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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]

The array‐based frequency‐Bessel transform method has been demonstrated to effectively extract dispersion curves of higher‐mode surface waves from the empirical Green's functions (EGFs) of displacement fields reconstructed by ambient noise interferometry. Distributed acoustic sensing (DAS), a novel dense array observation technique, has been widely implemented in surface wave imaging to estimate subsurface velocity structure in practice. However, there is still no clear understanding in theory about how to accurately extract surface‐wave dispersion curves directly from DAS strain (or strain rate) data. To address this, we extend the frequency‐Bessel transform method by deriving Green's functions (GFs) for horizontal strain fields, making it applicable to DAS data. First, we test its performance using synthetic GFs and verify the correctness of extracted dispersion spectrograms with theoretical results. Then, we apply it to three field DAS ambient‐noise data sets, two recorded on land and one in the seabed. The reliability and advantages of the method are confirmed by comparing results with the widely used phase shift method. The results demonstrate that our extended frequency‐Bessel transform method is reliable and can provide more abundant and higher‐quality dispersion information of surface waves. Moreover, our method is also adaptable for active‐source DAS data with simple modifications to the derived transform formulas. We also find that the gauge length in the DAS system significantly impacts the polarity and value of extracted dispersion energy. Overall, our study provides a theoretical framework and practical tool for multimodal surface wave dispersion measurement using DAS data. Plain Language Summary: Ambient noise surface wave imaging is one of the most widely used methods for estimating the Earth's internal shear wave velocity structure, exploiting the dispersion characteristics of surface waves. The array‐based frequency‐Bessel transform method has been proven effective in extracting dispersion curves of higher‐mode surface waves from empirical Green's functions (EGFs) retrieved via ambient noise interferometry. Distributed acoustic sensing (DAS), which is a novel dense array observation technique, has become widely adopted in practical surface wave imaging. Nevertheless, there remains a theoretical gap in our understanding of how to accurately extract surface‐wave dispersion curves directly from DAS strain (or strain rate) data. To bridge this gap, starting from the perspective of strain field theory, we propose an extension of the frequency‐Bessel transform method, which can account for Green's functions of horizontal strain fields and the reconstructed EGFs from DAS ambient noise data. Both synthetic tests and applications to field DAS data demonstrate that our proposed frequency‐Bessel transform method can be confidently and effectively utilized for multimodal dispersion measurement of surface waves derived from DAS observation data. This work can offer a theoretical basis and practical tool for DAS‐based surface wave imaging. Key Points: We derive Green's functions for horizontal strain fields, extending the frequency‐Bessel transform method for applications in distributed acoustic sensing (DAS) dataThe extended frequency‐Bessel transform method reliably measures multimodal surface‐wave dispersion in both synthetic and field DAS recordsThe method excels in extracting high‐quality multimodal dispersion information from both active and passive DAS data for surface waves [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]