The single-station microtremor horizontal-to-vertical spectral ratio (MHVSR) method was initially proposed to retrieve the site amplification function and its resonance frequencies produced by unconsolidated sediments overlying high-velocity bedrock. Presently, MHVSR measurements are predominantly conducted to obtain an estimate of the fundamental site frequency at sites where a strong subsurface impedance contrast exists. Of the earthquake site characterization methods presented in this special issue, the MHVSR method is the furthest behind in terms of consensus towards standardized guidelines and commercial use. The greatest challenges to an international standardization of MHVSR acquisition and analysis are (1) thewhat— the underlying composition of the microtremor wavefield is site-dependent, and thus, the appropriate theoretical (forward) model for inversion is still debated; and (2) thehow— many factors and options are involved in the data acquisition, processing, and interpretation stages. This paper reviews briefly a historical development of the MHVSR technique and the physical basis of an MHVSR (thewhat). We then summarize recommendations for MHVSR acquisition and analysis (thehow). Specific sections address MHVSR interpretation and uncertainty assessment.

Quantitative dynamic strain measurements of the ground would be useful for engineering scale problems such as monitoring for natural hazards, soil-structure interaction studies, and non-invasive site investigation using full waveform inversion (FWI). Distributed acoustic sensing (DAS), a promising technology for these purposes, needs to be better understood in terms of its directional sensitivity, spatial position, and amplitude for application to engineering-scale problems. This study investigates whether the physical measurements made using DAS are consistent with the theoretical transfer function, reception patterns, and experimental measurements of ground strain made by geophones. Results show that DAS and geophone measurements are consistent in both phase and amplitude for broadband (10 s of Hz), high amplitude (10 s of microstrain), and complex wavefields originating from different positions around the array when: (1) the DAS channels and geophone locations are properly aligned, (2) the DAS cable provides good deformation coupling to the internal optical fiber, (3) the cable is coupled to the ground through direct burial and compaction, and (4) laser frequency drift is mitigated in the DAS measurements. The transfer function of DAS arrays is presented considering the gauge length, pulse shape, and cable design. The theoretical relationship between DAS-measured and pointwise strain for vertical and horizontal active sources is introduced using 3D elastic finite-difference simulations. The implications of using DAS strain measurements are discussed including directionality and magnitude differences between the actual and DAS-measured strain fields. Estimating measurement quality based on the wavelength-to-gauge length ratio for field data is demonstrated. A method for spatially aligning the DAS channels with the geophone locations at tolerances less than the spatial resolution of a DAS system is proposed.

Full waveform inversion (FWI) and distributed acoustic sensing (DAS) are powerful tools with potential to improve how seismic site characterization is performed. FWI is able to provide true 2D or 3D images of the subsurface by inverting stress wave recordings collected over a wide variety of scales. DAS can be used to efficiently collect high-resolution stress wave recordings from long and complex fiber optic arrays and is well-suited for large-scale site characterization projects. Due to the relative novelty of combining FWI and DAS, there is presently little published literature regarding the application of FWI to DAS data for near-surface (depths <30 m) site characterization. We perform 2D FWI on DAS data collected at a well-characterized site using four different, site-specific 1D and 2D starting models. We discuss the unique benefits and challenges associated with inverting DAS data compared to traditional geophone data. We examine the impacts of using the various starting models on the final 2D subsurface images. We demonstrate that while the inversions performed using all four starting models are able to fit the major features of the DAS waveforms with similar misfit values, the final subsurface images can be quite different from one another at depths greater than about 10 m. As such, the best representation(s) of the subsurface are evaluated based on: (1) their agreement with borehole lithology logs that were not used in the development of the starting models, and (2) consistency at shallow depths between the final inverted images derived from multiple starting models. Our results demonstrate that FWI applied to DAS data has significant potential as a tool for near-surface site characterization while also emphasizing the significant impact that starting model selection can have on FWI results.

A fixed base is generally assumed in various dynamic response analyses and the design of bridges. However, soil–foundation flexibility and energy absorption and radiation by the soil system can alter the response of bridges to dynamic loads. This interaction between the structure, foundation, and soil, which in some cases may even change the dynamic load transmitted through the ground, is, in general, referred to as dynamic soil–structure interaction (DSSI). DSSI can either have detrimental or beneficial effects on a bridge response, particularly forces and displacements. These effects depend on several factors such as the rigidity ratio (ratio of the stiffness of the structure to the same of the soil–foundation system), slenderness ratio (height of the structure to the base width ratio), the foundation type, and the mass of the structure relative to the mass of the engaged soil–foundation system. In this paper, the dynamic characteristics of an actual bridge are inferred via an experimental study and numerical simulations. The research concentrated on the evaluation of the significance of DSSI effects under operational live load levels. The bridge was shaken using T-Rex, a large-amplitude mobile shaker from the National Hazards Engineering Research Infrastructure (NHERI) facilities. Two finite-element models were created to assess the DSSI effects on the dynamic response of the bridge. One model included elements that incorporate the DSSI effects, while the other had fixed-base boundary conditions. The response from the DSSI FEM model matched the field results better than that from the fixed-base model, in terms of the peak response amplitudes and identified natural frequencies and modes. In addition, the model incorporating the DSSI effects led to a reduction in stress levels in various bridge components, compared with that of the fixed-base model. The results of this study are applicable to bridges with similar features and site conditions.

Frequency-domain beamforming (FDBF) and cylindrical frequency-domain beamforming (CFDBF) techniques are among the most robust methods for extracting experimental phase velocity dispersion data from wavefields recorded during either active- or passive-source surface wave testing. FDBF and CFDBF transformations rely on calculating the spatiospectral correlation matrix to compute the steered power response spectrum, which is essential for extracting surface wave dispersion data. The dimensions of the spatiospectral correlation matrix are directly influenced by the frequency sampling and the number of sensors used in the survey setup. When the number of sensors is large, and/or the frequency range is broad, and/or the frequency sampling is dense, the spatiospectral correlation matrix size leads to a greater number of required computations to calculate the steered power response spectrum for the FDBF and CFDBF techniques. Therefore, we develop a simplified and computationally efficient FDBF algorithm for active and passive surface wave surveys. This method avoids the calculation of the spatiospectral correlation matrix and its multiplication with the Hermitian transpose of the steering vector, thereby reducing the computational complexity by an order of magnitude. Furthermore, by leveraging vectorization techniques, the developed algorithm uses matrix multiplications instead of loops, significantly heightening computational efficiency. We rigorously test the algorithm using surface wave data sets collected across diverse subsurface conditions with varying sensor arrays and acquisition parameters (e.g., sampling frequencies and window lengths) to evaluate its efficacy. The results demonstrate that our developed algorithm outperforms the conventional FDBF method in processing time, highlighting its practical effectiveness. This method shows promise for integration into surface wave data processing software, offering substantial improvements in computational efficiency without compromising accuracy.