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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.

A robust, in situ estimate of shear-wave velocity VS and the small-strain damping ratio DS (or equivalently, the quality factor QS) is crucial for the design of buildings and geotechnical systems subjected to vibrations or earthquake ground shaking. A promising technique for simultaneously obtaining both VS and DS relies on the Multichannel Analysis of Surface Waves (MASW) method. MASW can be used to extract the Rayleigh wave phase velocity and phase attenuation data from active-source seismic traces recorded along linear arrays. Then, these data can be inverted to obtain VS and DS profiles. This paper introduces two novel methodologies for extracting the phase velocity and attenuation data. These new approaches are based on an extension of the beamforming technique which can be combined with a modal filter to isolate different Rayleigh propagation modes. Thus, the techniques return reliable phase velocity and attenuation estimates even in the presence of a multimode wavefield, which is typical of complex stratigraphic conditions. The reliability and effectiveness of the proposed approaches are assessed on a suite of synthetic wavefields and on experimental data collected at the Garner Valley Downhole Array and Mirandola sites. The results reveal that, under proper modelling of wavefield conditions, accurate estimates of Rayleigh wave phase velocity and attenuation can be extracted from active-source MASW wavefields over a broad frequency range. Eventually, the estimation of soil mechanical parameters also requires a robust inversion procedure to map the experimental Rayleigh wave parameters into soil models describing VS and DS with depth. The simultaneous inversion of phase velocity and attenuation data is discussed in detail in the companion paper. [ABSTRACT FROM AUTHOR]

This paper deals with in situ characterization of the small-strain shear-wave velocity VS and damping ratio DS from an advanced interpretation of Multi-channel Analysis of Surface Waves (MASW) surveys. A new approach based on extracting Rayleigh wave data using the CFDBFa method has been discussed in the companion paper. This paper focuses on mapping the experimental Rayleigh wave phase velocity and attenuation into profiles of VS and DS versus depth, which is achieved through a joint inversion procedure. The joint inversion of phase velocity and attenuation data utilizes a newly developed Monte Carlo global search algorithm, which implements a smart sampling procedure. This scheme exploits the scaling properties of the solution of the Rayleigh eigenvalue problem to modify the trial earth models and improve the matching with the experimental data. Thus, a reliable result can be achieved with a limited number of trial ground models. The proposed algorithm is applied to the inversion of synthetic data and of experimental data collected at the Garner Valley Downhole Array site, as described in the companion paper. In general, inverted soil models exhibit well-defined VS profiles, whereas DS profiles are affected by larger uncertainties. Greater uncertainty in the inverted DS profiles is a direct result of higher variability in the experimental attenuation data, the limited wavelength range at which reliable values of attenuation parameters can be retrieved, and the sensitivity of attenuation data to both DS and VS. Nonetheless, the resulting inverted earth models agree well with alternative in situ estimates and geological data. The results stress the feasibility of retrieving both stiffness and attenuation parameters from active-source MASW testing and the effectiveness of extracting in situ damping ratio estimates from surface wave data. [ABSTRACT FROM AUTHOR]

The horizontal-to-vertical spectral ratio (HVSR) of ambient noise is commonly used to infer a site's resonance frequency (⁠|${f_{0,site}}$|⁠). HVSR calculations are performed most commonly using the Fourier amplitude spectrum obtained from a single merged horizontal component (e.g. the geometric mean component) from a three-component sensor. However, the use of a single merged horizontal component implicitly relies on the assumptions of azimuthally isotropic seismic noise and 1-D surface and subsurface conditions. These assumptions may not be justified at many sites, leading to azimuthal variability in HVSR measurements that cannot be accounted for using a single merged component. This paper proposes a new statistical method to account for azimuthal variability in the peak frequency of HVSR curves (⁠|${f_{0,HVSR}}$|⁠). The method uses rotated horizontal components at evenly distributed azimuthal intervals to investigate and quantify azimuthal variability. To ensure unbiased statistics for |${f_{0,HVSR}}$| are obtained, a frequency-domain window-rejection algorithm is applied at each azimuth to automatically remove contaminated time windows in which the |${f_{0,HVSR}}$| values are statistical outliers relative to those obtained from the majority of windows at that azimuth. Then, a weighting scheme is used to account for different numbers of accepted time windows at each azimuth. The new method is applied to a data set of 114 HVSR measurements with significant azimuthal variability in |${f_{0,HVSR}}$|⁠ , and is shown to reliably account for this variability. The methodology is also extended to the estimation of a complete lognormal-median HVSR curve that accounts for azimuthal variability. To encourage the adoption of this statistical approach to accounting for azimuthal variability in single-station HVSR measurements, the methods presented in this paper have been incorporated into hvsrpy , an open-source Python package for HVSR processing. [ABSTRACT FROM AUTHOR]

