Mapping surface wave dispersion uncertainty in Vs Profiles to VS,30 and site response analysis
Introduction
Multichannel analysis of surface wave (MASW) technique [[1], [2], [3]] serves a popular alternative to the available invasive techniques for dynamic site characterisation. Shear wave velocity (VS) measured using surface wave technique provides small strain shear modulus, i.e. maximum shear modulus (Gmax), which is required in 1D seismic ground response analysis. To predict the design ground motion accurately, a proper and reliable estimate of VS profiles should be of prime importance. Uncertainty associated with surface wave dispersion measurements and its propagation in the extracted VS models to seismic ground response analysis has drawn the attention of several researchers recently. Uncertainty associated with surface wave testing may be grouped into two broad categories: (i) Model based uncertainty and (ii) Data measurement uncertainty/inversion uncertainty. Model based uncertainty mainly arises in the form of near-field effects [[4], [5], [6]] and lateral heterogeneity. Data measurement uncertainty mainly results in a scatter in the experimental dispersion curve. Several studies have been carried out to study the propagation of data uncertainty in VS,30 and seismic ground response analysis [[7], [8], [9], [10], [11], [12], [13], [14]]. Inversion and data measurement uncertainty are often combined as one and treated as data measurement uncertainty. [15] made an effort to separate out both the uncertainties. However, as the measurement uncertainty band gets wider, it in fact encompasses the band of inversion uncertainty. So, if a dispersion curve is inverted considering data measurement uncertainty (i.e., COVVR), the effect of inversion non-uniqueness will be taken care indirectly. This is so because as we are filling up the uncertainty bound, the possible consequence of inversion non-uniqueness, i.e. profiles with comparable misfit values, will automatically be considered.
Uncertainty associated with dispersion measurement including acquisition and processing (epistemic or aleatory) may be quantified in terms of standard deviation of Rayleigh wave phase velocity at different frequencies. During the data acquisition, repetition of tests can be performed with different array configurations, i.e. for different receiver spacing and source to receiver distances, to estimate the variation in dispersion estimate [[15], [16], [17], [18]]. Dispersion estimate from different types of sources and from passive surface wave measurements can also be combined in order to estimate the final data scatter in an experimental dispersion curve for a site. Once the dispersion measurement with associated standard deviation at each frequency is available, inversion can be performed and a set of VS profiles whose theoretical dispersion curves will fall within that uncertainty estimate can be extracted. On the other hand, inverse problem solution is non-unique and several different VS models may exhibit a good fit with the experimental dispersion curve [7], [12], [28]. So, all uncertainties, epistemic or aleatory in nature, may be combined into one and represented by the standard deviation at each frequency in the dispersion curve. Now, the propagation of this dispersion uncertainty into the extracted VS profiles and into other subsequent analyses (like VS,30 and ground response study) should be performed carefully in order to estimate the site specific design ground motion with greater accuracy.
This article studies the propagation of dispersion uncertainty on Vs profiles to VS,30 and ground response analysis and at the same time it attempts to infer some insights on how the inversion non-uniqueness plays a role in the extracted Vs profiles and subsequent analyses. Three synthetic VS profiles, one normally dispersive and two inversely dispersive profiles, and two real case studies have been presented to accomplish this. Theoretical dispersion curve has been generated for each considered synthetic soil profile and an uncertainty estimate has been assigned at each frequency in terms of standard deviation of Rayleigh wave phase velocity. Inversion is performed using Neighborhood algorithm and VS models have been extracted for different misfit ranges. To quantify the variation in extracted VS profiles, the concept of VS-misfit has been introduced. Then, the propagation of dispersion uncertainty on VS-misfit, VS,30 and soil amplification has been studied. In the end, the variation of VS-misfit, VS,30 and soil amplification is mapped with dispersion misfit. Two site specific studies have also been presented in order to verify the outcomes of synthetic cases.
Section snippets
Generation of target dispersion curve with associated uncertainty
Three typical synthetic velocity profiles and two real case studies have been considered in the present study. Among three synthetic profiles, one normally dispersive (ND), one inversely dispersive with soft layer (ID-Soft) and one inversely dispersive with stiff layer (ID-Stiff) soil profiles have been used with an error estimate in terms of coefficient of variation of Rayleigh wave phase velocity (). [19] proposed a prediction equation for estimation of as a function of frequency
Normally dispersive profile
For normally dispersive soil profile, the computed dispersion curve with associated standard deviation at each frequency is defined as the target for inversion. During the inversion, a wide range of values of VS and layer thicknesses have been assigned for each layer so that maximum combinations of velocity model can be generated, which will lead to different misfit values. VS has been assigned a range of 100–1000 m/s for all the layers and layer thickness has been assigned a range of 1–15 m
Mapping with VS-misfit
In order to get little more insights on how the effect of inversion non-uniqueness propagates in the subsequent analyses, plots have been prepared to map VS,30 and peak amplification with VS-misfit. For synthetic cases, as the true solutions are known, it is possible to plot the variations of VS,30 and peak amplification with VS-misfit. Fig. 17 presents the Variation of VS,30, peak amplification with Vs-misfit and distribution of Vs-misfit for ND, IS-soft and IS-stiff soil profiles. All the
Conclusions
The paper studies the propagation of surface wave dispersion uncertainty in Vs Profiles to VS,30 and site response analysis. The variation of VS-misfit, VS,30 and peak amplification values, have been mapped with the dispersion misfit. Three different synthetic soil profiles, one normally dispersive and two inversely dispersive, and two real case studies have been considered in the study. For synthetic cases, five different misfit ranges have been considered, and then 1000 profiles have been
CRediT authorship contribution statement
Narayan Roy: Conceptualization, Formal analysis, Funding acquisition, Data curation, Writing - original draft, Conception and design of study, funding acquisition of data curation, formal analysis and/or interpretation of data, drafting the manuscript. Ravi S. Jakka: Supervision, Writing - original draft, Supervision of the work carried out & revising the manuscript critically for important intellectual content.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (29)
- et al.
Near-offset effects on Rayleigh-wave dispersion measurements: physical modelling
J Appl Geophys
(2009) - et al.
Near-field effects on site characterization using MASW technique
Soil Dynam Earthq Eng
(2017) - et al.
Non-uniqueness in surface-wave inversion and consequences on seismic site response analyses
Soil Dynam Earthq Eng
(2009) - et al.
Implications of surface wave data measurement uncertainty on seismic ground response analysis
Soil Dynam Earthq Eng
(2014) - et al.
Site response implications associated with using non-unique vs profiles from surface wave inversion in comparison with other commonly used methods of accounting for vs uncertainty
Soil Dynam Earthq Eng
(2016) - et al.
Variability of shallow soil amplification from surface-wave inversion using the Markov-chain Monte Carlo method
Soil Dynam Earthq Eng
(2018) - et al.
Effect of data uncertainty and inversion non-uniqueness of surface wave tests on VS,30 estimation
Soil Dynam Earthq Eng
(2018) - et al.
Combination of dispersion curves from
MASW measurements”
(2018) - et al.
Multi-channel analysis of surface waves
Geophysics
(1999) - et al.
Using MASW to map bedrock in Olathe. Kansas [exp. abs.]
Soc Explor Geophys
(1999)
Multistation methods for geotechnical characterization using surface waves
Near-field effects on array-based surface wave methods with active sources
J Geotech Geoenviron Eng
Effect of surface wave inversion non-uniqueness on 1-D seismic ground response analysis
Nat Hazards J
Surface-wave dispersion approach for evaluating statistical models that account for shear-wave velocity uncertainty
J Geotech Geoenviron Eng
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