Reconstruction, with tunable sparsity levels, of shear wave velocity profiles from surface wave data

Abstract

Summary The analysis of surface wave dispersion curves is a way to infer the vertical distribution of shear-wave velocity. The range of applicability is extremely wide: going, for example, from seismological studies to geotechnical characterizations and exploration geophysics. However, the inversion of the dispersion curves is severely ill-posed and only limited efforts have been put in the development of effective regularization strategies. In particular, relatively simple smoothing regularization terms are commonly used, even when this is in contrast with the expected features of the investigated targets. To tackle this problem, stochastic approaches can be utilized, but they are too computationally expensive to be practical, at least, in case of large surveys. Instead, within a deterministic framework, we evaluate the applicability of a regularizer capable of providing reconstructions characterized by tunable levels of sparsity. This adjustable stabilizer is based on the minimum support regularization, applied before on other kinds of geophysical measurements, but never on surface wave data. We demonstrate the effectiveness of this stabilizer on: i) two benchmark—publicly available— datasets at crustal and near-surface scales; ii) an experimental dataset collected on a well-characterized site. In addition, we discuss a possible strategy for the estimation of the depth of investigation. This strategy relies on the integrated sensitivity kernel used for the inversion and calculated for each individual propagation mode. Moreover, we discuss the reliability, and possible caveats, of the direct interpretation of this particular estimation of the depth of investigation, especially in the presence of sharp boundary reconstructions.

1D Stochastic Inversion of Airborne Time-Domain Electromagnetic Data with Realistic Prior and Accounting for the Forward Modeling Error

“…In fact, this is a very well-known result (e.g., [36,58,59]), to some extent, reconciling probabilistic and deterministic approaches; in particular, if C −1 m is taken equal to λ 2 L T Lwith λ being the Tikhonov parameter controlling the relative importance of the regularization term with respect of the data misfit, and L a discrete approximation of the spatial derivativethen, the minimization of the objective functional coincides with the standard Occam's inversion [60].…”

“…Moreover, novel strategies to effectively incorporate prior information into the translation of the observed data into conductivity models have led to the development of, for example, spatially constrained inversion schemes [29][30][31][32] (again, similarly to approaches utilized for other, very different, kinds of data [33][34][35][36][37]). This capability of enforcing spatial coherence allowed the reconstruction of (pseudo-)3D conductivity distributions even by means of simple 1D forward modeling [38,39].…”

A Flexible Single Loop Setup for Water-Borne Transient Electromagnetic Sounding Applications

“…Another approach to determine the DOI is based on assessing the sensitivity of each layer by evaluating the Jacobian matrix (e.g., [ 37 ]), which offers the additional advantage of providing the sensitivity of each layer individually to identify possible ill-determined parts of the model. Such an approach was also used to evaluate the DOI in the inversion of seismic surface wave data [ 38 ]. In our study, we use only the DOI and DOI approaches as described above.…”

Laterally constrained inversion (LCI) of multi-configuration EMI data with tunable sharpness

“…One regularization strategy to enforce a sharp or blocky solution is based on the minimum gradient support 40 (MGS) method (Portniaguine & Zhdanov, 1999;Zhdanov, 2002). Within the MGS regularization, a focusing parameter controls the characteristics of the used stabilizer; i.e., a small parameter value promotes sharp solutions while a large value promotes smoother models (Vignoli et al, 2015;Deidda et al, 2020;Vignoli et al, 2021). The MGS regularization has been implemented in sev-45 eral inversion approaches for other geophysical methods.…”

“…The MGS regularization has been implemented in sev-45 eral inversion approaches for other geophysical methods. For example, it has been successfully used for the inversion of gravity data (Last & Kubik, 1983), electrical resistivity data (Blaschek et al, 2008;Fiandaca et al, 2015;Thibaut et al, 2021), seismic dispersion curves (Vignoli et al, 2021), traveltime data sets (Zhdanov et al, 2006;Vignoli et al, 2012), and time-domain electromagnetic 50 data (Ley-Cooper et al, 2015;Vignoli et al, 2015Vignoli et al, , 2017. For FDEM data, VCI strategies using the MGS regularization have been presented by Deidda et al (2020).…”