Surface Waves Research Articles

Integrating deep learning and discrete cosine transform for surface waves full waveform inversion

Summary Accurate estimations of near-surface S-wave velocity (Vs) models hold particular significance in geological and engineering investigations. On the one hand, the popular Multichannel Analysis of Surface Waves (MASW) is limited to the 1D and the plane wave assumptions. On the other hand, the more advanced and computationally expensive full-waveform inversion (FWI) approach is often solved within a deterministic framework that hampers an accurate uncertainty assessment and makes the final predictions heavily reliant on the starting model. Here we combine deep learning with Discrete Cosine Transforms (DCT) to solve the FWI of surface waves and to efficiently estimate the inversion uncertainties. Our neural network approach effectively learns the inverse non-linear mapping between DCT-compressed seismograms and DCT-compressed S-velocity models. The incorporation of DCT into the deep learning framework provides several advantages: it notably reduces parameter space dimensionality and alleviates the ill-conditioning of the problem. Additionally, it decreases the complexity of the network architecture and the computational cost for the training phase compared to training in the full domain. A Monte Carlo simulation is also used to propagate the uncertainties from the data to the model space. We first test the implemented inversion method on synthetic data to showcase the generalization capabilities of the trained network and to explore the implications of incorrect noise assumptions in the recorded seismograms and inaccurate wavelet estimations. Further, we demonstrate the applicability of the implemented method to field data. In this case, available borehole information is used to validate our predictions. In both the synthetic and field applications, the predictions provided by the proposed method are compared with those of a deterministic FWI and the outcomes of a network trained in the full data and model spaces. Our experiments confirm that the implemented deep-learning inversion efficiently and successfully solves the FWI problem and yields more accurate and stable results than a network trained without the DCT compression. This opens the possibility to efficiently train a neural network that provides accurate instantaneous predictions of Vs near-surface models and related uncertainties.

Time-Domain-Filtered Terahertz Nanoscopy of Intrinsic Light-Matter Interactions.

Terahertz (THz) technology holds great potential across diverse applications, including biosensing and information communications, but conventional far-field techniques are limited by diffraction. Near-field optical microscopy overcomes this barrier through a sharp tip that concentrates incident THz waves into nanometric volumes, detecting scattered near-field to reveal nanoscale optical properties. However, owing to the large THz wavelengths, resonant surface waves arising on the tip and cantilever obscure the intrinsic response. Here we combine near-field microscopy with THz time-domain spectroscopy and implement time-domain filtering with an elongated cantilever to eliminate this artifact, achieving intrinsic nanospectroscopy and nanoimaging. By applying this technique, we distinguish and characterize historical pigments of an ancient sculpture, such as vermilion and red lead, on the nanoscale. We also unravel deep-subwavelength localized resonance modes in THz optical antennas, demonstrating capabilities for THz nanophotonics. Our work advances THz nanoimaging and nanospectroscopy techniques to probe intrinsic nanoscale THz light-matter interactions.

Isotropic ↔ anisotropic surface geometry transitions induced by adsorbed surfactants at water/vapor interfaces.

Adsorbates at a water/vapor interface change the surface geometry through altered surface tension, yet detailed theoretical studies are relatively sparse, and many applications focus on ensemble average characteristics. Here, we demonstrate that different interpretations of surface geometry emerge when considering the distributions of surface curvature and orientation as a function of adsorbed surfactant concentration and sterics. At low surface densities, the tributyl phosphate (TBP) sorbed water/vapor surface has an increased presence of ridges that are defined by principal curvatures κ1 and κ2 of opposite signs yet close in magnitude. As the TBP surface density increases, the difference in principal curvatures slowly increases. There is a distinct transition of the surface geometry, where the ridge-like features become much more pronounced, having sides whose orientation is normal to a flat interfacial plane. Thus, as the TBP surfactant is added to the surface, the surface curvatures become anisotropic in terms of the difference in magnitude of κ1 and κ2. We label this an isotropic → anisotropic geometric transition. Comparing the surface geometry as a function of the carbon tail length of the alkyl phosphate surfactant reveals that smaller surfactants also anisotropically enhance surface curvatures and that adsorbed alkyl tails to the surface stabilize and increase the symmetry of surface waves along the two principal curvature axes. We label this an anisotropic → isotropic geometric transition. These results reflect the opportunity to incorporate more realistic distributions of surface geometry within the collective understanding of statistical theories of surfaces, including capillary wave theory.

