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Full-waveform inversion (FWI) methods rely on accurate numerical simulation of wave propagation in the analysed medium. Acoustic or elastic wave equations are often used to model seismic wave propagation. These types of simulations do not account for intrinsic attenuation effects due to material anelasticity, and thus correction techniques have been utilized in practice to partially compensate the anelasticity. These techniques often only consider the waveform amplitude correction based on averaging of overall amplitude response over the entire data set, and ignore the phase correction. Viscoelastic wave equations account for the anelastic response in both waveform amplitude and phase, and are therefore a more suitable alternative. In this study, we present a novel 3-D Gauss–Newton viscoelastic FWI (3-D GN-VFWI) method. To address the main challenge of the Gauss–Newton optimization, we develop formulas to compute the Jacobian efficiently by the convolution of virtual sources and backward wavefields. The virtual sources are obtained by directly differentiating the viscoelastic wave equations with respect to model parameters. In order to resolve complex 3-D structures with reasonable computational effort, a homogeneous attenuation (Q factor) is used throughout the analysis to model the anelastic effects. Synthetic and field experiments are performed to demonstrate the utility of the method. The synthetic results clearly demonstrate the ability of the method in characterizing a challenging velocity profile, including voids and reverse velocity layers. The field experimental results show that method successfully characterizes the complex substructure with two voids and undulating limestone bedrock, which are confirmed by invasive tests. Compared to 3-D elastic FWI results, the presented viscoelastic method produces more accurate results regarding depths of the voids and bedrock. This study suggests that the improvement of imaging accuracy would warrant the widespread use of viscoelastic wave equations in FWI problems. To our best knowledge, this is the first reported study on 3-D GN-VFWI at any scale. This study provides the new theory and formulation for the use of Gauss–Newton optimization on the 3-D viscoelastic problem.

 

We develop a new 3D ambient noise tomography (3D ANT) method for geotechnical site characterization. It requires recording ambient noise fields using a 2D surface array of geophones, from which experimental crosscorrelation functions (CCFs) are then extracted and directly inverted to obtain an S-wave velocity ([Formula: see text]) structure. The method consists of a forward simulation using 3D P-SV elastic wave equations to compute the synthetic CCF and an adjoint-state inversion to match the synthetic CCFs to the experimental CCFs for extraction of [Formula: see text]. The main advantage of the presented method, as compared with conventional passive-source seismic methods using characteristics of Green’s function (GF), is that it does not require equal energy on both sides of each receiver pair or far-field wavefields to retrieve the true GF. Instead, the source power spectrum density is inverted during the analysis and incorporated into the forward simulation of the synthetic CCFs to account for source energy distribution. After testing on synthetic data, the 3D ANT method is applied to 3 h of ambient noise recordings at the Garner Valley Downhole Array (GVDA) site in California, using a surface array of 196 geophones placed on a 14 × 14 grid with 5 m spacing. The inverted 3D [Formula: see text] model is found to be consistent with previous invasive and noninvasive geotechnical characterization efforts at the GVDA site.