The horizontal-to-vertical spectral ratio (HVSR) of ambient noise measurement is commonly used to estimate a site's resonance frequency (⁠|${f_0}$|⁠). For sites with a strong impedance contrast, the HVSR peak frequency (⁠|${f_{0,\mathrm{ HVSR}}}$|⁠) has been shown to be a good estimate of |${f_0}$|⁠. However, the random nature of ambient noise (both in time and space), in conjunction with variable environmental conditions and sensor coupling issues, can lead to uncertainty in |${f_{0,\mathrm{ HVSR}}}$| estimates. Hence, it is important to report |${f_{0,\mathrm{ HVSR}}}$| in a statistical manner (e.g. as a mean or median value with standard deviation). In this paper, we first discuss widely accepted procedures to process HVSR data and estimate the variance in |${f_{0,\mathrm{ HVSR}}}$|⁠. Then, we propose modifications to improve these procedures in two specific ways. First, we propose using a lognormal distribution to describe |${f_{0,\mathrm{ HVSR}}}$| rather than the more commonly used normal distribution. The use of a lognormal distribution for |${f_{0,\mathrm{ HVSR}}}$| has several advantages, including consistency with earthquake ground motion processing and allowing for a seamless transition between HVSR statistics in terms of both frequency and its reciprocal, period. Second, we introduce a new frequency-domain window-rejection algorithm to decrease variance and enhance data quality. Finally, we use examples of 114 high-variance HVSR measurements and 77 low-variance HVSR measurements collected at two case study sites to demonstrate the effectiveness of the new rejection algorithm and the proposed statistical approach. To encourage their adoption, and promote standardization, the rejection algorithm and lognormal statistics presented in this paper have been incorporated into hvsrpy , an open-source Python package for HVSR processing. [ABSTRACT FROM AUTHOR]

Surface wave methods provide a cost effective means of developing shear wave velocity (Vs) profiles for applications such as dynamic site characterization and seismic site response analyses. However, the inverse problem involved in obtaining a realistic layered earth model from surface wave dispersion data is inherently ill-posed, non-linear and mix-determined, without a unique solution. When available, a priori information such as geotechnical boreholes or geologic well logs should be used to aid in constraining site-specific inversion parameters. Unfortunately, a priori information is often unavailable, particularly at significant depths, and a 'blind analysis' must be performed. In these situations, the analyst must decide on an appropriate number of layers and ranges for their corresponding inversion parameters (i.e. trial number of layers and ranges in their respective thicknesses, shear wave velocities, compression wave velocities and mass densities). Selection of these parameters has been shown to significantly impact the results of an inversion. This paper presents a method for conducting multiple inversions utilizing systematically varied inversion layering parametrizations in order to identify and encompass the most reasonable layered earth models for a site. Each parametrization is defined by a unique layering ratio, which represents a multiplier that systemically increases the potential thickness of each layer in the inversion parametrization based on the potential thickness of the layer directly above it. The layering ratio method is demonstrated at two sites associated with the InterPacific Project, wherein it is shown to significantly aid in selecting reasonable Vs profiles that are close representations of the subsurface. While the goal of the layering ratio inversion methodology is not necessarily to find the 'optimal' or 'best' Vs profile for a site, it may be successful at doing so for certain sites/datasets. However, the primary reason for using the layering ratio method is to find Vs profiles that realistically represent the uncertainty in Vs resulting from surface wave inversion, and to avoid selection of Vs profiles that are unrealistic and adversely influenced by the choice of inversion parametrization. [ABSTRACT FROM AUTHOR]