High-Quality Damaged Building Instance Segmentation Based on Improved Mask Transfiner Using Post-Earthquake UAS Imagery: A Case Study of the Luding Ms 6.8 Earthquake in China

Unmanned aerial systems (UASs) are increasingly playing a crucial role in earthquake emergency response and disaster assessment due to their ease of operation, mobility, and low cost. However, post-earthquake scenes are complex, with many forms of damaged buildings. UAS imagery has a high spatial resolution, but the resolution is inconsistent between different flight missions. These factors make it challenging for existing methods to accurately identify individual damaged buildings in UAS images from different scenes, resulting in coarse segmentation masks that are insufficient for practical application needs. To address these issues, this paper proposed DB-Transfiner, a building damage instance segmentation method for post-earthquake UAS imagery based on the Mask Transfiner network. This method primarily employed deformable convolution in the backbone network to enhance adaptability to collapsed buildings of arbitrary shapes. Additionally, it used an enhanced bidirectional feature pyramid network (BiFPN) to integrate multi-scale features, improving the representation of targets of various sizes. Furthermore, a lightweight Transformer encoder has been used to process edge pixels, enhancing the efficiency of global feature extraction and the refinement of target edges. We conducted experiments on post-disaster UAS images collected from the 2022 Luding earthquake with a surface wave magnitude (Ms) of 6.8 in the Sichuan Province of China. The results demonstrated that the average precisions (AP) of DB-Transfiner, APbox and APseg, are 56.42% and 54.85%, respectively, outperforming all other comparative methods. Our model improved the original model by 5.00% and 4.07% in APbox and APseg, respectively. Importantly, the APseg of our model was significantly higher than the state-of-the-art instance segmentation model Mask R-CNN, with an increase of 9.07%. In addition, we conducted applicability testing, and the model achieved an average correctness rate of 84.28% for identifying images from different scenes of the same earthquake. We also applied the model to the Yangbi earthquake scene and found that the model maintained good performance, demonstrating a certain level of generalization capability. This method has high accuracy in identifying and assessing damaged buildings after earthquakes and can provide critical data support for disaster loss assessment.

Real-time ocean wave prediction in time domain with autoregression and echo state networks

This study evaluates the potential of applying echo state networks (ESN) and autoregression (AR) for dynamic time series prediction of free surface elevation for use in wave energy converters (WECs). The performance of these models is evaluated on time series data at different water depths and wave conditions, including both measured and simulated data with a focus on real-time prediction of ocean waves at a given location without resolving for the surrounding ocean surface, in other words, short-time single-point forecasting. The work presented includes training the models on historical wave data and testing their ability to predict phase-resolved future surface wave patterns for short-time forecasts. Additionally, this study discusses the feasibility of deploying these models for extended time intervals. It provides valuable insights into the trade-offs between accuracy and practicality in the real-time implementation of predictive models for wave elevation, which are needed in wave energy converters to optimise the control algorithm.

Evaluation of the Influence of Surface Roughness Parameters on Ultrasonic Rayleigh Waveforms

Ultrasonic nondestructive testing is widely used not only in the laboratory, but also in industry. The tests use various types of ultrasonic waves, diverse measurement techniques and different apparatus. One of the problems encountered is the high susceptibility of the surface wave to interference. Some of the interference is random in nature and can be minimized (e.g., contamination of the surface or resting a finger on the surface under study). Some of the interference is permanent in nature, such as variable surface roughness. The aim of the conducted research was to evaluate the influence of roughness on ultrasonic wave propagation. The study used samples with surface roughness Sa from 0.28 to 219 µm, and ultrasonic surface wave probes with frequencies from 1.41 to 8.02 MHz. It was observed that roughness significantly affects the attenuation of the ultrasonic wave, and the differences in signal amplification reached more than 15 dB. Similarly, the effect of the ultrasonic wave’s transit time through surfaces of different roughness was noted. It was found that the difference in the ultrasonic wave transition time was more than 50 µs. The results of the study can be helpful for the ultrasonic testing of materials with different surface conditions.

