A Wavelet-based Seismogram Inversion Algorithm for the In Situ Characterization of Nonlinear Soil Behavior

We present a full waveform inversion algorithm of downhole array seismogram recordings that can be used to estimate the inelastic soil behavior in situ during earthquake ground motion. For this purpose, we first develop a new hysteretic scheme that improves upon existing nonlinear site response models by allowing adjustment of the width and length of the hysteresis loop for a relatively small number of soil parameters. The constitutive law is formulated to approximate the response of saturated cohesive materials, and does not account for volumetric changes due to shear leading to pore pressure development and potential liquefaction. We implement the soil model in the forward operator of the inversion, and evaluate the constitutive parameters that maximize the cross-correlation between site response predictions and observations on ground surface. The objective function is defined in the wavelet domain, which allows equal weight to be assigned across all frequency bands of the non-stationary signal. We evaluate the convergence rate and robustness of the proposed scheme for noise-free and noise-contaminated data, and illustrate good performance of the inversion for signal-to-noise ratios as low as 3. We finally employ the proposed scheme to downhole array data, and show that results compare very well with published data on generic soil conditions and previous geotechnical investigation studies at the array site. By assuming a realistic hysteretic model and estimating the constitutive soil parameters, the proposed inversion accounts for the instantaneous adjustment of soil response to the level and strain and load path during transient loading, and allows results to be used in predictions of nonlinear site effects during future events.