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SUMMARY: In this study, we propose a systematic and effective method, that is, an extended version of the generalized reflection/transmission (R/T) coefficient method, for computing the phase-velocity (${c}_r$) dispersion curves, attenuation coefficient ($\alpha $) curves, and eigenfunctions of both Rayleigh and Love waves as well as the ellipticity of Rayleigh waves in layered viscoelastic-vertical transversely isotropic (VTI) media. The numerical scheme of combining the root-searching method with the local optimization method is designed for determining the complex-valued modal solutions (i.e. complex wavenumber $k = {\omega {/ {\vphantom {\omega {{c}_r - i\alpha }}}} {{c}_r - i\alpha }}$) of surface waves. The near-surface sedimentary geological environment is taken as the model example because it is typical viscoelastic-VTI media. Besides the anisotropic-viscoelastic (AV) media, our algorithm can also compute surface waves in isotropic-elastic (IE), isotropic-viscoelastic (IV) and anisotropic-elastic (AE) media by resetting the corresponding parameters. Using the six-layer half-space models and in these four media, we verify the correctness of our algorithm by benchmarking the modal solutions against those from other methods. In the four-layer half-space model, by comparing the results of IE, IV, AE and AV media, we analyse the effects of velocity anisotropy, viscoelasticity and attenuation anisotropy on the dispersion and attenuation characteristics of both Rayleigh and Love waves in detail. Our study can provide a theoretical basis and useful tool for surface wave imaging considering the anisotropy and/or viscoelasticity of the medium, which has the potential to better investigate the solid Earth's internal structure. [ABSTRACT FROM AUTHOR]

Effective extraction of higher mode dispersion information has been a research hotspot in the study of surface waves. In this study, we introduce a novel approach of refining Rayleigh wave higher modes by using seismoelectric signals, namely, electromagnetic (EM) signals originating from seismoelectric conversion. Adopting a weight‐drop source, we simulate seismic and EM signals for several porous models. An extended version of the frequency‐Bessel transform method is introduced to extract dispersion information from seismic and EM signals. Results suggest that the evanescent seismoelectric waves, which are induced at subsurface interfaces penetrated by Rayleigh waves and finally are recorded nearby the ground surface after undergoing amplitude decay, can reflect dispersion characteristics of Rayleigh waves and can provide extra higher‐mode dispersion information that seismic waves cannot. We find the vadose zone with higher water saturation will cause the seismoelectric signals to have stronger strengths and change their frequency coverage of dispersion information. Electric fields obtained from potential differences between longer dipole electrodes suffer more severe distortion. In an electrically resistive environment, predicted seismoelectric signal amplitudes in the frequency band with dominant energy are well above expected background noise levels. We also find seismoelectric signals have a stronger antialiasing ability than seismic waves and their dispersion energy values are sensitive to salinity and fluid viscosity. Generally speaking, our study suggests Rayleigh wave dispersion information with abundant higher modes and good frequency‐range coverage can be obtained by using seismic and seismoelectric signals together due to their complementarity. Key Points: The seismic and seismoelectric wavefields in porous media are simulated when a weight‐drop source hitting the ground surface is adoptedThe frequency‐Bessel transform method is used to obtain Rayleigh wave dispersion information from seismic and seismoelectric signalsThe seismoelectric signals and seismic waves are very complementary in providing dispersion information of Rayleigh wave higher modes [ABSTRACT FROM AUTHOR]

Effects of anisotropy and viscoelasticity of Earth media on Rayleigh waves propagation are studied by numerical simulation based on a finite-difference (FD) scheme, which calculates the spatial derivatives via a 12th-order staggered grid difference operator and the time derivatives through the fourth-order Runge-Kutta method. In the homogeneous half-space, the accuracy of FD algorithm is tested against the isotropic-elastic (IE) analytical solution; the calculation method of the theoretical phase velocities of the anisotropic-viscoelastic (AV) Rayleigh waves is developed to verify the correctness of modeling results; the characteristics of Rayleigh-wave are analyzed by comparisons among IE, anisotropic-elastic (AE) and AV modeling results in terms of the wave field snapshots, the synthetic seismograms, and the dispersive images, respectively. Then, the two-layer models and the four-layer models are utilized to further analyze the characteristics of Rayleigh waves in the AV layered media. Results show the substantial differences among these three kinds of media. Anisotropy of medium leads to the significant changes of Rayleigh-wave in amplitude, waveform and phase velocity due to anisotropy of velocity, but does not cause the phase velocity dispersion of Rayleigh-wave. Viscoelasticity of media arouses the amplitude attenuation and phase velocity dispersion of Rayleigh-wave. This is the first report for FD modeling and characteristics analysis of Rayleigh-wave in the AV media, which will provide a valuable reference for near-surface geophysical investigation. [ABSTRACT FROM AUTHOR]