Rayleigh wave propagation in an initially stressed orthotropic elastic solid half-space lying under inviscid liquid and viscous liquid layers

PurposeThe purpose of this article is the propagation of Rayleigh waves in a homogeneous, isotropic, initially stressed orthotropic elastic solid half-space lying under a homogeneous, viscous, inviscid liquid layer of finite thickness.Design/methodology/approachIn the presence of both viscous and inviscid liquids, it derives the phase velocity, initial stress, and wave number-dependent frequency equation for an orthotropic elastic solid. With the help of the MATLAB program, the thickness effects of liquid layers, initial stress, and viscosity on the phase velocity and attenuation coefficient of the Rayleigh wave are explained for a particular model.FindingsThe phase velocity-dependent dispersion relation of Rayleigh waves at the interface of viscous liquid and solid half-space is a function of initial stress and wave number. Rayleigh waves along the free surface of an orthotropic elastic half-space are also derived as a particular case. The classical results of an inviscid liquid are achieved when the thickness of a viscous liquid approaches zero. Well-known classical results for initially stressed orthotropic elastic solids were also derived.Originality/valueSo far, many researchers have looked into the propagation of surface waves at the interfaces of solid–inviscid liquid, solid–solid, and multilayer interfaces. But in this article, the dispersion behavior of Rayleigh wave propagation in an initially stressed homogeneous orthotropic elastic solid half-space under a double layer of viscous liquid and inviscid liquid is studied.

Performance Characteristics of Newly Developed Real-Time Wave Measurement Buoy Using the Variometric Approach

Accurate measurement of ocean wave parameters is critical for applications including ocean modeling, coastal engineering, and disaster management. This article introduces a novel global navigation satellite system (GNSS) drifting buoy for surface wave measurements that addresses the challenges of performing real-time, high-precision measurements and realizing cost-effective large-scale deployment. Unlike traditional approaches, this buoy uses the kinematic extension of the variometric approach for displacement analysis stand-alone engine (Kin-VADASE) velocity measurement method, thus eliminating the need for additional high-precision measurement units and an expensive complement of satellite orbital products. Through testing in the South China Sea and Laoshan Bay, the results showed good consistency in significant wave height and main wave direction between the novel buoy and a Datawell DWR-G4, even under mild wind and wave conditions. However, wave mean period disparities were observed partially because of sampling frequency differences. To validate this idea, we used Joint North Sea Wave Project (Jonswap) spectral waves as input signals, the bias characteristics of the mean periods of the spectral calculations were compared under conditions of identical input signals and gradient-distributed wind speeds. Results showed an average difference of 0.28 s between the sampling frequencies of 1.28 Hz and 5 Hz. The consequence that high-frequency signals have considerable effects on the mean wave period calculations indicates the necessity of the buoy’s high-frequency operation mode. This GNSS drifting buoy offers a cost-effective, globally deployable solution for ocean wave measurement. Its potential for large-scale networked ocean wave observation makes it a valuable oceanic research and monitoring instrument.

Integral Representations of Solution in the Problem on Skew Incidence of a Surface Wave on the Straight Shoreline Water Wedge

In the linear approximation of the surface gravitational waves of small amplitude a classical model problem about the incursion of a surface wave under some angle on the shoreline is solved. The problem is formulated for the harmonic potential of velocity of the fluid in the 3D water wedge with the Robin-Steklov boundary condition on the free surface and with the no-flow condition along the normal on the bed of the water domain. Some critical comments about a known in the literature solution having a “non-physical” singularity of the logarithmic type on the coastal line are given. The asymptotics with respect to distance from the shoreline of the obtained solution, bounded on the edge, is constructed. The reflection coefficient of the wave reflected from the shoreline is calculated.

