Mapping surface wave dispersion uncertainty in Vs Profiles to V_S,30 and site response analysis

Highlights

• The article studies the propagation of dispersion uncertainty in Vs profiles to V_S,30 and linear soil amplification.

• The range of variation of V_S-misfit, V_S,30 and peak amplification increases as the dispersion misfit increases.

• As the dispersion misfit increases, more number of solutions are found to exist at very similar misfit values.

• If the minimum misfit achieved during inversion is higher the effect of inversion non-uniqueness manifests more noticeably in the subsequent analyses.

Abstract

The article studies the propagation of dispersion uncertainty in Vs profiles to V_S,30 and linear soil amplification, and at the same time, it also attempts to infer some insights on how the inversion non-uniqueness plays a role in the extracted Vs profiles and subsequent analyses. Three synthetic and two field studies have been presented for this purpose. Target dispersion curve has been assigned with an uncertainty estimate and inversion has been performed using Neighbourhood algorithm. Profiles have been selected from different misfit ranges and combined into one in order to map dispersion misfit with V_S-misfit, V_S,30 and peak soil amplification. The term V_S-misfit has been introduced for synthetic cases to represent the deviation of an extracted V_S profile after inversion from the true solution using a single value. The results clearly depict that the range of variation of V_S-misfit, V_S,30 and peak amplification increases as the dispersion misfit increases. This implies that if the minimum misfit achieved during inversion is higher, the inversion non-uniqueness might play a bigger role in the subsequent analyses. As the dispersion misfit increases, more number of solutions are found to exist at very similar misfit values and the non-uniqueness of inversion manifests more noticeably in the subsequent analyses. Standard deviation is found to increase with the increase in misfit ranges. In terms of COV, V_S-misfit exhibits the highest variation, whereas the variations get reduced in V_S,30 and in peak amplification.

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 (V_S) measured using surface wave technique provides small strain shear modulus, i.e. maximum shear modulus (G_max), which is required in 1D seismic ground response analysis. To predict the design ground motion accurately, a proper and reliable estimate of V_S profiles should be of prime importance. Uncertainty associated with surface wave dispersion measurements and its propagation in the extracted V_S 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 V_S,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., COV_VR), 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 V_S 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 V_S 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 V_S profiles and into other subsequent analyses (like V_S,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 V_S,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 V_S 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 V_S models have been extracted for different misfit ranges. To quantify the variation in extracted V_S profiles, the concept of V_S-misfit has been introduced. Then, the propagation of dispersion uncertainty on V_S-misfit, V_S,30 and soil amplification has been studied. In the end, the variation of V_S-misfit, V_S,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.