveform associated with that structure. This waveform is then compared with a measured or reference waveform to establish its fitness. The layered structure is generationally mutated until the predicted waveforms converge on the reference signal. As this occurs the predicted layered body reveals insights into the cell structure under inspection.Initially, the algorithm was tested against an idealised model battery and its predicted waveform, giving a model-model verification. Further, experimental ultrasonic reflection signals were captured from small capacity lithium-ion cells. Estimations of layer structure predicted by the model were compared with CT-scans of the cells to assess performance. The genetic algorithm was found to be effective in converging the predicted wave response to the reference signal and creating accurate battery structures. It was shown that only part of the waveform was required to generate accurate predictions, which is helpful in avoiding parts of the signal contaminated by near field transducer effects.It was demonstrated that the genetic algorithm can predict material wave speed to 40–1100 m/s (3–29 %) accuracy when battery layer geometry is provided; and thicknesses to within approximately 0.2–7.5 μm (1–13 %) when material properties are provided. Providing the genetic algorithm with parameter constraints; either the layer topology and/or the material properties, substantially improved predictions to estimate the wave speeds on average to approximately ±50 m/s (3–4 %) and the layer thicknesses ±5 μm (7–8 %).This raises the possibility of the use of this approach to predict state of charge when the battery construction is known, or the presence of internal defects and damage to a known battery material composition.

Time‐domain scaled boundary perfectly matched layer for elastic wave propagation

AbstractA novel artificial boundary method called the scaled boundary perfectly matched layer (SBPML) is proposed for the transient analysis of elastic wave propagation in unbounded domains. This method constructs a generalized perfectly matched layer (PML) around the finite interior subdomain based on a coordinate transformation inspired by the scaled boundary finite element method (SBFEM). It can model the infinite exterior subdomains of heterogeneous materials, featuring both parallel and radial straight‐line physical surfaces and interfaces. In addition, generally‐shaped (even nonconvex‐shape) artificial boundaries can be used to provide high flexibility in choosing the geometry of the finite interior subdomain. Two coordinate mapping technologies, namely the modified scaled boundary coordinate transformation from the SBFEM and the complex coordinate stretching from the PML, are successively utilized to construct the proposed method. By introducing the integral of stress as an auxiliary variable, the resulting SBPML subdomain is represented in the time domain using a mixed displacement‐stress unsplit‐field formulation. This has the added benefit of allowing for easy incorporation into standard dynamic finite element methods. The performance of the SBPML is demonstrated through several numerical examples, including P‐SV and SH wave propagation problems occurring in unbounded domains with complex geometries and heterogeneous material properties. The numerical results are evaluated in comparison to both reference solution and existing artificial boundary methods, ultimately demonstrating the flexibility, robustness, accuracy, and stability of the proposed approach.

Guided wave propagation and skew effects in anisotropic carbon fiber reinforced laminates

Guided ultrasonic waves provide a promising structural health monitoring (SHM) solution for composite structures as they are able to propagate relatively long distances with low attenuation. However, the material anisotropy results in directionally dependent phase and group velocities, in addition to energy focusing, wave skewing, and beam spreading phenomena. These effects could lead to inaccurate damage localization if not accounted for. In this contribution, the guided wave propagation behavior (A0 mode) for a highly anisotropic, unidirectional carbon fiber reinforced polymer laminate is systematically investigated through both finite element analysis and non-contact laser measurements and compared to theoretical predictions. The directional dependency of phase and group velocity measured for a point and line source shows good agreement with theoretical predictions, once a correction for wave skew effects is applied. Wave skew angles were evaluated from the experimental and numerical wave propagation in multiple directions and matched theoretical predictions based on the phase slowness curve. Significant guided wave beam spreading from a line source was observed and quantified from both experiments and simulations and compared with theoretical predictions using the anisotropy factor. The impact of anisotropic guided wave propagation behavior on SHM is discussed.

Stress wave propagation analysis of 2D-FGM axisymmetric finite hollow thick cylinder

In this paper, a numerical axisymmetric elastic stress wave propagation analysis of the 2D-FGM hollow thick finite cylinder has been performed. The new accurate material distribution model based on Mori-Tanaka scheme and third-order transition function for 2D-FGMs has been implemented in the graded finite element method with higher-order quadrilateral elements. A non-uniform impulsive pressure has been applied on the one-third of the top inner cylinder wall. Consequently, different wave velocities and reflections from the boundaries have been observed due to the graded distribution of material along with two directions. Moreover, the effects of two-dimensional material property distributions on the stress wave propagations and displacements through the cylindrical wall at different locations have been studied systematically. Normalized effective stresses based on von-Mises criteria has been performed in comparison with the internal impulsive pressure amplitude to provide a measure of the cylinder wall response to the mechanical impact loading, the effective stresses are nearly 2.5 times the internal pressure loading amplitude, closed to the impact location. According to the results, 2D material property gradations has effected the stresses significantly. Alternatively, desired stress values can be achieved through optimal design and appropriate choice of property distribution.

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

Numerical wave propagation aided by deep learning

We propose a deep learning approach for wave propagation in media with multiscale wave speed, using a second-order linear wave equation model. We use neural networks to enhance the accuracy of a given inaccurate coarse solver, which under-resolves a class of multiscale wave media and wave fields of interest. Our approach involves generating training data by the given computationally efficient coarse solver and another sufficiently accurate solver, applied to a class of wave media (described by their wave speed profiles) and initial wave fields. We find that the trained neural networks can approximate the nonlinear dependence of the propagation on the wave speed as long as the causality is appropriately sampled in training data. We combine the neural-network-enhanced coarse solver with the parareal algorithm and demonstrate that the coupled approach improves the stability of parareal algorithms for wave propagation and improves the accuracy of the enhanced coarse solvers.