Nonlinear joint inversion of Rayleigh and Love wave dispersion curves based on Pearson correlation coefficient and thickness mean sharing

AbstractThe joint inversion of Rayleigh and Love waves plays a crucial role in mitigating the non‐uniqueness of surface wave inversion results and enhancing the stability of these inversions. Existing approaches to the joint inversion of Rayleigh and Love wave dispersion curves, which rely on conventional objective functions, often struggle with complex stratigraphic configurations and yield results of limited accuracy. This study introduces two novel nonlinear joint inversion techniques for Rayleigh and Love waves: Pearson correlation coefficient and thickness mean sharing. The Pearson correlation coefficient approach employs the Pearson correlation coefficient and alternating iterative objective functions to synchronize the shear wave velocity structures derived from Rayleigh and Love waves, thereby enhancing the accuracy of the joint inversion. Conversely, the thickness mean sharing method computes an average of the thickness values obtained in each iteration of the inversion, utilizing the traditional joint inversion objective function. Tests on three distinct stratigraphic structures—characterized by increasing velocity, high‐speed hard interlayers and low‐speed soft interlayers—as well as on measured data, demonstrate that the proposed methods significantly improve the stability and accuracy of nonlinear joint inversion.

Repeatability of instantaneous position in rotational motion of a submerged Savonius turbine driven by water surface waves using image processing: an experimental investigation

Repeatability of instantaneous position in rotational motion of a submerged Savonius turbine driven by water surface waves using image processing: an experimental investigation

Time-lapsed in-situ monitoring of mechanical property in deep soil mixing with surface wave

Evaluating the mechanical properties of deep soil mixing (DSM) requires destructive borehole coring because they are mainly situated underground. Although surface wave method offers potential for quality assurance, its complexity arises from multi-mode phenomena and the need to re-evaluate inversion results, often necessitating manual interpretation. This paper presents a data-driven surface wave framework to retrieve field DSM profile Vs over time, incorporating a mode-free forward operator and the Monte Carlo Tree Search (MCTS) inversion. Validations using synthetic data affirmed the framework’s accuracy and efficiency in tracking subsurface shear wave velocity. In a real-world DSM site, the proposed method successfully captures the mechanical properties evolution across two DSM layers over the curing period, aligning well with site investigations and borehole coring. This pioneering monitoring framework integrates geotechnical engineering with geophysics expertise, underscoring the value of non-destructive seismic methods for measuring subsurface property evolution.

Ambient Noise‐Derived SmS Splitting: A New Approach to Constraining Crustal Radial Anisotropy

AbstractRecent studies have shown that crustal body wave phases, such as PmP or SmS, can be effectively retrieved from ambient noise cross‐correlations. However, few studies have used these phases to constrain crustal structures. In this study, we successfully retrieve SmS signals from ambient noise data and observe SmS splitting caused by crustal radial anisotropy. Furthermore, through simulations of synthetic tests and application to field data, we demonstrate that these SmS signals can be used to constrain crustal radial anisotropy structures through joint inversion with surface waves. Our findings suggest that SmS signals obtained from noise data can significantly enhance the understanding of fine crustal radial anisotropic structures.

Development and performance of a high-resolution surface wave and storm surge forecast model: application to a large lake

Abstract. A real-time forecast model of surface hydrodynamics in Lake Ontario (Coastlines-LO) was developed to automatically predict storm surges and surface waves. The system uses a dynamically coupled Delft3D–SWAN model with a structured grid to generate 48 h predictions for the lake that are updated every 6 h. The lake surface is forced with meteorological data from the High Resolution Deterministic Prediction System (HRDPS). The forecast model has been running since May 2021, capturing a wide variety of storm conditions. Good agreement between observations and modelled results is achieved, with root mean squared errors (RMSEs) for water levels and waves under 0.02 and 0.26 m, respectively. During storm events, the magnitude and timing of storm surges are accurately predicted at nine monitoring stations (RMSE <0.05 m), with model accuracy either improving or remaining consistent with decreasing forecast length. Forecast significant wave heights agree with observed data (1 %–12 % relative error for peak wave heights) at four wave buoys in the lake. Coastlines-LO forecasts for storm surge prediction for two consecutive storm events were compared to those from the Great Lakes Coastal Forecasting System (GLCFS) to further evaluate model performance. Both systems achieved comparable results with average RMSEs of 0.02 m. Coastlines-LO is an open-source wrapper code driven by open data and has relatively low computational requirements compared to GLCFS, making this approach suitable for forecasting marine conditions in other coastal regions.

