Propagation of Data Uncertainty in Surface Wave Inversion

Abstract

Although in recent years surface wave methods have undergone significant development that has greatly enhanced their capabilities, little effort has been spent to determine the uncertainty associated with surface wave measurements. The objective of this study is to determine how the uncertainty of the experimental data is mapped into the uncertainty of the shear wave velocity profile via the inversion algorithm. The methodology developed in this study for estimating the uncertainty of the shear wave velocity profile from surface wave measurements is based on the assumption that the experimental data are normally distributed. The validity of this hypothesis was experimentally verified using data gathered at two sites in Italy where surface wave tests were performed using linear arrays of multiple receivers. The experimental dispersion curve measured at the site was subsequently inverted to obtain the expected shear wave velocity profile together with an estimate of the associated standard deviation. The final results show that uncorrelated noise has a very little influence on multistation surface wave tests, confirming their robustness for applications in noisy environments.

Time-lapse monitoring of climate effects on earthworks using surface waves

“…(a) Comparison between the best-fitting theoretical dispersion curves (in grayscale, according to misfit values) and the inverted dispersion curve (red dots). The uncertainty intervals (red bars) correspond to the assumption of a 5% phase velocity standard deviation at all frequencies consistent with the hypothesis of a Gaussian distribution for the population of phase velocity at each frequency (Lai et al, 2006;Safani et al, 2006;Pasquet, 2014). (b) Feasible V S profiles (in grayscale, according to misfit value) and selected model for inclusion in the initial model (for the dispersion curves comprised between 35 < x < 75 m).…”

“…The temporal variability of the acquired data sets (dispersion and attenuation curves) and the inverted V S models were investigated to quantitatively define a seasonal trend that can be correlated with the correspond to the assumption of a 5% phase velocity standard deviation at all frequencies, consistent with the hypothesis of a Gaussian distribution for the population of phase velocity at each frequency (Lai et al, 2006;Safani et al, 2006;Pasquet, 2014). The illustrated dispersion curves are spatially referenced to x ¼ 25, 50, 75, and 100 m.…”

Guidelines for the good practice of surface wave analysis: a product of the InterPACIFIC project

“…The Jacobian can also be used to propagate uncertainties on the dispersion curve to uncertainties on the shear wave velocity profile (Lai et al 2005).…”

Comment on ‘Shear wave profiles from surface wave inversion: the impact of uncertainty on seismic site response analysis’

“…They claim that the Comment on "Shear wave profiles from surface wave inversion: the impact of uncertainty on seismic site response analysis" By Socco et al 4 uncertainty bounds are based on the results reported in Lai et al (2005), but the relation adopted by the Authors [±∆VR = ±(0.05VR + 100/f)] is not reported by Lai et al (2005) and it leads to results which are not consistent with experimental data of Lai et al (2005). It is also to be observed that the expression proposed by the Authors, can lead to uncertainties higher than 100% and negative velocity values for soft soils at low frequencies (e.g.…”