Three-dimensional Wave Field Research Articles

A fast amplitude preserving three-parameter 3D parabolic Radon transform and its application on multiple attenuation

Seismic wavefields propagate through three-dimensional (3D) space, and their precise characterization is crucial for understanding subsurface structures. Traditional 2D algorithms, due to their limitations, are insufficient to fully represent three-dimensional wavefields. The classic 3D Radon transform algorithm assumes that the wavefield's propagation characteristics are consistent in all directions, which often does not hold true in complex underground media. To address this issue, we present an improved 3D three-parameter Radon algorithm that considers the wavefield variation with azimuth and provides a more accurate wavefield description. However, introducing new parameters to describe the azimuthal variation also poses computational challenges. The new Radon transform operator involves five variables and cannot be simply decomposed into small matrices for efficient computation; instead, it requires large matrix multiplication and inversion operations, significantly increasing the computational load. To overcome this challenge, we have integrated the curvature and frequency parameters, simplifying all frequency operators to the same, thereby significantly improving computation efficiency. Furthermore, existing transform algorithms neglect the lateral variation of seismic amplitudes, leading to discrepancies between the estimated multiples and those in the data. To enhance the amplitude preservation of the algorithm, we employ orthogonal polynomial fitting to capture the amplitude spatial variation in 3D seismic data. Combining these improvements, we propose a fast, amplitude-preserving, 3D three-parameter Radon transform algorithm. This algorithm not only enhances computational efficiency while maintaining the original wavefield characteristics, but also improves the representation of seismic data by increasing amplitude fidelity. We validated the algorithm in multiple attenuation using both synthetic and real seismic data. The results demonstrate that the new algorithm significantly improves both accuracy and computational efficiency, providing an effective tool for analyzing seismic wavefields in complex subsurface structures.

Nonlinear ray tracing in focused fields, part 2. Tracing the flux: tutorial

In this three-part paper series, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name “nonlinear ray tracing.” In the first part we focused on the high-speed calculation of focused three-dimensional complex wavefields in the paraxial approximation for TEM00 and TEM01 laser modes. The algorithms developed in the first paper are first used to generate the three-dimensional grid of samples of the complex wavefield in the focal region. In this second part, we focus on tracing a flux through this three-dimensional point cloud. For a given “ray” at an arbitrary position in the 3D volume, interpolation of the three-dimensional samples is applied to determine the derivative of the phase (normal to the direction of propagation) at the ray position, which is then used to direct the ray as it “propagates” forward in a straight line over a short distance to a subsequent plane; the process is repeated between consecutive planes. The initial origin of the ray can be chosen arbitrarily at any point, and the ray can then be traced through the volume with appropriate interpolation. Results are demonstrated for focused wavefields in the absence of aberrations, corresponding to the cases highlighted in the first paper. Some of the most interesting results relate to focused Laguerre-Gaussian beams, for which the rays are found to spiral at different rates of curvature. In the third paper we extend the application of this algorithm to the investigation of lens aberration.

Nonlinear ray tracing in focused fields, part 1. Calculation of 3D focused wavefields: tutorial

In this three-part paper series, we develop a method to trace the lines of flux through a three-dimensional wavefield by following a direction that is governed by the derivative of the phase at each point, a process that is best described as flux tracing but which we interchangeably name “nonlinear ray tracing.” In this first part, we provide a tutorial on the high-speed calculation of three-dimensional complex wavefields, which is a necessary precursor to flux tracing. The basis of this calculation is the angular spectrum method, a well-known numerical algorithm that can be used to efficiently and accurately calculate diffracted fields for numerical apertures <0.7. It is known that this approach yields identical predictions to the first Rayleigh–Sommerfeld solution. We employ the angular spectrum method to develop two algorithms that generate the 3D complex wavefield in the region of focus of a lens. The first algorithm is based on the thin lens approximation, and the second is based on the concept of an ideal lens, which can be modeled using an optical Fourier transform. We review how these algorithms can be used to calculate focused laser beams with TEM00 and TEM01 laser profiles. The three-dimensional sampling requirements of the focused field are explained in detail, and expressions for the computational and memory efficiency of the two algorithms are developed. These two algorithms generate the 3D scaffold for the flux tracing method developed in the second paper, and in the third paper we highlight the application of the method to understanding monochromatic lens aberration. Disregarding the second and third papers, this first paper will serve as a practical tutorial for anyone seeking to compute focused fields in three dimensions.

