2D Quantitative Imaging by Elastic Full Waveform Inversion: Application to a Physical Scale Model

Bretaudeau, François; Leparoux, D.; Brossier, Romain; Operto, S.; Abraham, Odile

doi:10.3997/2214-4609.20144895

Cited by 5 publications

(9 citation statements)

References 4 publications

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“…On the ultrasonic scale Bretaudeau et al . () reconstructed the P‐ and S‐wave velocity model of a physical scale model by a FWI of surface and body wave data. Köhn et al .…”

Section: Introductionmentioning

confidence: 99%

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

Dokter

Köhn

Wilken

et al. 2017

Geophysical Prospecting

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We develop a two‐dimensional full waveform inversion approach for the simultaneous determination of S‐wave velocity and density models from SH ‐ and Love‐wave data. We illustrate the advantages of the SH/Love full waveform inversion with a simple synthetic example and demonstrate the method's applicability to a near‐surface dataset, recorded in the village Čachtice in Northwestern Slovakia. Goal of the survey was to map remains of historical building foundations in a highly heterogeneous subsurface. The seismic survey comprises two parallel SH‐profiles with maximum offsets of 24 m and covers a frequency range from 5 Hz to 80 Hz with high signal‐to‐noise ratio well suited for full waveform inversion. Using the Wiechert–Herglotz method, we determined a one‐dimensional gradient velocity model as a starting model for full waveform inversion. The two‐dimensional waveform inversion approach uses the global correlation norm as objective function in combination with a sequential inversion of low‐pass filtered field data. This mitigates the non‐linearity of the multi‐parameter inverse problem. Test computations show that the influence of visco‐elastic effects on the waveform inversion result is rather small. Further tests using a mono‐parameter shear modulus inversion reveal that the inversion of the density model has no significant impact on the final data fit. The final full waveform inversion S‐wave velocity and density models show a prominent low‐velocity weathering layer. Below this layer, the subsurface is highly heterogeneous. Minimum anomaly sizes correspond to approximately half of the dominant Love‐wavelength. The results demonstrate the ability of two‐dimensional SH waveform inversion to image shallow small‐scale soil structure. However, they do not show any evidence of foundation walls.

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“…On the ultrasonic scale Bretaudeau et al . () reconstructed the P‐ and S‐wave velocity model of a physical scale model by a FWI of surface and body wave data. Köhn et al .…”

Section: Introductionmentioning

confidence: 99%

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

Dokter

Köhn

Wilken

et al. 2017

Geophysical Prospecting

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“…While “classical” FWI approaches (e.g., Virieux and Operto ; Operto et al . ) on the exploration scale are based on reflection seismic data, the use of surface waves seem to be more appropriate to characterise the near surface, due to their large amplitudes and sensitivity with respect to the S‐wave velocity distribution. First approaches to explain waveform data (e.g., Forbriger a, b) derived 1D S‐wave velocity models from Rayleigh wave data by fitting phase slowness–frequency spectra (multi‐channel analysis of surface waves MASW).…”

Section: Introductionmentioning

confidence: 99%

“…Bretaudeau et al . () successfully applied FWI to ultrasonic data from a physical scale model. Due to the scale invariance of the problem, the FWI approaches developed on the ultrasonic scale are also applicable to larger scale geophysical problems if scaling problems such as wavelength‐to‐heterogeneity dimensions, maximum acquisition offsets, or different attenuations, which shift the frequency content of the recorded data, are taken into account.…”

Section: Introductionmentioning

confidence: 99%

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

Köhn

Meier

Fehr

et al. 2016

Near Surface Geophysics

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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.

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“…Previous studies have shown the high potential of 2-D elastic FWI being applied to surface waves (Romdhane et al 2011;Tran & McVay 2012;Bretaudeau et al 2013;Tran et al 2013). They all use a Cartesian 2-D solver.…”

Section: Previous Studiesmentioning

confidence: 99%

“…Additionally a phase transformation is applied by convolving the point-source waveforms with √ t −1 , where t is the traveltime. Bretaudeau et al (2013) convert the 3-D geometrical spreading into 2-D spreading by applying a factor √ t to each sample. Additionally, they infer a source wavelet with appropriate phase by inversion.…”

Section: Previous Studiesmentioning

confidence: 99%

Line-source simulation for shallow-seismic data. Part 2: full-waveform inversion—a synthetic 2-D case study

Schäfer

Groos

Forbriger

et al. 2014

Geophysical Journal International

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S U M M A R YFull-waveform inversion (FWI) of shallow-seismic surface waves is able to reconstruct lateral variations of subsurface elastic properties. Line-source simulation for point-source data is required when applying algorithms of 2-D adjoint FWI to recorded shallow-seismic field data. The equivalent line-source response for point-source data can be obtained by convolving the waveforms with √ t −1 (t: traveltime), which produces a phase shift of π/4. Subsequently an amplitude correction must be applied. In this work we recommend to scale the seismograms with 2r v ph at small receiver offsets r, where v ph is the phase velocity, and gradually shift to applying a √ t −1 time-domain taper and scaling the waveforms with r √ 2 for larger receiver offsets r. We call this the hybrid transformation which is adapted for direct body and Rayleigh waves and demonstrate its outstanding performance on a 2-D heterogeneous structure. The fit of the phases as well as the amplitudes for all shot locations and components (vertical and radial) is excellent with respect to the reference line-source data. An approach for 1-D media based on Fourier-Bessel integral transformation generates strong artefacts for waves produced by 2-D structures. The theoretical background for both approaches is presented in a companion contribution. In the current contribution we study their performance when applied to waves propagating in a significantly 2-D-heterogeneous structure. We calculate synthetic seismograms for 2-D structure for line sources as well as point sources. Line-source simulations obtained from the point-source seismograms through different approaches are then compared to the corresponding line-source reference waveforms. Although being derived by approximation the hybrid transformation performs excellently except for explicitly backscattered waves. In reconstruction tests we further invert point-source synthetic seismograms by a 2-D FWI to subsurface structure and evaluate its ability to reproduce the original structural model in comparison to the inversion of line-source synthetic data. Even when applying no explicit correction to the point-source waveforms prior to inversion only moderate artefacts appear in the results. However, the overall performance is best in terms of model reproduction and ability to reproduce the original data in a 3-D simulation if inverted waveforms are obtained by the hybrid transformation.

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2D Quantitative Imaging by Elastic Full Waveform Inversion: Application to a Physical Scale Model

Cited by 5 publications

References 4 publications

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

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

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

Line-source simulation for shallow-seismic data. Part 2: full-waveform inversion—a synthetic 2-D case study

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