Application of 2D elastic Rayleigh waveform inversion to ultrasonic laboratory and field data

Abstract

In addition to geophysical applications from the near surface to a global scale, seismic full‐waveform inversion can be applied to ultrasonic data on the centimetre and decimetre scales for nondestructive testing of pavements, facades, plaster, sculptures, and load‐bearing structures such as pillars or core samples from boreholes, which can consist of geo‐materials and non‐geomaterials. Classical non‐destructive testing approaches are based on the inversion of body‐wave travel times to deduce P‐wave velocity models. In contrast, surface waves (especially Rayleigh waves) are well suited to quantify surficial alterations of material properties, e.g., due to weathering. Furthermore, ultrasonic measurements of test samples with known material parameters close the gap between synthetic tests or analytical solutions and field data applications to estimate the accuracy of seismic modelling and inversion codes. Due to the scale invariance of the problem, the full‐waveform‐inversion approaches developed on the ultrasonic scale are also applicable to larger scale geophysical problems. In this paper, we demonstrate the potential of two‐dimensional Rayleigh waveform inversion on the ultrasonic scale using two data examples acquired with a single‐fold, low‐coverage acquisition geometry. For a simple homogeneous Plexiglas block in a controlled laboratory environment, we discuss the accuracy of visco‐elastic Rayleigh wave modelling, as well as the sensitivity of two‐dimensional elastic full‐waveform inversion with respect to small data residuals. While the inversion is restricted to the recovery of the S‐wave velocity model, a passive visco‐elastic modelling approach with a homogeneous average Qs‐model is required in order to describe amplitude loss and dispersion of the Rayleigh wave. The applicability of this approach under field conditions is illustrated for an ultrasonic data example from the weathered sandstone facade of the Porta Nigra in Trier (Germany). In addition to a random medium resolution analysis of the full‐waveform‐inversion result, we particularly emphasise the importance of lateral model smoothing to mitigate small‐scale inversion artefacts and to avoid erroneous interpretations. The estimated two‐dimensional S‐wave velocity anomalies correlate well with prominent surficial weathering effects in the upper about 3 cm.

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

“…1). Based on full-wavefield modeling, FWI is able to fully exploit the waveform information and is getting increasingly popular on continental (Fichtner et al 2008), explorational , near-surface (Groos et al 2017), and laboratory (Köhn et al 2016) scales. Due to the specific wavefield characteristics (e.g., frequency range and wave type) and recording systems in each scale, the successful application of FWI on different scales is not simply a matter of scale.…”

Forward and Inverse Studies on Scattering of Rayleigh Wave at Surface Flaws

“…Furthermore, Xia et al [27] and Shao et al [28] extended the tomographic approach to the detection of near-surface shallow cavities. Köhn et al [29] used a similar inversion method to reconstruct surface layer stiffness of an ancient sandstone façade. Chen et al [30] adopted an inversion procedure to detect residual stresses from general Rayleigh wave dispersion of a weakly anisotropic media.…”

“…Chen et al [30] adopted an inversion procedure to detect residual stresses from general Rayleigh wave dispersion of a weakly anisotropic media. These methods stem from wave signal processing theories (in earlier works [27,28]) or discretized equations of motion (in later works [29,30]). Through the formulation of an "operator matrix" of inverse problem, the researchers try to find an optimum solution of the "model vector" that is feasible to the "data set".…”

Full waveform inversion of SH‐ and Love‐wave data in near‐surface prospecting

“…Köhn et al . () used single‐folded ultrasonic Rayleigh waveform inversion to map 2D near‐surface S‐wave velocity variations due to weathering effects at the Porta Nigra in Trier (Germany). Schäfer () applied a multi‐parameter 2D Rayleigh‐FWI including density to a seismic line over a thrust fault.…”

“…On the ultrasonic scale Bretaudeau et al (2013) reconstructed the Pand S-wave velocity model of a physical scale model by a FWI of surface and body wave data. Köhn et al (2016) used single-folded ultrasonic Rayleigh waveform inversion to map 2D near-surface S-wave velocity variations due to weathering effects at the Porta Nigra in Trier (Germany). Schäfer (2014) applied a multi-parameter 2D Rayleigh-FWI including density to a seismic line over a thrust fault.…”