Ludovic Bodet

Surface-wave inversion limitations from laser-Doppler physical modeling

Surface-wave dispersion inversion is growing in popularity for geotechnical applications, due to its noninvasive character, relative straightforward field procedures and interpretation, especially when the subsurface structure is locally assumed to be one-dimensional (1D). Here, laser-Doppler physical modeling of surface-wave propagation is used to address issues of surface-wave depth penetration, the presence of dipping layers, and the associated limitations and systematic errors propagated in conventional 1D surface-wave inversion. Flat-layered models show that, with an active source and linear spread, the maximum resolvable wavelength of the Rayleigh-wave fundamental mode is on the order of 40% of the spread length. Linearised inversions confirm the rule of thumb that the depth penetration is 20–25% of the spread length, and that correct a priori layer interface depths from refraction analysis allow more accurate results. However, even under optimal conditions, failing to account for a dominant higher mode at low frequency when a stiff shallow layer is present, causes an overestimate of deeper layer shear-wave velocity. Moreover, a layer dip of only a few degrees can significantly bias the surface-wave inversion. If the incorrect a priori information from a single-shot refraction analysis is incorporated in the inverse problem, estimated interface depth depends on the shot position and deeper layer shear-wave velocity is underestimated. Even if correct a priori constraints are used, an underestimate of half-space shear-wave velocity of up to 25% remains.

Seismic Surface-wave Prospecting Methods for Sinkhole Hazard Assessment along the Dead Sea Shoreline

The Dead Sea (DS) coastal areas have been dramatically hit by sinkhole occurrences since around 1990. It has been shown that the sinkholes along both Israeli and Jordanian shorelines are linked to evaporate karst cavities that are formed by slow salt dissolution. Both the timing and location of sinkholes suggest that: 1) the salt weakens as the result of unsaturated water circulation, thus enhancing the karstification process; and 2) sinkholes appear to be related to the decompaction of the sediments above karstified zones. The location, depth, thickness and weakening of salt layers along the DS shorelines, as well as the thickness and mechanical properties of the upper sedimentary deposits, are thus considered as controlling factors of this on-going process. The knowledge of shear-wave velocities (Vs) should add valuable insights on mechanical properties of both the salt and its overburden. We have suggested Vs estimation using surface-wave prospecting methods, based on surface-wave dispersion measurements and inversion. Two approaches have been used. Along the Israeli shoreline, Vs mapping has been performed to discriminate weak and hard zones within salt layers, after calibration of inverted Vs near boreholes. It has been shown that there is a Vs increase in the DS direction. Initially examined weak zones, located near the salt edge, associated with karstified salt, are characterized by Vs values of 760–1,050 m/s, and extend 60–100 m from the salt edge in the DS direction. Hard salt zones with velocity Vs values greater than 1,500 m/s are located at distances of more than 100–220 m from the salt edge. Finally, transition zones (1,050 , Vs , 1,500 m/s) have a 40–160 m spread. On a Jordanian site, roll-along acquisition and dispersion stacking has been performed to achieve multi-modal dispersion measurements along linear profiles. Inverted pseudo-2-D Vs sections present low Vs anomalies in the vicinity of existing sinkholes and made it possible to detect decompacted sediments associated with potential sinkhole occurrences. Moreover, Vs profiles showed a high velocity unit at 40–50 m depth that can be interpreted as a salt layer.

2D characterization of near-surface V P/V S: surface-wave dispersion inversion versus refraction tomography