A model of the earthquake cycle along the Gofar oceanic transform faults

The Gofar oceanic transform fault at the East Pacific Rise has one of the best seismic cycles recorded by modern instruments. The timing, location, and magnitude of major earthquakes (Mw>5.5) have been well constrained by data from global seismic networks for the past 30 years. The earthquake interval is short, about 3-5 years. Several segments have already experienced 5 cycles since 1995, when the seismic network was good enough for surface wave relocation. Two ocean bottom seismometer deployments (2008-2009, 2021-2023) also provide constraints on the seismic properties on the fault. This makes Gofar an ideal place to study earthquake cycles. Here, we developed a model for the seismic cycle along the Gofar transform fault using a semi-analytical approach for rapidly calculating 3D time-dependent deformation and stress caused by screw dislocations embedded within an elastic layer overlying a Maxwell viscoelastic half-space. The 160-km long fault is divided into three major segments with six asperities. Our model simulates the earthquake pattern on this fault for the past 30 years. Most of the time, each asperity ruptured as a large earthquake every 3-5 years. Most segments have a nearly constant Coulomb stress threshold of 2-3 MPa, providing optimal conditions for the forecasting of future earthquakes along Gofar. For three cases that deviated from this simple regular pattern, a large earthquake occurred with a centroid location between two asperities. This is likely due to concurrent rupture that involved both asperities. We also modeled surface deformation with different elastic layer thicknesses and mantle viscosities. Even though most deformation is in the horizontal direction, the difference in both horizontal and vertical directions between models can be as large as a few centimeters per year. Several seafloor geodesy methods can be used to differentiate between models, and seafloor pressure might be the most appropriate one at this remote location.

Waves Generated by the Horizontal Motions of a Bottom Disturbance

Waves generated by a horizontally moving disturbance on the seabed have been studied by developing two numerical models, namely, the Navier–Stokes and the Green–Naghdi equations. Various geometries of the bottom disturbances are considered, and waves generated due to a single motion and multiple oscillatory motions of the bottom disturbances are investigated by the two models. Discussion is provided on how the motion of the disturbance on the seafloor results in the generation of surface waves. The wave-field parameters investigated include the surface elevation, velocity, pressure fields and wave celerity. A parametric study is conducted to assess the effect of the geometry of the disturbance and the kinematic characteristics on the wave generation. It is shown that both linear and nonlinear waves can be generated by a horizontally moving disturbance on the seabed. Long waves, followed by a series of dispersive waves, are produced by the single motion of the bottom disturbance. It is also found that, under appropriate conditions, there would be a balance between nonlinearity and dispersion, such that the generated waves propagate over a flat seafloor with little to no change in their form and shape.

Experimental investigation on treating dredged silt ground using vibratory probe compaction combined with well-point dewatering

This study improved the vibratory probe compaction (VPC) technique by combining it with well-point dewatering to address the challenges of treating newly dredged silt ground. Specific methods were presented to determine the operating frequency based on multi-channel analysis of surface waves (MASW) results, as well as the spacing between compaction points derived from vertical vibration velocity measurements. The effects of well-point dewatering were analyzed through field monitoring of groundwater level, pore water pressure, and ground settlement. A comparative evaluation of the reinforcement of the improved and conventional VPC techniques was conducted through in-situ tests. The results indicate that continuous dewatering suppresses the excessive rise of excess pore water pressure during compaction, effectively eliminating equipment tilting and settlement due to sandblasting water, and enhancing construction efficiency by over 40%. The average standard penetration blow count (N 63.5) increases from 4.3 to 11.4, the ground bearing capacity reaches 140.8 kPa and the average ground settlement is 42.5 cm. The cone resistance and sleeve resistance also exhibit higher values, and the risk of soil liquefaction is effectively eliminated. The experiments and practices provide some successful experiences for the wider application of this technique in similar newly reclamation grounds.

