Multimode Wave Research Articles

An integrated numerical and analytical model to understand the effect of relative phase in a dual-port solid-state microwave heating process

The utilization of multi-port solid-state microwave heating systems presents promise in improving heating performance but lacks a deep understanding of the effect of source phase difference. This study developed an integrated numerical and analytical approach that allows efficient modeling and a better understanding of multi-mode wave interactions with source phase differences. First, two numerical models simulated the complex electric fields of individual-port microwave heating processes. The simulated nodal electric fields were used as inputs in the analytical model to predict the resultant power dissipation for dual-port heating with arbitrary source phase differences. The integrated approach was validated by comparing the predicted nodal electric field and power densities with numerical modeling results. The phase-dependent nodal and volumetric average power revealed wave-like patterns with great variances. The constructive, destructive, and interference effects were influenced by the source phase differences, emphasizing the importance of proper control of source phases for efficient and uniform heating.

Laser ultrasonic imaging of defect in bimetallic media with frequency domain synthetic aperture focusing technology

A laser ultrasonics (LU) based frequency domain synthetic aperture focusing technology (LUB-F-SAFT), which uses 2D equivalent velocity (SEV) and fuses multi-mode ultrasound, is developed to image the internal horizontal hole defects with a diameter of ∼1.0mm in bimetallic composites. Bulk waves non-destructively excited by a line-shaped laser are detected by a vibrometer away from the excitation. The results indicate that the LUB-F-SAFT with SEV can improve the imaging quality and locating capability, and the testing error is about 0.02mm. The improvement in the imaging quality using SEV for different ratios of the first layer thickness to defect-to-interface distances is discussed. In addition, a theoretical approach based on the directionality of the detected ultrasound is applied to determine a reasonable excitation-detection distance for better defect imaging. A LUB-F-SAFT imaging combining multi-mode waves is employed to improve the range of defect profiles. The results show that the range of the imaged defect profile becomes larger using the multi-mode fused LUB-F-SAFT imaging, which is an improvement of about 49.2% compared to the shear wave imaging result.

A multimodal lithium niobate-based SAW gas sensor for accurate detection of carbon dioxide at elevated temperature

Carbon dioxide (CO2) detection is crucial for safety control, monitoring of the environment, and other industrial applications. The diverse fields of applications make the detection of CO2 a challenging task. In this paper, a study on a multimodal surface acoustic wave (SAW) CO2 sensing system was conducted to scrutinize the sensitivity of the lithium niobate-based multimodal SAW sensor towards CO2 with temperature compensation. The study focused on developing and evaluating a SAW temperature-compensated gas sensor using time-of-flight measurements. The sensor exhibited good repeatability and sensitivity toward different concentrations of CO2.

Long-term characterisation of directional wave spectra in the Black Sea and the Sea of Azov

Directional wave spectra describe complex sea-states in frequency and directional domains and provide more detailed information than the bulk wave parameters. Using hourly directional wave spectra hindcasted for 42 years (1979–2020), this study aims to assess long-term spectral wave climate in the Black and Azov Seas. Variance densities are averaged over the frequencies and directions for annual, seasonal, and monthly scales to determine spectral wave climate. Furthermore, The individual wave systems observed in each directional wave spectra are determined by referring to the independent spectral peak at each observation. The different sea state conditions, including the uni-modal and multi-modal wave systems, are classified and analysed; The energy, frequency, and direction of the three first prominent individual wave system peaks are deeply evaluated as a function of the sea state conditions. Occurrences as the function of spectral peak density and directions of the prominent individual wave system peaks are also computed and discussed. The results reveal that multi-modal spectra are more frequent, although the highest peak density values and lowest peak frequencies were observed within the wave spectra of uni-modal sea states. The spectral peak densities, frequencies, and directions depend on the number of wave systems in the wave spectrum and geographic location. The first peaks in the wave spectra are primarily derived from two dominant directions, and ∼54 % of the peaks had a density greater than 2 m2/Hz. In contrast, second and third peaks in the wave spectra are typically derived from three or more dominant directions and rarely exceed 2 m2/Hz density.