Combining different 3-D global and regional seismic wave propagation solvers towards box tomography in the deep Earth

SUMMARY In previous publications, we presented a general framework, which we called ‘box tomography’, that allows the coupling of any two different numerical seismic wave propagation solvers, respectively outside and inside a target region, or ‘box’. The goal of such hybrid wavefield computations is to reduce the cost of computations in the context of full-waveform inversion for structure within the target region, when sources and/or receivers are located at large distances from the box. Previously, we had demonstrated this approach with sources and receivers outside the target region in a 2-D acoustic spherical earth model, and demonstrated and applied this methodology in the 3-D spherical elastic Earth in a continental scale inversion in which all stations were inside the target region. Here we extend the implementation of the approach to the case of a 3-D global elastic earth model in the case where both sources and stations are outside the box. We couple a global 3-D solver, SPECFEM3D_GLOBE, for the computation of the wavefield and Green’s functions in a reference 3-D model, with a regional 3-D solver, RegSEM, for the computation of the wavefield within the box, by means of time-reversal mirrors. We briefly review key theoretical aspects, showing in particular how only the displacement is needed to be stored at the boundary of the box. We provide details of the practical implementation, including the geometrical design of the mirrors, how we deal with different sizes of meshes in the two solvers, and how we address memory-saving through the use of B-spline compression of the recorded wavefield on the mirror. The proposed approach is numerically efficient but also versatile, since adapting it to other solvers is straightforward and does not require any changes in the solver codes themselves, as long as the displacement can be recovered at any point in time and space. We present benchmarks of the hybrid computations against direct computations of the wavefield between a source and an array of stations in a realistic geometry centred in the Yellowstone region, with and without a hypothetical plume within the ‘box’, and with a 1-D or a 3-D background model, down to a period of 20 s. The ultimate goal of this development is for applications in the context of imaging of remote target regions in the deep mantle, such as, for example, Ultra Low Velocity Zones.

Representation of random media in acoustic scattering calculations

Turbulence, internal waves, surface roughness, and other environmental variations in the atmosphere and ocean randomly scatter sound. Realistic representation of these variations is important for numerical wave propagation calculations. In principle, there are two primary approaches to create these representations: (1) physics-based, dynamical models for the atmosphere or ocean and (2) kinematic synthesis of random fields with prescribed statistical properties that do not necessarily capture the medium dynamics. The most common kinematic approach involves synthesizing fields from randomly phased Fourier modes. For statistically inhomogeneous media, the Fourier modes generalize to empirical orthogonal functions. An alternative kinematic approach, called filtered Poisson processes, distribute spatially localized functions with randomized positions and orientations. Quasi-wavelets (QWs) are a filtered Poisson process intended for turbulence and other self-similar media. While both the Fourier and QW approaches can be formulated to reproduce specified second moments of the random field, if the representations are constructed too sparsely, higher-order moments such as the kurtosis will be unrealistic. The kinematic approaches also underlie phase screen methods, which can be quite useful when the Markov approximation is valid.

Modeling and simulation of multispectral imaging through anisoplanatic atmospheric optical turbulence

We explore the modeling and simulation of multispectral imaging through anisoplanatic atmospheric optical turbulence. We analyze the impact of wavelength on a number of key atmospheric optical turbulence statistics. This includes the impact of wavelength on tilt and tilt variance. The modeling analysis also includes the impact of wavelength on the atmospheric optical transfer function. Here, we investigate the balance between diffraction and turbulence degradation as a function of wavelength. We also present a method for simulating atmospheric degradation for multispectral imagery using numerical wave propagation. Our approach uses a phase screen resampling method to allow for modeling the same atmospheric realization but with sampling parameters tailored to each wavelength. A number of multispectral simulation results, along with a validation study that compares the empirical statistics from the simulation to their theoretical counterparts, are presented. Real image data are also studied to validate theoretical multispectral tilt statistics.

Simulation of anisoplanatic lucky look imaging and statistics through optical turbulence using numerical wave propagation: erratum.

We present an erratum to our previously published work [Appl. Opt.60, G19 (2021)APOPAI0003-693510.1364/AO.427716] that corrects errors in the body of the paper. The corrections do not affect the results and conclusion of the original paper.

A Statistical Approach Towards Fast Estimates of Moderate-To-Large Earthquake Focal Mechanisms

Emerging high-performance computing systems, combined with increasingly detailed 3-D Earth models and physically consistent numerical wave propagation solvers, are opening up new opportunities for urgent seismic computing. This may help, for instance, to guide emergency response teams in the wake of large earthquakes. A key component of urgent seismic computing is the early availability of source mechanism estimates, well before conventional and time-consuming moment tensor inversions are carried out and published. Here, we introduce a methodology that rapidly estimates focal mechanisms (FM) for moderate and large earthquakes (Mw > 4.0) by means of statistical and clustering algorithms. The fundamental rationale behind the method is that events of a certain size tend to be similar to other events of similar size in similar locations. In this work, two different strategies are used to provide different FM solutions: the first is based only in spatial considerations including statistical analysis, and the other one is based on a data clustering algorithm. We exemplify our methodology with six different subsets of the open-access Global Centroid Moment Tensor (GCMT) catalog. Specifically, our study datasets include events from Japan, New Zealand, California, Mexico, Iceland, and Italy, which represent six seismically active regions, with a large FM variability. Our results show a 70–85% agreement between our fast FM estimates and inversion results, depending on the particular tectonic region, dataset size, and magnitude threshold. In addition, our FM estimation strategies only spend few seconds for processing, since they are totally independent of seismic record retrieval and inversion. Albeit not meant to be a substitute for CMT inversions, our methodologies can bridge the time gap between earthquake detection and FM inversion.