The joint study of pressure (P-) and shear (S-) wave velocities (Vp and Vs ), as well as their ratio (Vp /Vs), has been used for many years at large scales but remains marginal in near-surface applications. For these applications, and are generally retrieved with seismic refraction tomography combining P and SH (shear-horizontal) waves, thus requiring two separate acquisitions. Surface-wave prospecting methods are proposed here as an alternative to SH-wave tomography in order to retrieve pseudo-2D Vs sections from typical P-wave shot gathers and assess the applicability of combined P-wave refraction tomography and surface-wave dispersion analysis to estimate Vp/Vs ratio. We carried out a simultaneous P- and surface-wave survey on a well-characterized granite-micaschists contact at Ploemeur hydrological observatory (France), supplemented with an SH-wave acquisition along the same line in order to compare Vs results obtained from SH-wave refraction tomography and surface-wave profiling. Travel-time tomography was performed with P- and SH- wave first arrivals observed along the line to retrieve Vtomo p and Vtomo s models. Windowing and stacking techniques were then used to extract evenly spaced dispersion data from P-wave shot gathers along the line. Successive 1D Monte Carlo inversions of these dispersion data were performed using fixed Vp values extracted from Vtomo p the model and no lateral constraints between two adjacent 1D inversions. The resulting 1D Vsw s models were then assembled to create a pseudo-2D Vsw s section, which appears to be correctly matching the general features observed on the section. If the pseudo-section is characterized by strong velocity incertainties in the deepest layers, it provides a more detailed description of the lateral variations in the shallow layers. Theoretical dispersion curves were also computed along the line with both and models. While the dispersion curves computed from models provide results consistent with the coherent maxima observed on dispersion images, dispersion curves computed from models are generally not fitting the observed propagation modes at low frequency. Surface-wave analysis could therefore improve models both in terms of reliability and ability to describe lateral variations. Finally, we were able to compute / sections from both and models. The two sections present similar features, but the section obtained from shows a higher lateral resolution and is consistent with the features observed on electrical resistivity tomography, thus validating our approach for retrieving Vp/Vs ratio from combined P-wave tomography and surface-wave profiling.

Surface-wave Dispersion Inversion versus SH-wave Refraction Tomography in Saturated and Poorly Dispersive Quick Clays

A seismic survey involving two distinct acquisition setups, with vertical and horizontal component geophones, has been carried out along the same line on a site presenting a simple vertical structure (peat, quick clays and bedrock) and no strong lateral variations. SH-wave refraction tomography and Rayleigh-wave dispersion inversion provided the same shear-wave velocity gradient in the quick clays. SH-wave tomography failed to correctly depict the peat layer and to reach the bedrock. A collection of Rayleigh-wave dispersion images were extracted along the line using windowing and stacking techniques. A thorough analysis of these images made it possible to give a complete description of the site velocity structure, illustrating the complementarity of both methods.

Seismic-Wave Propagation Modeling in Viscoelastic Media Using the Auxiliary Differential Equation Method

In many seismic applications, a constant quality factor is used to describe the constitutive laws of viscoelastic materials, characterized by frequency-independent attenuation characteristics. In such cases, the frequency dependence of the medium’s properties is not taken into account. To overcome this drawback, we proposed an elegant finite difference time domain implementation, with an auxiliary differential equation technique to explicitly solve any stress-strain relation. This scheme is inherited from the formalism of electromagnetism and is based on the separation of the propagation equations from the constitutive law defined in the stress-strain equation. The conventional assumption of a constant quality factor assumption can then be easily avoided in the modeling of seismic-wave propagation in viscoelastic media. We developed such a method and simulated synthetic traces over a simple, 2D viscoelastic homogeneous medium using a Zener model. Wave propagation phase velocities were estimated by means of dispersion analysis and appeared to match theoretical values over a reasonable frequency range. We also measured the material’s attenuation behavior by studying the quality factor, thereby validating our approach.

Temporal Variations of Near-surface Seismic Data at the Ploemeur (France) Hydrogeological Observatory

Near-surface seismic methods are mainly used to determine the geometrical characteristics of hydrosystems (and to provide elements that are interesting for hydrogeologists such as separating aquifer layers, setting up systems boundaries, highlighting fractures etc.). Recent methodological advances suggest the high potential of seismic methods to investigate the mechanical properties of the Critical Zone (CZ), by exploiting the full wealth of seismic records. Indeed, the behavior of Shear (S) and Pressure (P) waves in the presence of water is partially decoupled, so that the ratio of their propagation velocities VP/VS is strongly linked to water saturation. We propose here a time-lapse application of this approach. Two seismic acquisitions were carried out under distinct hydrogeological conditions along the same line at the Ploemeur hydrogeological observatory (South Brittany, France). Vertical component seismic data were recorded to extract: (i) P-wave first arrival times and (ii) Rayleigh-wave phase velocities. The significant variations with time and space, of both datasets, indicate marked changes in mechanical properties of the CZ that have to be compared to soil moisture variations in the unsaturated zone and groundwater level variations.