Rayleigh-wave exploration method, which is non-invasive, high-efficiency and high-resolution approach, has been used widely for estimation of Shear-wave velocities of near-surface materials by inverting dispersive Rayleigh-wave phase velocities. Love waves are the result of constructive interference of multiple reflections of SH waves at the free surface, and their particle motion is parallel to the surface but perpendicular to the direction of propagation. Like Rayleigh waves, Love waves are also one kind of surface waves. Nevertheless, unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity. This characteristic not only makes Love-wave dispersion curves simpler but also reduces the degree of non-uniqueness leading to more stable inversion of Love-wave dispersion curves. Therefore, Love-wave exploration method has received increased attention from the near-surface geophysics community interested in application to a variety of near-surface geological and geophysical problems. So far, Love-wave exploration method is still based on the theoretical framework of elastic media. However, the Earth has been recognized as the anisotropic-viscoelastic media with the significant effects on seismic-wave propagation, especially on surface waves. Thus, it is of great importance to study the characteristics of Love waves in viscoelastic media for further broadening the application field of Love-wave exploration method and guiding the practical exploration works.In this study, the first-order SH velocity-stress wave equations of 2-D viscoelastic media in time domain, which are based on the viscoelastic theory of generalized Zener body (GZB), are used for modeling the propagation of Love waves. In order to obtain results with high accuracy, we adopt a standard staggered grid (SSG) finite-difference (FD) scheme, which incorporates the free-surface boundary condition of the stress image method (SIM) and the absorbing boundary condition of the multiaxial perfectly matched layer (M-PML). We also extend the generalized reflection and transmission coefficients method (GRTM) from the elastic media to the viscoelastic media, which can be used for demonstrating the accuracy of FD method by the analytical seismogram and verifying the correctness of modeling results by the theoretical dispersion curves. In a two-layer model, we analyze the characteristics of attenuation and dispersion of Love waves by comparisons of modeling results between elastic media and viscoelastic media in terms of synthetic seismograms and dispersive images, respectively. In addition, we also utilize three typical four-layer models to further analyze the characteristics of Love waves in the viscoelastic layered media. [ABSTRACT FROM AUTHOR]

Rayleigh wave exploration is capable of reconstructing seismic properties at high resolution. The dispersion curve inversion methods are mainly based on 1D layered-model assumptions and require picking the dispersion curves manually. The success is highly dependent on personal subjectivity. Full waveform inversion (FWI) has received particular attention in recent years due to the fact that it has no need for manual dispersion curve extraction and no restriction on medium distribution. However, there are still many challenges limiting the application of FWI in field data, e.g., cycle-skipping issues, dependence on the initial model, and difficulty in estimating the seismic source signature. We adapt a particle swarm optimization (PSO) algorithm for Rayleigh wave frequency-velocity spectrum (FVS) inversion. Compared with conventional dispersion curve inversion, we directly fit the FVS without manually extracting the dispersion curves. Compared with FWI, we avoid cycle-skipping issues by transforming the observed data from the space-time domain to the frequency-velocity domain. We reduce the dependence on the initial model by adopting a global optimal inversion strategy, and improve the inversion efficiency by introducing GPU parallel computing. In addition, we find that the seismic source dependence of FVS inversion is much less than that of FWI. Both synthetic and field examples verify the effectiveness of the method, making it a valuable tool for retrieving the subsurface structure. • FVS inversion has no need to manually extract dispersion curves. • FVS inversion is low source-dependent. • FVS contains rich dispersion information that reduces inversion non-uniqueness. [ABSTRACT FROM AUTHOR]