Numerical Investigation of Hydrodynamic Responses of a Moored Liquefied Natural Gas Ship under Multimodal Waves

Ocean waves typically consist of wind, sea, and swell trains. Conventionally, the treatment of multimodal waves has been to conceptualize them as a unified wave system and employ a single set of aggregate wave parameters for the representation of their collective characteristics. Nevertheless, a better understanding of multimodal waves is important when analyzing the interactions between waves and moored vessels, considering the pronounced sensitivity of a ship’s responses to wave periods and directions. Many spectral partitioning methodologies have been proposed to discern and segregate multimodal waves into two or more distinct wave systems, providing fundamental information for investigating moored ship responses to multimodal waves. Utilizing the wave spectra data acquired from a specific water region in South America, a comprehensive numerical study was undertaken by employing the specialized ocean engineering software ORCAFLEX 11.2e. The primary objective of this investigation is to analyze the dynamic response of a moored liquefied natural gas (LNG) vessel in ballast conditions subjected to waves defined by distinct wave identification methods (i.e., overall method and spectral partition method). Furthermore, the waves are categorized into two groups: beam waves and head waves. Results show that beam waves induce a substantial ship response, whereas head waves pose a comparatively lower risk to maritime vessels. Furthermore, the conventional overall wave approach tends to neglect the roll motion generated by multimodal waves when they propagate as head waves. Nevertheless, when the wave direction aligns with beam waves, the overall wave approach tends to produce the roll motion. These findings indicate the importance of considering multimodal waves in quay layout and mooring configuration design.

High-order Harmonics of a Kink Wave and a Narrow Quasiperiodic Fast-propagating Wave Train Excited Simultaneously in a Plasma Resonator

We present the observations of multimode kink waves and a narrow quasiperiodic fast-propagating (QFP) wave train in association with a jet on 2011 December 11. The jet impinged on a loop, which excited a propagating kink mode transitioning into a standing kink mode and also excited a QFP wave train away from the jet. Motion magnification is used to fit the higher harmonic standing wave oscillation profile with three periods at three different spatial locations. The periods have the ratio 6:3:2. The ratio of the fundamental mode to the second harmonic of the standing wave is about 1.95, suggesting that the magnetic field strength variation effect is strong enough to cancel out the density stratification. The differential emission measure is used to estimate the loop’s plasma property at these three points, and it found the density and the temperature are roughly constant. The magnetic field strength, B = 51 ± 16 G, is derived by the coronal seismology using the fundamental kink mode. It is striking to find that the the ratio of the second harmonic to the third harmonic of the kink wave coincides with that of the periods of the QFP wave train, and the ratio of periods is about 1.5 in both cases. We propose that the excitation of the high-order harmonics and the QFP wave train could be the nonlinear response of the steep density-gradient plasma interacting with electromagnetic field in the southwest foot region. This region, like a resonator, might play an important role in energy reservoir capture and act as a frequency filter to generate propagating waves of particular frequencies.

Borehole fibre-optic seismology inside the Northeast Greenland Ice Stream

SUMMARYIce streams are major contributors to ice sheet mass loss and sea level rise. Effects of their dynamic behaviour are imprinted into seismic properties, such as wave speeds and anisotropy. Here, we present results from a distributed acoustic sensing (DAS) experiment in a deep ice-core borehole in the onset region of the Northeast Greenland Ice Stream, with focus on phenomenological and methodological aspects. A series of active seismic surface sources produced clear recordings of the P and S wavefield, including internal reflections, along a 1500 m long fibre-optic cable that was placed into the borehole. The combination of nonlinear traveltime tomography with a firn model constrained by multimode surface wave data, allows us to invert for P and S wave speeds with depth-dependent uncertainties on the order of only 10 m s−1, and vertical resolution of 20–70 m. The wave speed model in conjunction with the regularly spaced DAS data enable a straightforward separation of internal upward reflections followed by a reverse-time migration that provides a detailed reflectivity image of the ice. While the differences between P and S wave speeds hint at anisotropy related to crystal orientation fabric, the reflectivity image seems to carry a pronounced climatic imprint caused by rapid variations in grain size. Further improvements in resolution do not seem to be limited by the DAS channel spacing. Instead, the maximum frequency of body waves below ∼200 Hz, low signal-to-noise ratio caused by poor coupling, and systematic errors produced by the ray approximation, appear to be the leading-order issues. Among these, only the latter has a simple existing solution in the form of full-waveform inversion. Improving signal bandwidth and quality, however, will likely require a significantly larger effort in terms of both sensing equipment and logistics.