Ambient noise surface-wave imaging in a hardrock environment: implications for mineral exploration

Summary The advancement of seismic methods is vital for mineral exploration in the ongoing energy transition. In this study, we investigate the application of ambient noise seismic interferometry and surface-wave analysis to characterize the subsurface in a mineral exploration context. We then confirm the results of the passive seismic investigation through an active source experiment. We collected ambient noise data using a 2D seismic line initially deployed for an active source reflection seismic study. By cross-correlating the signals, we retrieved the surface waves and constructed a 2D shear-wave velocity profile using conventional surface-wave analysis. We utilized the active source data to establish initial assumptions about the surveyed medium and then validated the passive seismic experiment. The passive seismic results are concordant with the active source results and allow for the interpretation of geological contacts and fault zones. Our work demonstrates the potential of passive seismic methods for investigating local tectonic settings and their role in hardrock mineral exploration.

Topological elastic wave transport and manipulation in three-dimensional metamaterials stacked with sandwich plates

Topological metamaterials demonstrate unprecedented wave manipulation abilities with topologically protected robustness, which have been extensively investigated in one-dimensional (1D) and two-dimensional (2D) mechanical systems, but less explored in three-dimensional (3D) systems. In this study, a 3D topological mechanical metamaterial with periodically stacked sandwich metamaterial plates is proposed to achieve 2D topological surface wave transport in a relatively low-frequency range. An innovative chiral compression-torsion coupling core is employed on the sandwich metamaterial plate to lower the band frequency. Analogous to the quantum valley Hall effect, the two-fold topological nodal line is lifted by breaking the spatial inversion symmetry, opening a topological band gap. By supercell analysis, the topological interface state is demonstrated to appear at the interface of two topologically different domains, and the topological boundary state can also be excited under appropriate free or fixed boundary conditions. Taking advantage of the 3D periodicity, the wave propagation based on both topological interface states and boundary states is examined in both 2D flat plates and 3D structures, realizing 1D topological waveguide and 2D topological surface wave transport respectively. It is found that mode symmetry matching is crucial for constructing the topological wave transport with both interface and boundary states. Leveraging the dependence of boundary states on boundary conditions, this work innovatively presents route-switchable and layer-selective wave manipulation by controlling boundary conditions without complicated structure design, enriching the strategies for tunable elastic wave manipulation. Besides, the topologically protected surface wave transport is demonstrated by introducing defects and disorders. These findings provide new insights into the topological transport of elastic waves in 3D mechanical metamaterials and contribute to the development of intelligent and robust devices for various purposes, such as vibration mitigation, energy harvesting, and signal sensing.

Multichannel Analysis of Surface Waves based on Common Virtual Source Gathers of Seismic Ambient Noise Cross-Correlations: A Case Study at an Earth Dam in Brazil

The S-wave velocity (Vs) is a valuable parameter for assessing the mechanical properties of subsurface materials for geotechnical purposes. Seismic surface wave methods have become prominent for estimating near-surface Vs models. Researchers have proposed methods based on passive seismic signals as efficient alternatives to enhance depth of investigation, lateral resolution and reduce field effort. This study presents the Multichannel Analysis of Surface Waves (MASW) utilizing Common Virtual Source Gathers (CVSGs) derived from seismic ambient noise cross-correlations, based on Ambient Noise Seismic Interferometry concepts. The method is applied to passive data acquired with an array of receivers at the Paranoá earth dam in Brasília, Brazil, to construct a pseudo-2D Vs image of the massif for interpretation. Our findings showcase the adopted processing flow and combination of methods as an effective approach for near-surface Vs estimation, demonstrating its usability also for large earth dam embankments.