Two-dimensional shallow soil profiling using time-domain waveform inversion

Abstract

Near-surface characterization has now gained significance among exploration geophysicists, and many methods are being proposed to retrieve the 2D structures of shallow soils. Because most of these methods are based on the modal inversion of the surface waves, they can only be applied to laterally homogeneous or smoothly heterogeneous soil models. We have developed a time-domain waveform inversion method for 2D near-surface exploration that offers an alternative approach to existing surface-wave techniques for layered soils with a flat surface. Our method directly fits the input Rayleigh waveforms to retrieve the 2D soil structure without need of any modal identification, allowing the inversion of soil models that can be challenging with modal-inversion-based approaches. In our method, the forward problem formulated in the time domain is based on a 2.5D staggered-grid finite-difference scheme to simulate the P-SV wavefield; soil modeling was achieved by dividing soil layers into specific number of blocks with discontinuous interfaces. The inversion strategy depends on attributing suitable values for the interface depth and S-wave velocity for each block to reconstruct a numerical soil model that fit the input waveforms. Because we cannot know the source signature during data acquisition, source deconvolution by a reference station is applied to observed and calculated waveforms to make a waveform inversion free of the source signature. Numerical experiments revealed that our method was able to sufficiently reconstruct soil structures with strong lateral velocity gradient or soils with a blind layer in noisy environments, using a single source and reasonable number of receivers. We also applied this method to real waveform data, and we succeeded in obtaining good correlation between the inverted 2D soil model and the existing borehole data.

Geotechnical Site Characterization via Deep Neural Networks: Recovering the Shear Wave Velocity Profile of Layered Soils

“…For a future part of this study, we intend to extend the current approach to 2D problems where Figure 5: Comparison of current model versus the published results of Seylabi et al (2020) [1] training data will be generated by solving the wave equation using the Finite Element method. This problem is known to be difficult to tackle even with modern statistical techniques, and few studies approached it such as [11].…”

Three-dimensional P- and S-wave velocity profiling of geotechnical sites using full-waveform inversion driven by field data

“…where temporal and spatial dependencies are suppressed for brevity; u is the displacement vector, ρ is mass density of the medium, λ and µ are the Lamé parameters, I is the secondorder identity tensor,Ṡ represents the stress tensor, a dot (˙) denotes differentiation with respect to time, and a bar (¯) indicates history of the subtended variable 3 ; Ω RD represents the interior (regular) domain, Ω PML denotes the region occupied by the PML buffer zone, Γ I is the interface boundary between the interior and PML domains, Γ RD N and Γ PML N denote the free (top surface) boundary of the interior domain and PML, respectively, J = (0, T ] is the time interval of interest, and g n is the prescribed surface traction. Moreover, Λ e , Λ p , and Λ w are the so-called stretch tensors, which enforce dissipation of waves in Ω PML , and a, b, c, and d are products of certain elements of the stretch tensors [15].…”

“…Due to these complexities, and in order to render the problem tractable, current techniques rely on simplifying assumptions. We classify these simplifications as follows: a) limiting the spatial variability of the soil properties, whereby it is assumed that the soil is horizontally layered (one-dimensional) [25,29,33], or has properties varying only within a plane (two-dimensional) [3,12,19,21]; b) assuming that the measured response of the soil at sensor locations is due only to Rayleigh waves, thus neglecting other wave types, such as compressional and shear waves, as is the case in the SASW [33], or its close variant, the MASW method [30]; c) idealizing the soil medium, which is porous, and, generally, partially or fully saturated, as an elastic solid; d) imaging only one elastic property, such as the shear wave velocity or an equivalent counterpart [2,11,27,28]; and e) grossly simplifying the boundary conditions associated with the semi-infinite extent of the medium, due to the complexity and computational cost that a rigorous treatment would require [11,36]. In recent years, the ubiquity of parallel computers, and significant advances in computational geosciences, has created the opportunity of developing a toolkit that is capable of robust, accurate, and three-dimensional characterization of geotechnical sites.…”

High-Resolution Characterization of Near-Surface Structures by Surface-Wave Inversions: From Dispersion Curve to Full Waveform

“…Numerical examples (Romdhane et al 2011;Zeng et al 2011a;Bretaudeau et al 2013;Borisov et al 2017;Pan et al 2018a) have demonstrated that FWI is a promising way in quantitatively imaging near-surface structures. Applications of FWI on field data sets (Tran et al 2013;Kallivokas et al 2013;Amrouche and Yamanaka 2015;Nguyen et al 2016;Pan et al 2016b;Dokter et al 2017) have also proved the applicability as well as the high resolution of FWI for characterizing near-surface heterogeneity. Shallow-seismic FWI is an ill-posed problem and could converge toward a local minimum especially when a poor initial model is provided ).…”