A recently developed PDE-constrained stochastic inverse analysis algorithm for spatial and statistical characterization of soil parameters from geophysical measurements, considering uncertainty due to limited measurements and sensor noise, is exemplified and validated. A 60m × ۶۰ m geotechnical site in Garner Valley, CA is used as the validation testbed. Advanced geophysical test measurements – in terms of velocity waveforms at a few locations on the surface due to surface excitations using a mobile shaker – are available for the site. The algorithm inversely analyzes the available measurements to probabilistically estimate the elastic parameters of the soil at the site up to a depth of 40 m. The algorithm relies on (1) hypothesizing the soil parameters to be heterogeneous, anisotropic random fields, (2) making prior assumptions on them, (3) numerically simulating the geophysical experiment using the finite element method in conjunction with a stochastic collocation approach, and (4) fusing simulated measurements with experimental measurements using a minimum variance framework to update the prior assumptions on the soil parameter random fields. The estimated elastic parameters of the soil are presented in terms of marginal mean and marginal standard deviation profiles of the soil’s P- and S-wave velocities as well as their correlation structures in the x-, y-, and z-direction. In ascertaining the accuracy of the inverse analysis algorithm, the geophysical experiment is numerically re-simulated with the estimated P- and Swave velocity profiles and the model predicted velocity waveforms are compared against the field observations at all the measurement locations. Comments are made at appropriate places regarding several aspects of the algorithm in highlighting the lessons learned through this validation effort towards accurate stochastic full waveform inversion of geophysical measurements.

Introduction

Estimation of soil parameters at any geotechnical sites using geophysical measurements typically relies on some kind of inverse analysis. Existing analysis techniques range from simplified but widely used spectral analysis of surface waves (SASW; [1]) to high-fidelity partial differential equation (PDE) constrained full waveform inversion (FWI; [2]) technique. The SASW approach analyzes only the surface waves and yields approximate, layered profiles of the S-wave velocity of soils. The FWI technique, on the other hand, analyzes all types of waves that result from a geophysical experiment. It is computationally more expensive, but yields more accurate estimates of the spatial variability of S- as well as P-wave velocities of soils at any sites. All the existing techniques, however, are deterministic in nature and can not account for uncertainty due to limited measurements and any measurement error, both of which are inevitable in characterizing any geotechnical sites using geophysical measurements. To overcome the drawbacks of the deterministic analysis techniques, the authors, recently, developed a scalable computational approach to perform PDE-constrained FWIs of geophysical measurements in the probability space by considering the main sources of uncertainties in the soil parameter estimation process [3]. Hypothesizing the soil properties to be three-dimensional, heterogeneous, anisotropic, non-Gaussian random fields, the developed approach utilized a Gaussian mixture model (GMM) in conjunction with the generalized polynomial chaos (gPC) to approximate the random field soil properties with a finite number of random variables.