Abstract High-frequency Rayleigh-wave method plays an important role in the near-surface seismic investigation. Rayleigh wave propagates along the free surface, and its propagation is seriously affected by the topographic surface. Rayleigh-wave propagation is more affected by canyon topography than by hill topography. Hence, it is critical to analyze effects of complex canyon topography on high-frequency Rayleigh waves. To further study effects of topography on Rayleigh-wave dispersion images and Rayleigh-wave conversion, we synthesized near-surface seismograms on 2D Gaussian shape canyon topography model through finite-difference modeling scheme. We compared the seismograms and their dispersion images of Rayleigh waves by using the horizontal offset along the horizontal direction and the real offset along the topographic free surface. These dispersion images were compared with the corresponding theoretical dispersion curves that were obtained by models with a flat free surface. Our numerical results indicated that using the real offset can obtain a better quality of Rayleigh-wave dispersion imaging and then obtain a higher precision of dispersion curves than those using the horizontal offset. Our numerical results also showed that errors of the picked Rayleigh-wave phase velocities can be constrained within 8% if the ratio of canyon depth to the predominant wavelength ( λ m ) of Rayleigh waves is <0.5 with canyon width being greater than the λ m . Modeling results of horizontal and slope free surface half-space models demonstrated that wavefield separation technique can be used to model Rayleigh-wave propagation on topography with high accuracy. Wavefield separation results indicated that the energy of S waves converted from Rayleigh waves is greater than that of P waves converted from Rayleigh waves in the left corner of the canyon. The analysis suggested that using this technique can distinguish complex waveforms and study the converted energy of Rayleigh waves on arbitrary topography. Highlights • Influences of the horizontal and real offsets on Rayleigh-wave dispersion images are discussed. • Influence of the d / λ m ratio of canyon on precision of Rayleigh-wave dispersion curves extracting is analyzed. • The wavefield separation technique on canyon topographic surface is applied. • The converted energy of Rayleigh waves is clarified by using the wavefield separation technique. [ABSTRACT FROM AUTHOR]

Conventional full waveform inversion (FWI) of Rayleigh wave updates the earth model iteratively by minimizing the difference between measured and synthetic data using single-objective function. However, FWI of Rayleigh wave is challenging due to its high nonlinearity and multimodality. Thus, single-objective inversion may lead to incorrect results, and multi-objective inversion is attractive to obtain global optimal solution. In this paper, we propose a multi-objective particle swarm optimization (MOPSO) scheme for FWI of Rayleigh wave. During the MOPSO inversion, the model is optimized iteratively by using multiple criteria simultaneously. We adopt four objective functions in our proposed MOPSO strategy to characterize the observed data: waveform, peak time, waveform envelope and phase velocity spectrum. The concept of Pareto optimal solution set is introduced in the MOPSO strategy to avoid the contradiction of multi-objective functions. Each non-dominated solution is recorded on the Pareto optimal set for model iteration. Both synthetic data and real field data demonstrate the effectiveness and practicability of the MOPSO strategy. • Multiple objective functions are independent and of equal status with each other. • The MOPSO inverse strategy has strong global search capability. • Multi-objective inversion is more accurate than single-objective inversion. [ABSTRACT FROM AUTHOR]

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. • A novel and powerful method (MOPSO) for Rayleigh wave multimode joint inversion is introduced. • Multimode joint inversion is effective in identifying some special strata. • Multimode joint inversion based on MOPSO doesn't require adjustment of the weighting coefficients. • The performance of MOPSO is compared to that of PSO and MOGWO algorithms for the multimode joint inversion. [ABSTRACT FROM AUTHOR]

Multichannel analysis of surface waves (MASW) is a vital method in near-surface exploration. Linear algorithms, such as damped least square method (DLS), are highly dependent on the initial model and are prone to trapping in local minima. While nonlinear algorithms such as genetic algorithm (GA) are globally optimal but inefficient, they are not very practical for complex calculations. In this paper, we propose a combined GA and DLS parallel algorithm (GA-DLS), which has a global search capability due to the GA framework, and has a quick local search capability due to the DLS parallel computing. To simulate the earth model in complex near-surface conditions, we set a low-velocity layer among a layered earth model (LVL) and a high-velocity layer among a layered earth model (HVL), we perform the inversion with DLS, GA, and GA-DLS, respectively. The comparison shows that the GA-DLS inversion gets an efficient and accurate result. Finally, we use the GA-DLS algorithm to invert the field data and achieve good results, verifying the effectiveness of the algorithm. • Multimode is useful in complex near-surface inversion. • Combined linear and nonlinear algorithm makes the inversion efficient and accurate. • The framework of GA makes the inversion globally optimal. • The DLS parallel computing makes the inversion efficient. [ABSTRACT FROM AUTHOR]