Measuring near-field wave elevation with monocular vision using self-supervised learning techniques

Ocean waves are among the most influential factors affecting marine mechanical systems. The existing methods for measuring wide-area wave-field data have limitations and require high maintenance costs. Therefore, it is crucial to develop a reliable and efficient field measurement method for wide-area wave fields. This study proposes a monocular vision-based approach for wave field measurement, where the depth of each pixel is equalised to summation of the depth of the mean water surface and the depth variation induced by wave elevation. A deep network was trained using a self-supervised algorithm to approximate the depth variation induced by wave elevation. A loss of representative features was proposed to improve the performance of deep networks. The images of an open-source dataset were used to train and validate the proposed model. By using the proposed method, the images were utilised to reconstruct the three-dimensional wave field of the test set. The time history and wave spectrum of the wave fields were compared with those calculated by existing method and measured by wave gauge. The influence of the training set on the measurement results was also investigated. The results indicate that the proposed method is capable of performing effective near-field wave measurements by monocular images, effectively reducing the device requirements, and increasing update frequency for ocean wave measurement.

Impact of internal waves on underwater acoustic propagation

The propagation of internal waves in the ocean can produce significant fluctuations in the local sound speed field. Understanding how these fluctuations affect acoustic propagation is an area of considerable interest in underwater acoustics. Previous studies have indicated that large fluctuations (of the order of 20 dB) in transmission loss (TL) of acoustic waves can occur due to focusing and defocusing effects as the acoustic waves propagate through an internal wave. This work looks to extend some of these studies by exploring the frequency and directional dependence of these fluctuations through the implementation of a 3D acoustic model (FOR3D) suitable for modelling low frequency (<1 kHz) acoustic propagation. The study utilises sound speed data produced using the non-hydrostatic model MITgcm, simulating a nonlinear three-dimensional internal wave field that was verified using in situ mooring observations. By also considering results from a study utilising an acoustic ray model (Bellhop3D) on the same data, this work gives a comprehensive picture of the internal wave induced TL fluctuations across a range of acoustic frequencies.

Stereo Reconstruction Method for 3D Surface Wave Fields around a Floating Body Using a Marker Net in a Wave Tank

Spatial wave fields around floating bodies are important for the understanding of hydrodynamics, and particularly the wave drift forces, of floating bodies in waves; however, experimental measurement of these fields is challenging. This paper presents a stereo reconstruction method for three-dimensional (3D) surface wave fields around floating bodies in a wave tank. Styrofoam markers were attached to a flexible net in a regular grid, called a marker net, and were placed on the water surface to be used as targets for stereo cameras (SCs). A thin plate spline was applied to the markers detected by the SCs to reconstruct the 3D surface wave profile around a floating body model. The proposed method was validated by measuring the wave field around a cylindrical floating body with a footing at its bottom. These experiments were conducted under regular wave incidence conditions. A wave elevation time series measured using a servo-controlled wave gauge was used as the benchmark data. The 3D surface wave field reconstruction method was applied under three different conditions: without the model, with a fixed model, and with a freely oscillating model. The results showed reliable reconstructions of the scattering and radiation waves. The marker net’s effects on the floating body’s motion and the surrounding wave fields were shown to be negligible by comparing the results acquired with and without the marker net.

The occurrence probability prediction model of 2D and 3D freak waves generated by wave superposition

The wave superposition is a common method to generate freak waves by assigning energy of wave spectrum to a focusing wave train and a random wave train. Traditionally, the freak wave generation by wave superposition requires repeatedly try for many times before obtaining satisfactory results. In this process, freak wave may not occur when wave component number or energy portion of focusing wave train is small and freak wave may break up when that is too large. It may also contribute to the discrepancy of significant wave height between target value and generated result when energy portion of focusing wave train is large. To improve simulation efficiency, the paper proposes a model to quantitatively predict the occurrence probability of freak waves in superposition cases of two and three wave trains. The error of significant wave height could be artificially controlled. The occurrence probability prediction model of freak wave is also extended to three-dimensional wave fields. The accuracy is well validated by statistical data. According to prediction results, two-dimensional and three-dimensional freak waves are successfully generated.