Optimized planar printed UCA configurations for OAM waves and the associated OAM mode content at the receiver

SummaryUtilization of planar printed uniform circular antenna arrays (UCA) to generate the orbital angular momentum (OAM) carrying waves in the millimeter‐wave (mmWave) frequency band is advantageous from the viewpoints of easy signal modulation and mode reconfiguration, low cost, low profile, and straightforward integration with the existing broadband wireless infrastructure. The OAM mmWave UCA are highly promising as the enablers of very high transmission data rates required by hybrid 5G/6G optical and wireless communication systems by complementing and enhancing other technologies currently in use. Therefore, we here contribute a detailed electromagnetic analysis of important constraints of such antenna arrangements aimed at short‐range multimode OAM wave transmission. We investigate (i) the required antenna array dimensions and optimized UCA arrangements for a particular link range and (ii) the corresponding mode structure of OAM waves in the plane of receiving arrays. Four relatively simple antenna configurations operating in the 60‐GHz band are compared. Theoretical assumptions based on ideal OAM modes are critically assessed and, using state‐of‐the‐art numerical electromagnetic analysis, compared to realistically generated OAM waves. The proposed “cyclic transmission setup” resulted in much lower unwanted field components in the region of receiving arrays. RMS magnitudes of unwanted modes are on average about 64% of the received mode, in comparison with 80% (up to 94%) for sequential transmission. The observed mode impurities and mode mixing effects at the receiver indicate the need to dedicate more attention to the system‐level design, the development of efficient receiving arrays, the MIMO processing, and the stream separation.

Basin testing of the 1-2-1 M4 WEC

The M4 family of Wave Energy Converters consist of 3 rows of floats, with the front two rows rigidly connected and a hinged connection(s) to the back row. The various possible configurations are commonly identified by the number of floats in each row – hence 1-2-1 has 1 float in front, 2 in the middle, and 1 at the rear. A study by Stansby et al 2017 [1] showed that the 1-2-1 and 1-3-2 variants had the lowest cost of energy of all configurations studied. The 1-3-2 variant has subsequently been extensively studied as it provides greater power per machine. However, the 1-2-1 machine has received less attention. In this paper we report, for the first time, wave basin testing of a 1-2-1 variant. The design is a 1:15 scaled version of a 1-2-1 M4 suitable for deployment in the prevailing short period wind waves in King George Sound, Albany, on the south coast of Western Australia. 
 
 The tests were carried out in the Model Test Basin at the Australian Maritime College, Tasmania. This basin is 35 m x 12 m and tests were run with a water depth of 0.8 m. For modelling operational conditions, the power take-off was represented by a pneumatic ram; in extreme seas the power take-off was removed.
 
 Decay tests, irregular operational seas and irregular extreme seas were tested. All waves were long crested. Sea states tested were taken from the scatter diagram for the deployment site in King George Sound. Body displacements, mooring loads, run-up on the middle floats and forces in the PTO (where installed) were measured. Measured motions and power were compared to a linear model. The level of agreement is compared with previous tests on other variants of M4 in the published literature, including the 1-3-2 variant tested in Carpintero-Moreno et al [2] and the 1-1-1 variant tested in Stansby et al [3]. Compared to some other configurations (such as 1-3-2) the 1-2-1 M4 is more prone to roll. Implications of the test results for deployment in King George Sound are discussed.
 
 [1] Stansby, P., Moreno, E.C. and Stallard, T., 2017. Large capacity multi-float configurations for the wave energy converter M4 using a time-domain linear diffraction model. Applied Ocean Research, 68, pp.53-64.
 
 [2] Carpintero-Moreno, E. and Stansby, P., 2019. The 6-float wave energy converter M4: Ocean basin tests giving capture width, response and energy yield for several sites. Renewable and Sustainable Energy Reviews, 104, pp.307-318.
 
 [3] Stansby, P., Moreno, E.C. and Stallard, T., 2015. Capture width of the three-float multi-mode multi-resonance broadband wave energy line absorber M4 from laboratory studies with irregular waves of different spectral shape and directional spread. Journal of Ocean Engineering and Marine Energy, 1, pp.287-298.

5.7 GHz Ultrasensitive Shear Horizontal-Surface Acoustic Wave Humidity Sensor Based on LiNbO3/SiO2/SiC Heterostructures with a Sensitive Layer of Polyethyleneimine-SiO2 Nanocomposites.