Contribution of Seismic Methods to Hydrogeophysics

The characterisation and monitoring of aquifer systems mainly rely on piezometric and log data. Delineating spatial variations of lithology between piezometers is a delicate task, which inevitably generates errors possibly propagating into hydrogeological models. Seismic methods have been proposed to: (i) improve the low spatial resolution of borehole data, (ii) provide a characterisation of the subsurface geometry, and (iii) estimate the physical parameters of the medium influenced by the presence of water and the associated flow and transport processes. The joint study of pressure (P-) and shear (S-) wave seismic velocities (VP and VS, respectively), whose evolution is strongly decoupled in the presence of fluid, has been proposed through the estimation of the VP/VS ratio and Poissons ratio. A specific methodology has been developed for the combined exploitation of P- and surface waves present on single seismic records. The use of this methodology in several geological and hydrogeological contexts allowed for estimating VP/VS ratio lateral and temporal variations in good agreement with a priori geological information and existing geophysical and piezometric data. Laser-based ultrasonic techniques were also proposed to put these processing techniques in practice on perfectly controlled physical models and study elastic wave propagation in partially saturated porous media.

Physical Modelling of Seismic-wave Propagation over a Two Dimensional Granular Medium

Laboratory small-scale physical models and non-contacting ultrasonic techniques are used to tackle theoretical or methodological issues of seismic wave propagation and seismic methods. Literature shows a wide range of experiments, both in terms of materials used for the production of the physical models but also regarding the models geometry and the recording techniques, which are chosen according to the issue that is being addressed. With a proper choice of granulometries and deposition processes, we managed here to create a two-layer granular physical model with a relatively complex geometry and characterized by 2D structures, property contrast and velocity gradients within layers. We performed several small scale seismic acquisitions using a mechanical source and a laser vibrometer. The acquired seismograms were interpreted by applying the surface-wave method and by extracting P-wave refraction data. We managed to correctly reconstruct the geometry of the model and estimated the parameters controlling the velocity gradients of P and S waves for both layers. The results we got are coherent with the different compaction degree we obtained for the two layers and with previous studies conducted over similar media.

Integrated Workflow for Surface-wave Dispersion Inversion and Profiling

While surface-wave prospecting methods are classically applied for the one-dimensional (1D) estimation of shear (S-) wave velocities (Vs), two-dimensional (2D) profiling still requires implementing specific processing and inversion tools that are not yet widely available in the community. We present here a free and open-source tool performing surface-wave inversion and profiling (SWIP) in order to retrieve 2D lateral variations of Vs from typical seismic shot records. Windowing and stacking techniques are implemented to compute dispersion images with smooth lateral variations and enhanced signal-to-noise ratio. Dispersion curves are extracted for each window with an error in phase velocity taking into account the higher uncertainties at low frequency. These curves are then inverted for each window position using a Monte Carlo approach and a refraction tomography-based parameterization. Models matching the observed data within the error bars are selected to build a misfit-weighted final model and estimate the investigation depth. Finally, 1D models obtained for each window position are merged into a 2D Vs section.

Seismic Surface-wave Analysis for Railway Platform Auscultation

The renewal of existent railways requires the characterisation of the mechanical properties of railway platforms (RP), thus raising the need to select appropriate maintenance actions. Conventional techniques (geotechnical soundings, coring) remain local, destructive, expensive and with low yields. Using non-destructive investigation techniques for local diagnosis and monitoring thus appears of great interest for enhancing RP control. Seismic surface-wave methods have been proposed to estimate in situ mechanical parameters of the superficial layers below railways. In this context, a joint geotechnical and seismic survey was carried out along the Northern Europe high-speed line (LGV) in order to precisely determine the origins of a phenomenon affecting the geometry of the track. Strong a priori knowledge of the RP structure allowed for inverting dispersion measurements for 1D VS models along the track. The results showed a contrast of VS in the loess lying below the RP, between areas where the phenomenon was observed and those it was not. This contrast was confirmed by Bender Elements measurements of VS performed on core drilling samples, and corresponded to the lateral variations observed along the track. These results encourage considering dispersion measurements as an appropriate tool of RP monitoring.