Following the Flux in diffracted fields – An efficient numerical method for tracing the Eikonal function

We report on our recently developed method for tracing lines of flux in three-dimensional diffracted wavefields using an approach we call ’non-linear ray tracing’ but which can be more accurately described as tracing the lines of flux in the context of the Eikonal function. These ’rays’ navigate through the diffracted field guided by the derivative of the phase at a sequence of successive points. Our approach is based on the Angular Spectrum method, a numerical algorithm that accurately and efficiently calculates diffracted fields for numerical apertures <0.7. This is used to generate a three-dimensional grid of complex wavefield samples in the focal region, followed by tracing the flux through this volume. The ray propagates in a straight line between two consecutive planes within the volume; the phase derivative is calculated at each plane to direct the ray on the next step of its journey. We demonstrate the effectiveness of our approach by generating results for focused laser beams with TEM00 and TEM01 laser profiles. We also simulate the effects of optical aberrations, described by Zernike polynomials, on the three-dimensional focused wavefield. Our non-linear ray tracing method provides a powerful and efficient approach for tracing lines of flux through complex three-dimensional wavefields, offering an exciting new tool for understanding these complex systems.

Inverse diffraction in phase space.

Inverse diffraction refers to recovering the input field in the plane z=0 from the knowledge of the field in some plane z>0 of the free half-space to which the input field propagates. With the rapid development of computational optics, inverse diffraction is increasingly used in optimization and imaging simulations involving round-trip wave propagation. This increasing usage makes it necessary and valuable to revisit this old, important problem and clarify some existing ambiguities. In this study, an exhaustive inverse diffraction analysis is presented from the perspective of phase space. With the help of the Wigner distribution function, it is shown that the forward and inverse diffraction processes in phase space are geometrically equivalent to the deformation and recovery of the phase space diagram (PSD). The symmetries of PSD transformations corresponding to different inverse diffraction forms are revealed. The ambiguities between the conjugation of diffraction kernels and the negative diffraction distance are clarified. The physical pictures of inverse diffraction are further given. This phase space analysis provides an intuitive view on problems involving inverse diffraction and a more concise approach for understanding propagation behaviors of three-dimensional wave fields, including the phase conjugation in holography.

Real-time digital twin for ship operation in waves

This paper introduces a real-time digital twin for ship operations in seaways. The concept of the digital twin is becoming popular, and it is adopted for ship operation systems in this study. In particular, this paper introduces a new and innovative concept of the digital twin to predict ocean waves and hydrodynamic performances, such as seakeeping and maneuvering, which enables the risk and optimum route to be forecast in real time. An essential element in the realization of such a real-time digital twin is the real-time prediction of ocean waves. Hence, a sophisticated algorithm for wave reconstruction using measured wave-radar images is developed, which is extended to predicting the future evolution of a three-dimensional wave field in front of a ship within a time window of the order of 10 min. As another essential element, an analysis program to solve the coupled seakeeping-maneuvering problem is developed. This analysis can also be used in real time. By combining this with wave prediction software, the future occurrence of ocean waves and ship responses can be predicted. By extending this approach, the risk and performance of ships in various ocean environments can be predicted. In this paper, concepts, approaches, and examples are introduced.

Horizontal Active Noise Control Based on Wave Field Reproduction Using a Single Circular Array in 3D Space

In this paper, we propose horizontal active noise control (ANC) using two-dimensional wave field information alone. By reducing the control space to a horizontal plane, the number of microphones and speakers was considerably reduced compared with ANC systems using three-dimensional wave field information. The radii of the reference, microphone, and loudspeaker array were determined based on the wave field reproduction error. Accordingly, the simulation and experimental results of the proposed ANC system were presented based on the use of five microphones and loudspeakers using conventional ANC algorithms. Overall, an average noise reduction of 20 dB was observed inside the microphone array with a radius of 0.5 m for tonal noise at 200 Hz. This performance is acceptable with a drastically reduced number of microphones and speakers. The findings of this study, along with further research conducted in a reverberant room, represent a significant contribution to global ANC commercialization.

Modeling of a 43 GHz microplasma within a photonic crystal

The electron density (ne) and argon metastable density (1s5) of a 43GHz microplasma are obtained using the zero-dimensional plasma kinetics solver (ZDPlasKin®) for an incident power of 160 and 1000mW and argon pressures of 10–600Torr (1.3×103 to 8.0×104Pa). These simulations are compared with previously published experimental data. To determine the self-consistent electric field in the modeled plasma, the three-dimensional millimeter wave fields are computed as a function of electron density using ANSYS EM19.2, HFSS®. This electromagnetic field model is coupled to ZDPlasKin such that any increase in the simulated plasma density correctly attenuates the simulated electric field within the microplasma. The electron density is found to be sensitive to argon gas temperature, so a two-zone temperature model was needed to obtain agreement with experimental measurements. The temperature in the central core of the microplasma was determined by a previous experimental study. That temperature was used as an input to the model for the simulation of volume recombination losses. The outer regions of the microplasma are assumed to be in equilibrium with the walls (300K). This second temperature was used in the model to determine diffusion losses. The modeled electron and metastable densities are of the order 1020 and 1018m−3, respectively. This is in good agreement with those measured experimentally as long as the two-zone temperature model is used. In the absence of a hot gas core, the modeled three-body recombination rates are excessive and the simulation severely under-predicts the electron density and over-estimates the metastable density. We conclude that the millimeter wave microplasma has a hot core (2500K at 600Torr) that rarifies the argon gas and effectively reduces three-body recombination. This allows one to achieve high electron density on the order of 1020m−3 with only 100mW of wave power.