Humidity sensing and water molecule monitoring have become hot research topics attributed to their potential applications in monitoring breathing/physiological conditions of humans, air conditioning in greenhouses, and soil moisture in agriculture. However, there is a huge challenge for highly sensitive and precision humidity detection with wireless and fast responsive capabilities. In this work, a hybrid/synergistic strategy was proposed using a LiNbO3/SiO2/SiC heterostructure to generate shear-horizontal (SH) surface acoustic waves (SAWs) and using a nanocomposite of polyethylenimine-silicon dioxide nanoparticles (PEI-SiO2 NPs) to form a sensitive layer, thus achieving an ultrahigh sensitivity of SAW humidity sensors. Ultrahigh frequencies (1∼15 GHz) of SAW devices were obtained on a high-velocity heterostructure of LiNbO3/SiO2/SiC. Among the multimodal wave modes, we selected SH waves for humidity sensing and achieved a high mass-sensitivity of 5383 MHz · mm2 · μg-1. With the PEI-SiO2 NP composite as the sensitive layer, an ultrahigh sensitivity of 2.02 MHz/% RH was obtained, which is two orders of magnitude higher than those of the conventional SAW humidity sensors (∼202.5 MHz frequency) within a humidity range of 20-80% RH.

The multi-mode acoustic gravitational wave experiment: MAGE

The Multi-mode Acoustic Gravitational wave Experiment (MAGE) is a high frequency gravitational wave detection experiment. In its first stage, the experiment features two near-identical quartz bulk acoustic wave resonators that act as strain antennas with spectral sensitivity as low as 6.6 × 10−21 [strain]/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\ ext {Hz}}$$\\end{document} in multiple narrow bands across MHz frequencies. MAGE is the successor to the initial path-finding experiments; GEN 1 and GEN 2. These precursor runs demonstrated the successful use of the technology, employing a single quartz gravitational wave detector that found significantly strong and rare transient features. As the next step to this initial experiment, MAGE will employ further systematic rejection strategies by adding an additional quartz detector such that localised strains incident on just a single detector can be identified. The primary goals of MAGE will be to target signatures arising from objects and/or particles beyond that of the standard model, as well as identifying the source of the rare events seen in the predecessor experiment. The experimental set-up, current status and future directions for MAGE are discussed. Calibration procedures of the detector and signal amplification chain are presented. The sensitivity of MAGE to gravitational waves is estimated from knowledge of the quartz resonators. Finally, MAGE is assembled and tested in order to determine the thermal state of its new components.

Generation of Terahertz OAM Waves with Six Modes Based on Three-Layer Z-Shaped Reflective Metasurface

In this paper, a broadband and efficient three-layer Z-shaped reflective metasurface for linear polarization conversion is designed and six different modes of orbital angular momentum (OAM) waves are generated in the terahertz band. The designed metasurface consisted of several units, and it is divided into twelve regions. The phase difference is achieved by changing the structural parameters of the units, and then different modes of OAM waves are generated. The terahertz OAM waves with the modes of ±1, ±2, and ±3 are generated by metasurface with high efficiency and wide bandwidth. The results show that the designed metasurface could produce high purity terahertz OAM waves with six different modes, and the reflection amplitude of the metasurface unit is more than 0.9 in the frequency range of 1.0 THz to 1.8 THz. The generated OAM waves with the modes of ±1 and ±2 have a mode purity more than 90%. The designed metasurface has good wavefront control ability, which provides an effective method to generate multimode OAM waves.

Retrieval of surface waves from high-speed-train-induced vibrations using seismic interferometry

Train traffic has recently been realized as a potential seismic source for imaging and monitoring shallow subsurface structures. High-speed trains usually move on viaducts and generate seismic wavefields through bridge piers. This kind of source is not randomly distributed in space and time and thus indicates the characteristic of self-correlation. We find that correlated sources of one high-speed train running over piers make time-delayed spurious signals in the crosscorrelation functions. The direct-wave interferometry with correlated sources is proposed and demonstrates that stacking the interferometric responses from high-speed trains with different speeds may reduce the spurious imprint of source self-correlations, but it cannot remediate the problem. The influence of the source wavelet can be eliminated by using cross coherence. Stationary-phase segment selection and stacking can reduce the bias generated by trains moving out of the stationary-phase zone of station pairs. The validity is demonstrated by using synthetic data with inline and out-of-line linear arrays. We apply the proposed scheme to field data with nine high-speed train events. Multimodal Rayleigh waves were retrieved and shallow shear-wave velocities were inverted from multimodal dispersion data in a range of 4–25 Hz. The results bring a novel approach for the imaging and monitoring of the shallow subsurface using high-speed-train-induced vibrations.

Quantitative detection of rail head internal hole defects based on laser ultrasonic bulk wave and optimized variational mode decomposition algorithm

This paper proposes a quantitative rail head internal defect detection method combining mode conversion and time-of-flight based on the theory of laser ultrasonic bulk wave scattering and diffraction. The interaction between laser ultrasonic bulk wave and rail internal hole defects is modeled using finite element simulation, and the modal conversion of bulk wave encountered defects is investigated. The feasibility of localization and the quantitative method are both confirmed. Simultaneously, an Optimized Variational Modal Decomposition (OP-VMD) method is proposed to solve the problem of low SNR of bulkwave signals and to facilitate multi-mode wave discrimination. This method can extract the defect diffraction Shear Wave (S) signal from complex ultrasonic signals. Finally, experiments are performed on the defects of artificial internal holes in rail heads with varying burial depths and sizes. The experimental results show that the method can not only detect but also quantify the defects of internal holes in rail heads. The location relative errors are within 3%, and the quantitative relative errors are within 7%.

Dispersion compensation of Lamb waves based on a convolutional auto-encoder

Lamb wave-based detection has become a promising technique for structural health monitoring in plate-like structures. However, the dispersion effect of Lamb waves makes the wave packets elongated, which degrades the resolution for damage identification. Hence, it is necessary to develop effective methods for the dispersion removal of Lamb waves. Recently, deep learning has drawn much attention for Lamb wave detection due to its powerful feature extraction capability. Most current deep learning models are developed directly for damage classification or location estimation tasks on the Lamb wave signals, rather than signal processing for further manipulation. Therefore, in this paper, a novel approach based on a convolutional auto-encoder is proposed for the dispersion compensation of Lamb waves. The convolutional auto-encoder model is utilized to construct the mapping relationship between the dispersive signal and the time of flight of the wave packet. The dispersion compensated signal is reconstructed by combining the estimated time of flight from the network with the waveform of the excitation signal. Numerical and experimental validations on aluminum and composite plates are implemented to verify the effectiveness of the proposed method. Compared with conventional methods for dispersion compensation, the results demonstrate that our proposed method not only separates the overlapped wave packets but also enables dispersion compensation of multimodal and multi-packet Lamb wave signals. In addition, this method is still applicable in the case of inaccurate dispersion data due to the generalizability of the data-driven model.

HyWaves: Hybrid downscaling of multimodal wave spectra to nearshore areas

Long-term and accurate wave hindcast databases are often required in different coastal engineering projects. The assessment of the nearshore wave climate is often accomplished by using downscaling techniques to translate offshore waves to coastal areas. However, dynamical downscaling approaches may incur huge computational cost. Additionally, the common use of bulk parameterizations are often not accurate for multidimensional waves. To overcome these limitations, we present a hybrid downscaling approach that combines mathematical algorithms (statistical downscaling) and numerical modeling (dynamical downscaling) over the individual spectral partitions. Every wave partition is downscaled and aggregated afterward by using principles of wave linear theory. By assuming linearity in the propagation of the wave celerity, the application of the method is limited from offshore to intermediate water depths. In addition, the method proposed uses a technique to simplify the spectral boundary conditions in complex domains. The methodology has been applied and validated in the island states of Samoa, American Samoa, Majuro, and Kwajalein, showing good skill at reproducing the spectral hourly time series of significant wave height, peak period, and peak direction. Moreover, an accurate representation of the observed energy spectrum was achieved. This study provides insight into the numerical approximation of the combined sea-swell states while improving the quality of fast spectral forecasting and early warning systems.

A fast and accurate elastic reverse-time migration method based on decoupled elastic wave equations

The extrapolation and decomposition of different mode waves are very important to efficiently obtain multi-wave depth images for elastic reverse-time migration (ERTM). To achieve this goal successfully, we firstly develop an efficient and accurate staggered-grid finite-difference method (SFDM) based on decoupled elastic wave equations. This developed SFDM uses two sets of difference operator lengths for decoupled elastic wave equations to respectively perform the extrapolation of decoupled P- and S-wavefields and employs the least squares (LS) to minimize the objective functions respectively constructed from the time-space dispersion equations of P- and S-waves to generate their corresponding difference coefficients. This developed method can theoretically be regarded as the optimal SFDM based on least squares (LSSFDM), and it can provide the high-precision separated wavefields of different mode waves simultaneously and reduce the computing time effectively for elastic wave modeling under the given accuracy requirements. The modeling results of different models illustrate that our developed LSSFDM based on decoupled elastic wave equations can generate the decomposed P- and S-wavefields and suppress their numerical dispersions effectively. Secondly, we present a fast and accurate ERTM method based on this developed LSSFDM to successfully achieve the multi-wave imaging results, including PP, PS, SP and SS images. The ERTM examples of different models demonstrate that our ERTM based on this developed LSSFDM can accurately obtain the high-precision depth images of multimode waves and effectively reduce the computing time of wavefield extrapolation.