Experimental investigation the characteristics of three-dimensional wave field and its effect on sandy sloping seabed

The three-dimensional topography of the seabed has a significant influence on the wave field and the failure characteristics of the sloping seabed. Nevertheless, previous experimental studies were predominantly limited to two-dimensional wave conditions. In this study, a series of regular wave experiments (including a rigid-slope seabed and a sandy-slope seabed) have been done in a large-scale three-dimensional harbor basin to investigate the three-dimensional wave field in the Zhoushan sea area and the response characteristics of the sloping seabed under the wave actions, respectively. The results of the rigid-seabed tests show that the wave field has obvious three-dimensional characteristics under the influence of three-dimensional topography. During the process of propagation, wave shoaling occurs which leads to wave breaking finally. At the same time, the wave will reflect when it meets the topography, and the reflected wave will affect the wave field in turn. The pore water pressure response and three-dimensional failure modes of sandy sloping seabed under the wave actions are obtained by the sandy-seabed experiment.

Adjoint tomography of the Italian lithosphere

The evolution and state of geological structure at Earth’s surface is best understood with an accurate characterization of the subsurface. Here we present seismic tomographic images of the Italian lithosphere based on ground motion recordings and characterized by compressional and shear wavespeed structure at remarkable resolution, corresponding to a minimum period of ~10 s. Enhanced accuracy is enabled by state-of-the-art three-dimensional wavefield simulations in combination with an adjoint-state method. We focus on three primary findings of our model Im25. It highlights the distribution of fluids and gas (CO2) within the Italian subsurface and their correlation with seismicity. It illuminates Mt. Etna volcano and supports the hypothesis of a deep reservoir (~30 km) feeding a shallower magma-filled intrusive body. Offshore of the eastern Italian coast, it reveals that the Adriatic plate is made of two distinct microplates, separated by the Gargano deformation zone, indicating a complex lithosphere and tectonic evolution.

Facial characteristics of air gun array wavelets in the time and frequency domain under real conditions

How to determine the wavelet of air gun source and how to improve the performance of air gun source have gradually become two important topics in the field of air gun. The existing performance evaluation system of air gun array can only evaluate the performance of air gun from a single point of view, and can not characterize the change of three-dimensional acoustic field produced by air gun array. We first use the Van der Waals air gun wavelet model to simulate the three-dimensional air gun spatial wave field under real conditions. The experimental and modeled data are in good agreement at different pressure amplitudes and frequencies. Then, based on the three-dimensional spatial acoustic field simulated by the model, we proposed a facial characteristics to evaluate the time domain and frequency domain characteristics of the three-dimensional acoustic field. In this air gun wavelet evaluation system, we extend the evaluation parameters such as zero peak, peak-to-peak amplitude, bubble period and main bubble ratio from single wavelet to acoustic field, from one dimension to three dimension. By introducing the instantaneous property of wavelet, we can observe the amplitude, phase and frequency of the far-field wavelet from different angles. The experimental results show that the proposed air gun wavelet evaluation system can evaluate the spatial wave field from any Angle with multiple parameters, and effectively guide the optimization of the structure of the air gun array.

Reverberant shear wave phase gradients for elastography

Reverberant shear wave fields are produced when multiple sources and multiple reflections establish a complex three-dimensional wave field within an organ. The expected values are assumed to be isotropic across all directions and the autocorrelation functions for velocity are expressed in terms of spherical Bessel functions. These results provide the basis for adroit implementations of elastography from imaging systems that can map out the internal velocity or displacement of tissues during reverberant field excitations. By examining the phase distribution of the reverberant field, additional estimators can be derived. In particular, we demonstrate that the reverberant phase gradient is shown to be proportional to the local value of wavenumber. This phase estimator is less sensitive to imperfections in the reverberant field distribution and requires a smaller support window, relative to earlier estimators based on autocorrelation. Applications are shown in simulations, phantoms, and in vivo liver.