Multiple Voronoi Partition Improves Multimodal Dispersion Imaging From Ambient Noise: A Case Study of LASSO Dense Array

AbstractRecent studies on the frequency‐Bessel transform (F‐J) method demonstrate the ability of the array‐based method to extract higher‐mode surface wave dispersion curves from ambient noise, which provides a new opportunity to reveal more accurate underground structures. However, problems with the subarray selection for three‐dimensional imaging remain. On the one hand, we need the subarray to be large enough such that the F‐J method can capture high‐quality dispersion curves, and on the other hand, we want the subarray to be small enough to maintain a sufficient horizontal resolution. To solve this problem, we propose a strategy that randomly and repeatedly partitions the subarray based on Voronoi diagrams. We call this the FJ‐VoroTomo method. The FJ‐VoroTomo method does not require tedious parameter tuning and can measure high‐quality dispersion while maintaining horizontal resolution. More importantly, this method can quantitatively analyze the uncertainty of the measured dispersion curves. In this work, we use the noise cross‐correlation functions from the LArge‐n Seismic Survey in Oklahoma array as an example to demonstrate the dispersion and its uncertainty obtained by the FJ‐VoroTomo method and evaluate the three‐dimensional S wave velocity structure beneath this dense array. We hope that by using this strategy, the multimodal surface wave method can be more feasible in dense arrays that are currently widely used.

Angular-dependent spin-wave modes observations and excitation origins in Yttrium iron garnet thin films

We present a study of the dynamic magnetic properties of sputtered-grown YIG films that were subsequently annealed at various temperatures. Our investigation involved the use of the ferromagnetic resonance technique enabled the observation of multimode spin waves spectra. A noticeable increase in the visibility of the multimode spin-wave modes was observed. This finding is ascribed to the rise in surface roughness and anti-site defects in our YIG films as the annealing temperatures increased. We analyzed the correlation between spin-wave modes and the orientation of the magnetic field H. Results showed that a spectrum made up of a variety of spin-wave modes is seen when the applied field H is normal to the film plane. Once the H is tilted from the normal, a critical angle of only one uniform precession mode was detected for some orientations. A fourfold symmetry of the resonance field emerges as H is in the film plane, ascribed to the anisotropy along different crystal orientations of YIG film. Finally, we were able to determine the exchange stiffness constant and distortion parameter by analyzing the spin waves resonance spectra.

Multi-objective particle swarm optimization for multimode surface wave analysis

Obtaining S-wave velocity profiles by inverting Rayleigh wave dispersion curves is crucial for the Rayleigh wave exploration method. Rayleigh wave inversion is a highly nonlinear and multi-extremum problem; therefore, global optimization algorithms are superior to local optimization methods for this inversion problem. Higher modes of dispersion curves have deeper penetration, which can improve the inversion quality. This study utilizes the multi-objective particle swarm optimization (MOPSO) algorithm, rather than a traditional single-objective optimization algorithm, to obtain S-velocity profiles from Rayleigh wave multimode phase velocity dispersion curves. The uncertainty of the inversion parameters is evaluated through the morphology of the Pareto front and the standard deviation of the Pareto optimal solution set. This is the first application of MOPSO in solving the multimode Rayleigh wave phase velocity dispersion curves joint inversion problem. It inverts three synthetic datasets, compares the inversion results with the synthetic data, and then conducts a comparative analysis with the particle swarm optimization (PSO) algorithm and the multi-objective grey wolf optimization (MOGWO) algorithm in one of these synthetic models to evaluate the accuracy and stability of MOPSO to the joint inversion. In addition, this research inverts observed data from an expressway roadbed in Henan, China, to examine the applicability of MOPSO for the joint inversion of multimode dispersion curves. The MOPSO inversion closely yields S-wave velocity profiles that match the borehole data. The synthetic and observed data inversion results indicated that the MOPSO algorithm accurately inverts multimode dispersion curves.