Guided wave imaging of thin lithium-ion pouch cell using scanning laser Doppler vibrometer

In order to achieve low-cost, non-radiation imaging inspection of lithium-ion pouch cell, a new in situ imaging detection method based on guided waves for thin lithium-ion pouch cell was proposed in this paper. According to the propagation theory of ultrasonic guided wave in plate, the propagation of guided waves in a thin lithium-ion pouch cell was analyzed. A guided wave imaging detection system for lithium-ion pouch cell was built up and a pouch cell lithium-ion battery with a thickness of 3.5 mm in a fully charged state was used as the specimen. A piezoelectric transducer was used to excite guided waves, and a scanning laser Doppler vibrometer (SLDV) was used to collect three-dimensional wave field matrix. In the obtained transient guided wave field diagram, there were phenomena such as wavefront lag, irregular patterns, and scattered irregular dots, and a defect of size 22 × 18 mm2 was also identified. Analysis of the mode conversion during the guided wave propagation in the battery reveals that the energy spectrum imaging of main mode can achieve the same effect as the transient guided wave imaging, and reduces the time of the selection moment. The imaging detection method in this paper was the first attempt of ultrasonic guided wave in the in situ imaging of lithium-ion battery.

Study on attenuation coefficient characteristics of the in-seam seismic wave in fault and collapse column

Various types of geological structures exist in the working face of coal mine stope. Failure to identify the structural development in advance could defer the timely implementation of reasonable management measures, which may eventually affect production safety and connectivity. As a matter of fact, fine detection and interpretation problems of in-seam seismic wave caused by different types of geological anomalies such as faults and collapse columns can exist simultaneously in the working face of mining. In view of these problems, forward modeling research of three-dimensional seismic wave fields on geological models with fault and collapse column are carried out in this study. Meanwhile, in combination with the imaging results of in-seam seismic wave attenuation coefficient of the exposed fault and collapse column, the characteristics of in-seam seismic wave were analyzed. Following comparative analysis, we found the attenuation coefficient anomaly of the fault is generally banded and weakens at both ends of the fault. The attenuation coefficient of the collapse column presents as an irregular ellipse. The energy of the smaller collapse column has a relatively small attenuation, while the energy of the larger collapse column shows a significantly obvious attenuation.

Wave Field Characteristics of Small Faults around the Loose Circle of Rock Surrounding a Coal Roadway

The geological conditions of coal roadway excavation are complicated. Seismic advanced detection is strongly influenced by the loose circle of fractured rock surrounding the competent coal seam. However, the three-dimensional wave field characteristics of small fault advanced detection in the condition of the loose circle of coal roadway have not examined. In this paper, numerical modeling and field tests were conducted to address this knowledge gap. The results indicate that when a seismic source near the tunnel face is excited, the body waves and a Love channel wave propagate in the tunneling direction toward the small fault, then produces reflected body waves whose amplitude is relatively weak, and a reflected Love channel wave whose amplitude is relatively strong. When reflected body waves and the reflected Love channel wave enter the loose circle of surrounding rock, the former's signal is unrecognizable in seismic record; but the latter converts to a Love wave whose amplitude is strong in the loose circle of coal seam. The Love wave which has a large interval from other wave trains in the time domain is easily recognizable in seismic record, which makes it suitable for advanced detection of small fault. The signal-to-noise ratio of seismic record of X component is higher than those of Y component and Z component.

An integrated SEM-Newmark model for physics-based regional coseismic landslide assessment

Earthquake-induced landslides are one of the most catastrophic effects of earthquakes, as evidenced by many historic events over the past decades, such as the 1994 Northridge earthquake in California and the 2008 Wenchuan earthquake in China. Realistic prediction of coseismic landslides is crucial for the design of key infrastructure and to protect human lives in seismically active regions. To date, analytical methods for estimating coseismic landslides have been based on highly simplified models. In this study, an integrated Spectral Element Method (SEM)-Newmark model is developed to directly simulate three-dimensional wave field in complex topography on a regional scale, while the associated landslide is indicated by the Newmark sliding displacement analysis considering key model factors. Topographic amplification, soil response, near-field characteristics of earthquake shaking and hydrogeological conditions can be simulated, and their effects on coseismic landslides are studied. In this paper, two regional-scale case studies were conducted using the developed SEM-Newmark model, including landslide hazard assessment for natural terrain in the western part of Hong Kong island, and the massive landslides occurred during the 2014 M6.5 Ludian earthquake in China. These case studies demonstrated that the proposed integrated model can be effectively used for regional-scale coseismic landslide hazard assessment under various earthquake scenarios and hydrogeological conditions.